Mechanism-Based Energy Regularization in Computational Modeling of Quasibrittle Fracture

Gorgogianni, Anna; Eliáš, Jan; Le, Jia-Liang

doi:10.1115/1.4047207

Mechanism-Based Energy Regularization in Computational Modeling of Quasibrittle Fracture

Journal Article · Fri May 29 00:00:00 EDT 2020 · Journal of Applied Mechanics

DOI:https://doi.org/10.1115/1.4047207· OSTI ID:1801296

Gorgogianni, Anna ^[1]; Eliáš, Jan ^[2]; Le, Jia-Liang ^[3]

Department of Civil, Environmental, and Geo- Engineering, University of Minnesota, Minneapolis, MN 55455; OSTI
Institute of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, Brno 60200, Czech Republic
Department of Civil, Environmental, and Geo- Engineering, University of Minnesota, Minneapolis, MN 55455

Abstract

Quasibrittle materials are featured by a strain-softening constitutive behavior under many loading scenarios, which could eventually lead to localization instability. It has long been known that strain localization would result in spurious mesh sensitivity in finite element (FE) simulations. Previous studies have shown that, for the case of fully localized damage, the mesh sensitivity can be mitigated through energy regularization of the material constitutive law. However, depending on the loading configuration and structural geometry, quasibrittle structures could exhibit a complex damage process, which involves both localized and diffused damage patterns at different stages of loading. This study presents a generalized energy regularization method that considers the spatial and temporal evolution of damage pattern. The method introduces a localization parameter, which describes the local damage pattern. The localization parameter governs the energy regularization of the constitutive model, which captures the transition from diffused to localized damage during the failure process. The method is cast into an isotropic damage model, and is further extended to rate-dependent behavior. The energy regularization scheme is directly incorporated into the kinetics of damage growth. The model is applied to simulate static and dynamic failures of ceramic specimens. It is shown that the present model is able to effectively mitigate the spurious mesh sensitivity in FE simulations of both types of failure. The present analysis demonstrates the essential role of mechanism-based energy regularization of constitutive relation in FE simulations of quasibrittle fracture.

Research Organization:: Univ. of Minnesota, Minneapolis, MN (United States)

Sponsoring Organization:: USDOE Office of Nuclear Energy (NE)

DOE Contract Number:: NE0008785

OSTI ID:: 1801296

Journal Information:: Journal of Applied Mechanics, Journal Name: Journal of Applied Mechanics Journal Issue: 9 Vol. 87; ISSN 0021-8936

Publisher:: ASME

Country of Publication:: United States

Language:: English

References (32)

Effect of high-rate dynamic comminution on penetration of projectiles of various velocities and impact angles into concrete Luo, Wen; Chau, Viet T.; Bažant, Zdeněk P. International Journal of Fracture, Vol. 216, Issue 2 https://doi.org/10.1007/s10704-019-00354-0	journal	March 2019
Mathematical analysis of strain localization Jirásek, Milan Revue Européenne de Génie Civil, Vol. 11, Issue 7-8 https://doi.org/10.1080/17747120.2007.9692973	journal	August 2007
Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress Bažant, Zdeněk P.; Jirásek, Milan Journal of Engineering Mechanics, Vol. 128, Issue 11 https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1119)	journal	November 2002
Finite element analysis of deformation of strain-softening materials Pietruszczak, St.; Mróz, Z. International Journal for Numerical Methods in Engineering, Vol. 17, Issue 3 https://doi.org/10.1002/nme.1620170303	journal	March 1981
A unified phase-field theory for the mechanics of damage and quasi-brittle failure Wu, Jian-Ying Journal of the Mechanics and Physics of Solids, Vol. 103 https://doi.org/10.1016/j.jmps.2017.03.015	journal	June 2017
About the dynamic uniaxial tensile strength of concrete-like materials Lu, Y. B.; Li, Q. M. International Journal of Impact Engineering, Vol. 38, Issue 4 https://doi.org/10.1016/j.ijimpeng.2010.10.028	journal	April 2011
A two-scale model for dynamic damage evolution Keita, Oumar; Dascalu, Cristian; François, Bertrand Journal of the Mechanics and Physics of Solids, Vol. 64 https://doi.org/10.1016/j.jmps.2013.11.003	journal	March 2014
Comminution of solids caused by kinetic energy of high shear strain rate, with implications for impact, shock, and shale fracturing Bazant, Z. P.; Caner, F. C. Proceedings of the National Academy of Sciences, Vol. 110, Issue 48 https://doi.org/10.1073/pnas.1318739110	journal	November 2013
Boundary effect on weight function in nonlocal damage model Krayani, Abbas; Pijaudier-Cabot, Gilles; Dufour, Frédéric Engineering Fracture Mechanics, Vol. 76, Issue 14 https://doi.org/10.1016/j.engfracmech.2009.07.007	journal	September 2009
Blunt Crack Band Propagation in Finite Element Analysis Bažant, Zdenĕk P.; Cedolin, Luigi Journal of the Engineering Mechanics Division, Vol. 105, Issue 2 https://doi.org/10.1061/JMCEA3.0002467	journal	April 1979
Instability, Ductility, and Size Effect in Strain-Softening Concrete Bažant, Zdeněk P. Journal of the Engineering Mechanics Division, Vol. 102, Issue 2 https://doi.org/10.1061/JMCEA3.0002111	journal	April 1976
Localization Analysis of Elastic Degradation with Application to Scalar Damage Rizzi, E.; Carol, I.; Willam, K. Journal of Engineering Mechanics, Vol. 121, Issue 4 https://doi.org/10.1061/(ASCE)0733-9399(1995)121:4(541)	journal	April 1995
Fracture of Concrete Subjected to Impact Loading Wedding, Pa; John, R.; Shah, Sp Cement, Concrete and Aggregates, Vol. 8, Issue 1 https://doi.org/10.1520/CCA10050J	journal	January 1986
Rate-Dependent Scaling of Dynamic Tensile Strength of Quasibrittle Structures Le, Jia-Liang; Eliáš, Jan; Gorgogianni, Anna Journal of Applied Mechanics, Vol. 85, Issue 2 https://doi.org/10.1115/1.4038496	journal	December 2017
Nonlocal Continuum Damage, Localization Instability and Convergence Bazˇant, Zdeneˇk P.; Pijaudier-Cabot, Gilles Journal of Applied Mechanics, Vol. 55, Issue 2 https://doi.org/10.1115/1.3173674	journal	June 1988
Dynamic fragmentation of an alumina ceramic subjected to shockless spalling: An experimental and numerical study Zinszner, J. L.; Erzar, B.; Forquin, P. Journal of the Mechanics and Physics of Solids, Vol. 85 https://doi.org/10.1016/j.jmps.2015.08.014	journal	December 2015
On the Processing of Spalling Experiments. Part II: Identification of Concrete Fracture Energy in Dynamic Tension Lukić, Bratislav B.; Saletti, Dominique; Forquin, Pascal Journal of Dynamic Behavior of Materials, Vol. 4, Issue 1 https://doi.org/10.1007/s40870-017-0138-y	journal	December 2017
Simulation of concrete tensile failure under high loading rates using three-dimensional irregular lattice models Hwang, Young Kwang; Bolander, John E.; Lim, Yun Mook Mechanics of Materials, Vol. 101 https://doi.org/10.1016/j.mechmat.2016.08.002	journal	October 2016
Conditions for the localization of deformation in pressure-sensitive dilatant materials Rudnicki, J. W.; Rice, J. R. Journal of the Mechanics and Physics of Solids, Vol. 23, Issue 6 https://doi.org/10.1016/0022-5096(75)90001-0	journal	December 1975
A Micromechanics Based Constitutive Model for Brittle Failure at High Strain Rates Bhat, Harsha S.; Rosakis, Ares J.; Sammis, Charles G. Journal of Applied Mechanics, Vol. 79, Issue 3 https://doi.org/10.1115/1.4005897	journal	April 2012
Numerical aspects of the crack band approach Jirásek, Milan; Bauer, Marco Computers & Structures, Vol. 110-111 https://doi.org/10.1016/j.compstruc.2012.06.006	journal	November 2012
A Probabilistic Crack Band Model for Quasibrittle Fracture Le, Jia-Liang; Eliáš, Jan Journal of Applied Mechanics, Vol. 83, Issue 5 https://doi.org/10.1115/1.4032692	journal	February 2016
Equivalent localization element for crack band approach to mesh-sensitivity in microplane model ?ervenka, Jan; Ba?ant, Zden?k P.; Wierer, Martin International Journal for Numerical Methods in Engineering, Vol. 62, Issue 5 https://doi.org/10.1002/nme.1216	journal	January 2005
Nonlocal Microplane Model for Fracture, Damage, and Size Effect in Structures Baznt, Zdeněk P.; Ožbolt, Joško Journal of Engineering Mechanics, Vol. 116, Issue 11 https://doi.org/10.1061/(ASCE)0733-9399(1990)116:11(2485)	journal	November 1990
An Experimental Method to Determine the Tensile Strength of Concrete at High Rates of Strain Erzar, B.; Forquin, P. Experimental Mechanics, Vol. 50, Issue 7 https://doi.org/10.1007/s11340-009-9284-z	journal	September 2009
A critical comparison of nonlocal and gradient-enhanced softening continua Peerlings, R. H. J.; Geers, M. G. D.; de Borst, R. International Journal of Solids and Structures, Vol. 38, Issue 44-45 https://doi.org/10.1016/S0020-7683(01)00087-7	journal	November 2001
Spall experiments for the measurement of the tensile strength and fracture energy of concrete at high strain rates Schuler, Harald; Mayrhofer, Christoph; Thoma, Klaus International Journal of Impact Engineering, Vol. 32, Issue 10 https://doi.org/10.1016/j.ijimpeng.2005.01.010	journal	October 2006
Impact comminution of solids due to local kinetic energy of high shear strain rate: I. Continuum theory and turbulence analogy Bažant, Zdeněk P.; Caner, Ferhun C. Journal of the Mechanics and Physics of Solids, Vol. 64 https://doi.org/10.1016/j.jmps.2013.11.008	journal	March 2014
Damage spreading in quasi-brittle disordered solids: I. Localization and failure Berthier, Estelle; Démery, Vincent; Ponson, Laurent Journal of the Mechanics and Physics of Solids, Vol. 102 https://doi.org/10.1016/j.jmps.2016.08.013	journal	May 2017
Predicting variability in the dynamic failure strength of brittle materials considering pre-existing flaws Daphalapurkar, Nitin P.; Ramesh, K. T.; Graham-Brady, Lori Journal of the Mechanics and Physics of Solids, Vol. 59, Issue 2 https://doi.org/10.1016/j.jmps.2010.10.006	journal	February 2011
Gradient damage models: Toward full-scale computations Lorentz, E.; Godard, V. Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 21-22 https://doi.org/10.1016/j.cma.2010.06.025	journal	May 2011
Gradient Enhanced Damage for Quasi-Brittle Materials Peerlings, R. H. J.; De Borst, R.; Brekelmans, W. A. M. International Journal for Numerical Methods in Engineering, Vol. 39, Issue 19 https://doi.org/10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D	journal	October 1996

Similar Records

Mesh objective stochastic simulations of quasibrittle fracture

Journal Article · Mon Jan 03 23:00:00 EST 2022 · Journal of the Mechanics and Physics of Solids · OSTI ID:1977341

Partitioning of regular computation on multiprocessor systems

Technical Report · Sun Jan 31 23:00:00 EST 1988 · OSTI ID:6695148

Partitioning of regular computation on multiprocessor systems

Journal Article · Sun Jul 01 00:00:00 EDT 1990 · Journal of Parallel and Distributed Computing; (USA) · OSTI ID:6467779

Related Subjects

Mechanics

Mechanism-Based Energy Regularization in Computational Modeling of Quasibrittle Fracture

Citation Formats

References (32)

Similar Records

Related Subjects