skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Validated simulations of dynamic crack propagation in single crystals using EFEM and XFEM

Abstract

Brittle and quasibrittle materials such as ceramics and geomaterials fail through dynamic crack propagation during impact events. Simulations of such events are important in a number of applications. In this paper, we compare the effectiveness of the embedded finite element method (EFEM) and the extended finite element method (XFEM) in modeling dynamic crack propagation by validating each approach against an impact experiment performed on single crystal quartz together with in-situ imaging of the dynamic fracture using X-ray phase contrast imaging (XPCI). The experiment is conducted in a Kolsky bar (generating a strain rate on the order of 103 s-1) that is operated at the synchrotron facilities at the advanced photon source (APS). The in situ XPCI technique can record the dynamic crack propagation with micron-scale spatial resolution and sub-microsecond temporal resolution, and the corresponding images are used to extract the time-resolved crack propagation path and velocity. A unified framework is first presented for the dynamic discretization formulations of EFEM and XFEM. This framework clarifies the differences between the two methods in enrichment techniques and numerical solution schemes. In both cases, a cohesive law is used to describe the fracture process after crack initiation. The simulations of the dynamic fracture experimentmore » using the two simulation approaches are compared with the in situ experimental observations and measurements. Finally, the performance of each method is discussed with respect to capturing the early crack propagation process.« less

Authors:
 [1];  [1];  [1]; ORCiD logo [2];  [1];  [1]
  1. Johns Hopkins Univ., Baltimore, MD (United States)
  2. Johns Hopkins Univ., Baltimore, MD (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1484639
Report Number(s):
LA-UR-18-21043
Journal ID: ISSN 0376-9429
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
International Journal of Fracture
Additional Journal Information:
Journal Volume: 215; Journal Issue: 1-2; Journal ID: ISSN 0376-9429
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Dynamic fracture; damage; crack velocity; x-ray phase contrast imaging

Citation Formats

Zeng, Q., Motamedi, M. H., Leong, A .F. T., Daphalapurkar, Nitin Pandurang, Hufnagel, T. C., and Ramesh, K. T. Validated simulations of dynamic crack propagation in single crystals using EFEM and XFEM. United States: N. p., 2018. Web. doi:10.1007/s10704-018-0330-7.
Zeng, Q., Motamedi, M. H., Leong, A .F. T., Daphalapurkar, Nitin Pandurang, Hufnagel, T. C., & Ramesh, K. T. Validated simulations of dynamic crack propagation in single crystals using EFEM and XFEM. United States. https://doi.org/10.1007/s10704-018-0330-7
Zeng, Q., Motamedi, M. H., Leong, A .F. T., Daphalapurkar, Nitin Pandurang, Hufnagel, T. C., and Ramesh, K. T. 2018. "Validated simulations of dynamic crack propagation in single crystals using EFEM and XFEM". United States. https://doi.org/10.1007/s10704-018-0330-7. https://www.osti.gov/servlets/purl/1484639.
@article{osti_1484639,
title = {Validated simulations of dynamic crack propagation in single crystals using EFEM and XFEM},
author = {Zeng, Q. and Motamedi, M. H. and Leong, A .F. T. and Daphalapurkar, Nitin Pandurang and Hufnagel, T. C. and Ramesh, K. T.},
abstractNote = {Brittle and quasibrittle materials such as ceramics and geomaterials fail through dynamic crack propagation during impact events. Simulations of such events are important in a number of applications. In this paper, we compare the effectiveness of the embedded finite element method (EFEM) and the extended finite element method (XFEM) in modeling dynamic crack propagation by validating each approach against an impact experiment performed on single crystal quartz together with in-situ imaging of the dynamic fracture using X-ray phase contrast imaging (XPCI). The experiment is conducted in a Kolsky bar (generating a strain rate on the order of 103 s-1) that is operated at the synchrotron facilities at the advanced photon source (APS). The in situ XPCI technique can record the dynamic crack propagation with micron-scale spatial resolution and sub-microsecond temporal resolution, and the corresponding images are used to extract the time-resolved crack propagation path and velocity. A unified framework is first presented for the dynamic discretization formulations of EFEM and XFEM. This framework clarifies the differences between the two methods in enrichment techniques and numerical solution schemes. In both cases, a cohesive law is used to describe the fracture process after crack initiation. The simulations of the dynamic fracture experiment using the two simulation approaches are compared with the in situ experimental observations and measurements. Finally, the performance of each method is discussed with respect to capturing the early crack propagation process.},
doi = {10.1007/s10704-018-0330-7},
url = {https://www.osti.gov/biblio/1484639}, journal = {International Journal of Fracture},
issn = {0376-9429},
number = 1-2,
volume = 215,
place = {United States},
year = {Sat Nov 17 00:00:00 EST 2018},
month = {Sat Nov 17 00:00:00 EST 2018}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Effect of random defects on dynamic fracture in quasi-brittle materials
journal, August 2017


Non-linear analysis of shells with arbitrary evolving cracks using XFEM
journal, January 2005


Numerical simulation of dynamic fracture using finite elements with embedded discontinuities
journal, October 2009


Concrete fracture models: testing and practice
journal, January 2002


Elastic and Piezoelectric Constants of Alpha-Quartz
journal, June 1958


Elastic crack growth in finite elements with minimal remeshing
journal, June 1999


Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment
journal, January 2003


A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation
journal, December 2000


Assumed enhanced strain and the extended finite element methods: A unification of concepts
journal, June 2008


Computational modelling of impact damage in brittle materials
journal, August 1996


Mesh-independent discrete numerical representations of cohesive-zone models
journal, January 2006


A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements
journal, November 2009


An extended finite element method for modeling crack growth with frictional contact
journal, October 2001


Instability in dynamic fracture
journal, July 1991


Wave Propagation in the Split Hopkinson Pressure Bar
journal, January 1983


A discrete crack approach to normal/shear cracking of concrete
journal, October 2002


A finite element method for the simulation of strong and weak discontinuities in solid mechanics
journal, August 2004


Cleavage of natural and synthetic single crystal quartz
journal, September 1987


[水晶,サファイア単結晶の室温における破壊じん性]<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1981-01-01">January 1981</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Iwasa, Mikio; Ueno, Tsutomu; Bradt, R. C.</span> </li> <li> Journal of the Society of Materials Science, Japan, Vol. 30, Issue 337</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.2472/jsms.30.1001" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.2472/jsms.30.1001<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1016/S0045-7825(99)00154-1" target="_blank" rel="noopener noreferrer" class="name">Comparative study on finite elements with embedded discontinuities<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2000-07-01">July 2000</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Jirásek, Milan</span> </li> <li> Computer Methods in Applied Mechanics and Engineering, Vol. 188, Issue 1-3</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1016/S0045-7825(99)00154-1" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1016/S0045-7825(99)00154-1<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/nme.4744" target="_blank" rel="noopener noreferrer" class="name">Reduction in mesh bias for dynamic fracture using adaptive splitting of polygonal finite elements: ADAPTIVE SPLITTING OF POLYGONAL FINITE ELEMENTS<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2014-08-11">August 2014</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Leon, S. E.; Spring, D. W.; Paulino, G. H.</span> </li> <li> International Journal for Numerical Methods in Engineering, Vol. 100, Issue 8</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/nme.4744" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/nme.4744<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1007/s11340-018-0414-3" target="_blank" rel="noopener noreferrer" class="name">Quantitative In Situ Studies of Dynamic Fracture in Brittle Solids Using Dynamic X-ray Phase Contrast Imaging<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2018-09-07">September 2018</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Leong, A. F. T.; Robinson, A. K.; Fezzaa, K.</span> </li> <li> Experimental Mechanics, Vol. 58, Issue 9</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1007/s11340-018-0414-3" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/s11340-018-0414-3<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1016/S0045-7825(96)01087-0" target="_blank" rel="noopener noreferrer" class="name">The partition of unity finite element method: Basic theory and applications<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1996-12-01">December 1996</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Melenk, J. M.; Babuška, I.</span> </li> <li> Computer Methods in Applied Mechanics and Engineering, Vol. 139, Issue 1-4</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1016/S0045-7825(96)01087-0" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1016/S0045-7825(96)01087-0<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/nme.1718" target="_blank" rel="noopener noreferrer" class="name">Efficient explicit time stepping for the eXtended Finite Element Method (X-FEM)<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2006-01-01">January 2006</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Menouillard, T.; Réthoré, J.; Combescure, A.</span> </li> <li> International Journal for Numerical Methods in Engineering, Vol. 68, Issue 9</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/nme.1718" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/nme.1718<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A" target="_blank" rel="noopener noreferrer" class="name">A finite element method for crack growth without remeshing<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1999-09-10">September 1999</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Moës, Nicolas; Dolbow, John; Belytschko, Ted</span> </li> <li> International Journal for Numerical Methods in Engineering, Vol. 46, Issue 1</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1016/j.ijsolstr.2016.02.002" target="_blank" rel="noopener noreferrer" class="name">Numerical simulation of mixed mode (I and II) fracture behavior of pre-cracked rock using the strong discontinuity approach<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2016-05-01">May 2016</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Motamedi, M. H.; Weed, D. A.; Foster, C. D.</span> </li> <li> International Journal of Solids and Structures, Vol. 85-86</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1016/j.ijsolstr.2016.02.002" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1016/j.ijsolstr.2016.02.002<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/(SICI)1097-0207(19961115)39:21<3575::AID-NME65>3.0.CO;2-E" target="_blank" rel="noopener noreferrer" class="name">Modelling Strong Discontinuities in Solid Mechanics via Strain Softening Constitutive Equations. part 1: Fundamentals<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1996-11-15">November 1996</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Oliver, J.</span> </li> <li> International Journal for Numerical Methods in Engineering, Vol. 39, Issue 21</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/(SICI)1097-0207(19961115)39:21<3575::AID-NME65>3.0.CO;2-E" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/(SICI)1097-0207(19961115)39:21<3575::AID-NME65>3.0.CO;2-E<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1016/S0013-7944(01)00060-1" target="_blank" rel="noopener noreferrer" class="name">From continuum mechanics to fracture mechanics: the strong discontinuity approach<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2002-01-01">January 2002</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Oliver, J.; Huespe, A. E.; Pulido, M. D. G.</span> </li> <li> Engineering Fracture Mechanics, Vol. 69, Issue 2</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1016/S0013-7944(01)00060-1" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1016/S0013-7944(01)00060-1<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1016/j.cma.2005.09.020" target="_blank" rel="noopener noreferrer" class="name">A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2006-07-01">July 2006</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Oliver, J.; Huespe, A. E.; Sánchez, P. J.</span> </li> <li> Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 37-40</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1016/j.cma.2005.09.020" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1016/j.cma.2005.09.020<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7" target="_blank" rel="noopener noreferrer" class="name">Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1999-03-30">March 1999</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Ortiz, M.; Pandolfi, A.</span> </li> <li> International Journal for Numerical Methods in Engineering, Vol. 44, Issue 9</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1155/2013/849231" target="_blank" rel="noopener noreferrer" class="name">Computational Methods for Fracture in Brittle and Quasi-Brittle Solids: State-of-the-Art Review and Future Perspectives<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2013-01-01">January 2013</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Rabczuk, Timon</span> </li> <li> ISRN Applied Mathematics, Vol. 2013</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1155/2013/849231" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1155/2013/849231<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1007/BF00017967" target="_blank" rel="noopener noreferrer" class="name">Mechanics of crack curving and branching ? a dynamic fracture analysis<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1985-01-01">January 1985</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Ramulu, M.; Kobayashi, A. S.</span> </li> <li> International Journal of Fracture, Vol. 27, Issue 3-4</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1007/BF00017967" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/BF00017967<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/nme.4731" target="_blank" rel="noopener noreferrer" class="name">Simulating curvilinear crack propagation in two dimensions with universal meshes: SIMULATING CURVILINEAR CRACK PROPAGATION WITH UNIVERSAL MESHES<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2014-08-18">August 2014</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Rangarajan, Ramsharan; Chiaramonte, Maurizio M.; Hunsweck, Michael J.</span> </li> <li> International Journal for Numerical Methods in Engineering, Vol. 102, Issue 3-4</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/nme.4731" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/nme.4731<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/2014JB011624" target="_blank" rel="noopener noreferrer" class="name">Fracture propagation in Indiana Limestone interpreted via linear softening cohesive fracture model: Fracture Interpreted via Cohesive Model<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2015-04-01">April 2015</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Rinehart, Alex J.; Bishop, Joseph E.; Dewers, Thomas</span> </li> <li> Journal of Geophysical Research: Solid Earth, Vol. 120, Issue 4</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/2014JB011624" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/2014JB011624<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/nme.4814" target="_blank" rel="noopener noreferrer" class="name">Combined continuum damage-embedded discontinuity model for explicit dynamic fracture analyses of quasi-brittle materials: COMBINED CONTINUUM DAMAGE-EMBEDDED DISCONTINUITY MODEL<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2014-11-11">November 2014</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Saksala, Timo; Brancherie, Delphine; Harari, Isaac</span> </li> <li> International Journal for Numerical Methods in Engineering, Vol. 101, Issue 3</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/nme.4814" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/nme.4814<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1111/j.1460-2695.2006.01076.x" target="_blank" rel="noopener noreferrer" class="name">An embedded cohesive crack model for finite element analysis of mixed mode fracture of concrete<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2006-12-01">December 2006</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Sancho, J. M.; Planas, J.; GÁLvez, J. C.</span> </li> <li> Fatigue & Fracture of Engineering Materials and Structures, Vol. 29, Issue 12</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1111/j.1460-2695.2006.01076.x" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1111/j.1460-2695.2006.01076.x<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1016/S0013-7944(03)00133-4" target="_blank" rel="noopener noreferrer" class="name">Simulation of cup–cone fracture using the cohesive model<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2003-09-01">September 2003</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Scheider, I.; Brocks, W.</span> </li> <li> Engineering Fracture Mechanics, Vol. 70, Issue 14</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1016/S0013-7944(03)00133-4" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1016/S0013-7944(03)00133-4<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1103/PhysRevB.54.7128" target="_blank" rel="noopener noreferrer" class="name">Microbranching instability and the dynamic fracture of brittle materials<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1996-09-01">September 1996</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Sharon, Eran; Fineberg, Jay</span> </li> <li> Physical Review B, Vol. 54, Issue 10</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1103/PhysRevB.54.7128" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1103/PhysRevB.54.7128<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/nme.1620290802" target="_blank" rel="noopener noreferrer" class="name">A class of mixed assumed strain methods and the method of incompatible modes<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1990-06-01">June 1990</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Simo, J. C.; Rifai, M. S.</span> </li> <li> International Journal for Numerical Methods in Engineering, Vol. 29, Issue 8</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/nme.1620290802" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/nme.1620290802<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1007/BF00372173" target="_blank" rel="noopener noreferrer" class="name">An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1993-01-01">January 1993</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Simo, J. C.; Oliver, J.; Armero, F.</span> </li> <li> Computational Mechanics, Vol. 12, Issue 5</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1007/BF00372173" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/BF00372173<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1115/1.3129711" target="_blank" rel="noopener noreferrer" class="name">Dynamic Fracture of Shells Subjected to Impulsive Loads<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2009-06-12">June 2009</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Song, Jeong-Hoon; Belytschko, Ted</span> </li> <li> Journal of Applied Mechanics, Vol. 76, Issue 5</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1115/1.3129711" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1115/1.3129711<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/nme.1652" target="_blank" rel="noopener noreferrer" class="name">A method for dynamic crack and shear band propagation with phantom nodes<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2006-01-01">January 2006</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Song, Jeong-Hoon; Areias, Pedro M. A.; Belytschko, Ted</span> </li> <li> International Journal for Numerical Methods in Engineering, Vol. 67, Issue 6</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/nme.1652" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/nme.1652<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1007/s00466-007-0210-x" target="_blank" rel="noopener noreferrer" class="name">A comparative study on finite element methods for dynamic fracture<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2007-08-15">August 2007</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Song, Jeong-Hoon; Wang, Hongwu; Belytschko, Ted</span> </li> <li> Computational Mechanics, Vol. 42, Issue 2</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1007/s00466-007-0210-x" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/s00466-007-0210-x<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1016/S0045-7825(01)00215-8" target="_blank" rel="noopener noreferrer" class="name">Modeling holes and inclusions by level sets in the extended finite-element method<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2001-09-01">September 2001</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Sukumar, N.; Chopp, D. L.; Moës, N.</span> </li> <li> Computer Methods in Applied Mechanics and Engineering, Vol. 190, Issue 46-47</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1016/S0045-7825(01)00215-8" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1016/S0045-7825(01)00215-8<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1109/FREQ.1984.200732" target="_blank" rel="noopener noreferrer" class="name">The Constants of Alpha Quartz<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">conference</span>, <span class="date" data-date="1984-01-01">January 1984</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Ward, R. W.</span> </li> <li> 38th Annual Symposium on Frequency Control</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1109/FREQ.1984.200732" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1109/FREQ.1984.200732<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1007/s11440-016-0474-4" target="_blank" rel="noopener noreferrer" class="name">A robust numerical framework for simulating localized failure and fracture propagation in frictional materials<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2016-07-08">July 2016</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Weed, D. A.; Foster, C. D.; Motamedi, M. H.</span> </li> <li> Acta Geotechnica, Vol. 12, Issue 2</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1007/s11440-016-0474-4" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/s11440-016-0474-4<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1016/S0013-7944(99)00120-4" target="_blank" rel="noopener noreferrer" class="name">Application of embedded discontinuities for softening solids<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2000-01-01">January 2000</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Wells, G. N.; Sluys, L. J.</span> </li> <li> Engineering Fracture Mechanics, Vol. 65, Issue 2-3</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1016/S0013-7944(99)00120-4" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1016/S0013-7944(99)00120-4<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/nme.143" target="_blank" rel="noopener noreferrer" class="name">A new method for modelling cohesive cracks using finite elements<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2001-01-01">January 2001</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Wells, G. N.; Sluys, L. J.</span> </li> <li> International Journal for Numerical Methods in Engineering, Vol. 50, Issue 12</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/nme.143" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/nme.143<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1007/s00466-014-1001-9" target="_blank" rel="noopener noreferrer" class="name">Modeling of dynamic crack branching by enhanced extended finite element method<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2014-03-13">March 2014</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Xu, Dandan; Liu, Zhanli; Liu, Xiaoming</span> </li> <li> Computational Mechanics, Vol. 54, Issue 2</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1007/s00466-014-1001-9" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/s00466-014-1001-9<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1080/14786445108561302" target="_blank" rel="noopener noreferrer" class="name">LXXV. The moving griffith crack<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="1951-07-01">July 1951</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Yoffe, Elizabeth H.</span> </li> <li> The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 42, Issue 330</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1080/14786445108561302" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1080/14786445108561302<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1007/s00466-017-1412-5" target="_blank" rel="noopener noreferrer" class="name">Fully coupled simulation of multiple hydraulic fractures to propagate simultaneously from a perforated horizontal wellbore<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2017-05-04">May 2017</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Zeng, Qinglei; Liu, Zhanli; Wang, Tao</span> </li> <li> Computational Mechanics, Vol. 61, Issue 1-2</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1007/s00466-017-1412-5" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/s00466-017-1412-5<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1002/nme.2030" target="_blank" rel="noopener noreferrer" class="name">Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2007-01-01">January 2007</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Zhang, Zhengyu (Jenny); Paulino, Glaucio H.; Celes, Waldemar</span> </li> <li> International Journal for Numerical Methods in Engineering, Vol. 72, Issue 8</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1002/nme.2030" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1002/nme.2030<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> <div> <h2 class="title" style="margin-bottom:0;" data-apporder=""> <a href="https://doi.org/10.1007/s10704-006-7135-9" target="_blank" rel="noopener noreferrer" class="name">Effects of material properties on the fragmentation of brittle materials<span class="fa fa-external-link" aria-hidden="true"></span></a> <small class="text-muted" style="text-transform:uppercase; font-size:0.75rem;"><br/> <span class="type">journal</span>, <span class="date" data-date="2006-05-01">May 2006</span></small> </h2> <ul class="small references-list" style="list-style-type:none; margin-top: 0.5em; padding-left: 0; line-height:1.8em;"> <li> <span style="color:#557B2D;"> Zhou, Fenghua; Molinari, Jean-François; Ramesh, K. T.</span> </li> <li> International Journal of Fracture, Vol. 139, Issue 2</li> <li> <span class="text-muted related-url"><a href="https://doi.org/10.1007/s10704-006-7135-9" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.1007/s10704-006-7135-9<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> <hr/> </div> </div> <div class="pagination-container small"> <a class="pure-button prev page" href="#" rel="prev"><span class="fa fa-angle-left"></span><span class="sr-only">Previous</span></a><ul class="pagination d-inline-block" style="padding-left:.2em;"></ul><a class="pure-button next page" href="#" rel="next"><span class="fa fa-angle-right"></span><span class="sr-only">Next</span></a> </div> </div> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a href="" class="reference-type-filter tab-nav" data-tab="biblio-references" data-filter="type" data-pattern="*"><span class="fa fa-angle-right"></span> All References</a></li> <li class="small" style="margin-left:.75em; text-transform:capitalize;"><a href="" class="reference-type-filter tab-nav" data-tab="biblio-references" data-filter="type" data-pattern="conference"><span class="fa fa-angle-right"></span> conference<small class="text-muted"> (1)</small></a></li> <li class="small" style="margin-left:.75em; text-transform:capitalize;"><a href="" class="reference-type-filter tab-nav" data-tab="biblio-references" data-filter="type" data-pattern="journal"><span class="fa fa-angle-right"></span> journal<small class="text-muted"> (56)</small></a></li> </ul> <div style="margin-top:2em;"> <form class="pure-form small text-muted reference-search"> <label for="reference-search-text" class="sr-only">Search</label> <input class="search form-control pure-input-1" id="reference-search-text" placeholder="Search" style="margin-bottom:10px;" /> <fieldset> <legend class="sr-only">Sort options</legend> <div style="margin-left:1em; font-weight:normal; line-height: 1.6em;"><input type="radio" class="sort" name="references-sort" data-sort="name" style="position:relative;top:2px;" id="reference-search-sort-name"><label for="reference-search-sort-name" style="margin-left: .3em;">Sort by title</label></div> <div style="margin-left:1em; font-weight:normal; line-height: 1.6em;"><input type="radio" class="sort" name="references-sort" data-sort="date" data-order="desc" style="position:relative;top:2px;" id="reference-search-sort-date"><label for="reference-search-sort-date" style="margin-left: .3em;">Sort by date</label></div> </fieldset> <div class="text-left" style="margin-left:1em;"> <a href="" class="filter-clear clearfix" title="Clear filter / sort" style="font-weight:normal; float:none;">[ × clear filter / sort ]</a> </div> <button type="submit" style="display:none;" aria-hidden="true" title="Submit"/> </form> </div> </div> </div> </section> <section id="biblio-related" class="tab-content tab-content-sec " data-tab="biblio"> <div class="row"> <div class="col-sm-9 order-sm-9"> <section id="biblio-similar" class="tab-content tab-content-sec active" data-tab="related"> <div class="padding"> <p class="lead text-muted" style="font-size: 18px; margin-top:0px;">Similar records in OSTI.GOV collections:</p> <aside> <ul class="item-list" itemscope itemtype="http://schema.org/ItemList" style="padding-left:0; list-style-type: none;"> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="0" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1538260" itemprop="url">An arc-length method for controlled cohesive crack propagation using high-order XFEM and Irwin’s crack closure integral</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Wang, Yongxiang</span>; <span class="author">Waisman, Haim</span><span class="text-muted pubdata"> - Engineering Fracture Mechanics</span> </span></div> <div class="abstract">Numerical modeling of cohesive crack growth in quasi-brittle materials is challenging, primarily due to the combination of (i) nonlinearity associated with the fracture process zone (FPZ), (ii) arbitrary directions to which a crack may propagate, and (iii) snap-back or snap-through instabilities encountered in the response of the structure. To address these challenges, here we propose a novel arc-length method that can follow the equilibrium path of cohesive crack propagation. The proposed approach is based on the extended finite element method (XFEM) with scalar high-order enrichment functions and Irwin’s crack closure integral, which allows for direct control of the applied loads<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> necessary to propagate cohesive cracks. This is achieved by augmenting a constraint equation written in terms of stress intensity factors (SIFs), and expressed explicitly in terms of the enriched degrees of freedom, which is an attractive feature achieved with Irwin’s integral, since SIFs can be written in closed-form. Note that singular enrichments are active in an unstable crack propagation state and automatically vanish in stable crack configurations. Furthermore, to propagate cracks in arbitrary directions, we employ a maximum circumferential stress criterion implemented by (i) direct usage of the SIFs, and by (ii) a new stress-based nonlocal implementation of this principle. Various benchmark problems including pure mode I and mixed-mode fracture are solved to demonstrate the predictive capability of the present framework for cohesive crack modeling.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <span class="fa fa-book text-muted" aria-hidden="true"></span> Cited by 25<div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1016/j.engfracmech.2018.05.018" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1538260" data-product-type="Journal Article" data-product-subtype="AM" >https://doi.org/10.1016/j.engfracmech.2018.05.018</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1538260" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1538260" data-product-type="Journal Article" data-product-subtype="AM" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="1" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/22395942" itemprop="url">Cracking in autoclaved aerated concrete: Experimental investigation and XFEM modeling</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Journal Article</small><span class="authors"> <span class="author">Michelini, E.</span>; <span class="author">Rosati, G.</span><span class="text-muted pubdata"> - Cement and Concrete Research</span> </span></div> <div class="abstract">The paper aims to investigate and model cracking development in beams and deep-beams made of autoclaved aerated concrete (AAC). Fracture mechanics of AAC has been first studied by performing three-point bending tests on beams, similar to those commonly used for ordinary concrete elements. In some of these tests, crack growth has been also monitored by using ESPI laser technique. In this way, it has been possible to calibrate the main parameters of a proper cohesive law by means of extended finite element inverse analysis. Subsequently, cracking tests have been also performed on deep-beams, whose behavior is more representative of full<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> scale walls. To validate the proposed cohesive law, deep-beam experimental behavior has been finally simulated through XFEM.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.1016/J.CEMCONRES.2014.09.005" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="22395942" data-product-type="Journal Article" data-product-subtype="AC" >https://doi.org/10.1016/J.CEMCONRES.2014.09.005</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="2" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/895072" itemprop="url">Modeling brittle fracture, slip weakening, and variable friction in geomaterials with an embedded strong discontinuity finite element.</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Technical Report</small><span class="authors"> <span class="author">Regueiro, Richard</span>; <span class="author">Borja, R</span>; <span class="author">Foster, C</span><span class="text-muted pubdata"></span> </span></div> <div class="abstract">Localized shear deformation plays an important role in a number of geotechnical and geological processes. Slope failures, the formation and propagation of faults, cracking in concrete dams, and shear fractures in subsiding hydrocarbon reservoirs are examples of important effects of shear localization. Traditional engineering analyses of these phenomena, such as limit equilibrium techniques, make certain assumptions on the shape of the failure surface as well as other simplifications. While these methods may be adequate for the applications for which they were designed, it is difficult to extrapolate the results to more general scenarios. An alternative approach is to use a<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> numerical modeling technique, such as the finite element method, to predict localization. While standard finite elements can model a wide variety of loading situations and geometries quite well, for numerical reasons they have difficulty capturing the softening and anisotropic damage that accompanies localization. By introducing an enhancement to the element in the form of a fracture surface at an arbitrary position and orientation in the element, we can regularize the solution, model the weakening response, and track the relative motion of the surfaces. To properly model the slip along these surfaces, the traction-displacement response must be properly captured. This report focuses on the development of a constitutive model appropriate to localizing geomaterials, and the embedding of this model into the enhanced finite element framework. This modeling covers two distinct phases. The first, usually brief, phase is the weakening response as the material transitions from intact continuum to a body with a cohesionless fractured surface. Once the cohesion has been eliminated, the response along the surface is completely frictional. We have focused on a rate- and state-dependent frictional model that captures stable and unstable slip along the surface. This model is embedded numerically into the element using a generalized trapezoidal formulation. While the focus is on the constitutive model of interest, the framework is also developed for a general surface response. This report summarizes the major research and development accomplishments for the LDRD project titled 'Cohesive Zone Modeling of Failure in Geomaterials: Formulation and Implementation of a Strong Discontinuity Model Incorporating the Effect of Slip Speed on Frictional Resistance'. This project supported a strategic partnership between Sandia National Laboratories and Stanford University by providing funding for the lead author, Craig Foster, during his doctoral research.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.2172/895072" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="895072" data-product-type="Technical Report" data-product-subtype="" >https://doi.org/10.2172/895072</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/895072" title="Link to document media" target="_blank" rel="noopener" data-ostiid="895072" data-product-type="Technical Report" data-product-subtype="" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="3" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1472089" itemprop="url">FY17 CAES LDRD Annual Report</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Technical Report</small><span class="authors"> <span class="author">Jiang, Chao</span>; <span class="author">Jiang, Wen</span>; <span class="author">Jaques, Brian</span>; <span class="author">...</span> <span class="text-muted pubdata"></span> </span></div> <div class="abstract">Metallic alloys are widely used or planned for use as structural and cladding materials in current and future reactors. Under irradiation, grain boundary (GB) cohesion strength decreases due to interaction with defects and impurities, leading to intergranular fracture and embrittlement of alloys. The objective of this project is to develop a technique for quantifying GB cohesion and its impact on fracture behavior in irradiated alloys, by utilizing transmission electron microscopic (TEM) in situ cantilever testing in concert with multi-scale modeling. The TEM in situ cantilever testing is a novel approach for studying the real-time mechanical response of materials. It will<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> be used in this work for studying intergranular fracture behavior in several irradiated iron-based ferritic alloys and providing key information to link atomistic level events with mesoscale/macroscopic mechanical properties. The Multi-Physics Object-Oriented Simulation Environment (MOOSE)-based cohesive zone model (CZM) and extended finite element method (XFEM) for intergranular fracture of irradiated ferritic alloys will be developed in this work by utilizing atomistic results as inputs and experimental results for validation.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.2172/1472089" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1472089" data-product-type="Technical Report" data-product-subtype="" >https://doi.org/10.2172/1472089</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1472089" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1472089" data-product-type="Technical Report" data-product-subtype="" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemprop="itemListElement" itemscope itemtype="http://schema.org/WebPage"><meta itemprop="position" content="4" /><div class="item-info"> <h2 class="title" itemprop="name headline"><a href="/biblio/1467403" itemprop="url">Improved Fracture Models for Relocation Modeling</a></h2> <div class="metadata"> <small class="text-muted" style="text-transform:uppercase;display:block;line-height:2.5em;">Technical Report</small><span class="authors"> <span class="author">Jiang, W.</span>; <span class="author">Spencer, B.</span>; <span class="author">Schwen, D.</span>; <span class="author">...</span> <span class="text-muted pubdata"></span> </span></div> <div class="abstract">The BISON fuel performance code is being developed to provide a modern tool that has the flexibility to analyze a wide variety of fuel forms and to model conditions and phenomena that could not be represented in legacy tools. There are a number of motivations for this, including providing support for development of advanced fuel with improved accident tolerance for existing light water (LWR) reactors, improved understanding of mechanisms in fuel designs in current use in a wider variety of conditions, and facilitating the development of fuel for advanced reactor designs. To accomplish these goals, it is clear that BISON<a href='#' onclick='$(this).hide().next().show().next().show();return false;' style='margin-left:10px;'>more »</a><span style='display:none;'> must rely on models of fuel behavior that are based on fundamental physical behavior, rather than on empirical correlations that represent that behavior in a simplified fashion. BISON still does employ many empirical models that were originally developed for other fuel performance codes, but efforts are underway to replace these with models that are more physically based. Radial relocation in LWR fuel is an example of a phenomenon that is currently represented by an empirical model, but which is ripe for replacement by physically based models. During normal operation, ceramic LWR fuel experiences significant fracturing that is driven by spatially nonuniform volumetric expansion. This occurs due to the significant thermal gradients within the fuel that occur in fresh and irradiated fuel, as well as nonuniform swelling due to fission products that occurs over longer-term irradiation. Fracture and fragmentation of fuel allows the outer radius of the fuel pellet to expand due to the loss of mechanical constraint and outward radial migration of fragments. This radial expansion has a significant effect on the fuel system response because it decreases the size of the gap between the fuel and cladding. This decreases the thermal resistance across that gap, which leads to decreased fuel centerline temperatures. This report documents recent work to improve the ability of BISON to model radial relocation using the extended finite element method (XFEM). These enhancements include the ability to include cohesive zone models, improved code architecture for propagating cracks based on fracture integrals, and improved handling of fuel and cladding interfaces with XFEM. These capabilities are demonstrated on a simulation of radial relocation including a surface interaction model that enforces residual opening.</span><a href='#' onclick='$(this).hide().prev().hide().prev().show();return false;' style='margin-left:10px;display:none;'>« less</a></div><div class="metadata-links small clearfix text-muted" style="margin-top:15px;"> <div class="pure-menu pure-menu-horizontal pull-right" style="width:unset;"> <ul class="pure-menu-list"> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc doi-link " href="https://doi.org/10.2172/1467403" target="_blank" rel="noopener" title="Link to document DOI" data-ostiid="1467403" data-product-type="Technical Report" data-product-subtype="" >https://doi.org/10.2172/1467403</a></span></li> <li class="pure-menu-item"><span class="item-info-ftlink"><a class="misc fulltext-link " href="/servlets/purl/1467403" title="Link to document media" target="_blank" rel="noopener" data-ostiid="1467403" data-product-type="Technical Report" data-product-subtype="" >Full Text Available</a></span></li> </ul> </div> </div> </div> <div class="clearfix"></div> </div> </li> </ul> </aside> </div> </section> </div> <div class="col-sm-3 order-sm-3"> <ul class="nav nav-stacked"> <li class="active"><a class="tab-nav disabled" data-tab="related" style="color: #636c72 !important; opacity: 1;"><span class="fa fa-angle-right"></span> Similar Records</a></li> </ul> </div> </div> </section> </div></div> </div> </div> </section> <footer class="" style="background-color:#f9f9f9; /* padding-top: 0.5rem; */"> <div class="footer-minor"> <div class="container"> <hr class="footer-separator" /> <div class="text-center" style="margin-top:1.25rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list" id="footer-org-menu"> <li class="pure-menu-item d-block d-inline-small"> <a href="https://energy.gov" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-us-doe-min" alt="U.S. Department of Energy" /> </a> </li> <li class="pure-menu-item d-block d-inline-small"> <a href="https://www.energy.gov/science/office-science" target="_blank" rel="noopener noreferrer"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-office-of-science-min" alt="Office of Science" /> </a> </li> <li class="pure-menu-item d-block d-inline-small"> <a href="/"> <img src="data:image/gif;base64,R0lGODlhAQABAIAAAP///wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==" class="sprite sprite-footer-osti-min" alt="Office of Scientific and Technical Information" /> </a> </li> </ul> </div> </div> <div class="text-center small" style="margin-top:0.5em;margin-bottom:2.0rem;"> <div class="pure-menu pure-menu-horizontal"> <ul class="pure-menu-list"> <li class="pure-menu-item"><a href="/disclaim" class="pure-menu-link"><span class="fa fa-institution"></span> Website Policies <span class="d-none d-sm-inline" style="color:#737373;">/ Important Links</span></a></li> <li class="pure-menu-item"><a href="/contact" class="pure-menu-link"><span class="fa fa-comments-o"></span> Contact Us</a></li> <li class="d-block d-md-none mb-1"></li> <li class="pure-menu-item"><a href="https://doe.responsibledisclosure.com/hc/en-us" target="_blank" class="pure-menu-link">Vulnerability Disclosure Program</a></li> <li class="d-block d-lg-none mb-1"></li> <li class="pure-menu-item"><a href="https://www.facebook.com/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-facebook"></span><span class="sr-only">Facebook</span></a></li> <li class="pure-menu-item"><a href="https://twitter.com/OSTIgov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-twitter"></span><span class="sr-only">Twitter</span></a></li> <li class="pure-menu-item"><a href="https://www.youtube.com/user/ostigov" target="_blank" rel="noopener noreferrer" class="pure-menu-link social"><span class="fa fa-youtube-play"></span><span class="sr-only">YouTube</span></a></li> </ul> </div> </div> </div> </div> </footer> <link href="/css/ostigov.fonts.240327.0425.css" rel="stylesheet"> <script src="/js/ostigov.240327.0425.js"></script><noscript></noscript> <script defer src="/js/ostigov.biblio.240327.0425.js"></script><noscript></noscript> <script async type="text/javascript" src="/js/Universal-Federated-Analytics-Min.js?agency=DOE" id="_fed_an_ua_tag"></script><noscript></noscript> </body> <!-- OSTI.GOV v.240327.0425 --> </html>