FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials

Ma, Ran; Sun, WaiChing

doi:10.1016/j.cma.2019.112781

Title: FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials

Journal Article · 19 January 2020 · Computer Methods in Applied Mechanics and Engineering

DOI: https://doi.org/10.1016/j.cma.2019.112781 · OSTI ID:1801240

Ma, Ran ^[1];

^[2]

Columbia Univ., New York, NY (United States); OSTI
Columbia Univ., New York, NY (United States)

This paper presents the application of a fast Fourier transform (FFT) based method to solve two phase field models designed to simulate crack growth of strongly anisotropic materials in the brittle regime. By leveraging the ability of the FFT-based solver to generate solutions with higher-order and global continuities, we design two simple algorithms to capture the complex fracture patterns (e.g. sawtooth, and curved crack growth) common in materials with strongly anisotropic surface energy via the multi-phase-field and high-order phase-field frameworks. A staggered operator-split solver is used where both the balance of linear momentum and the phase field governing equations are formulated in the periodic domain. The unit phase field of the initial failure region is prescribed by the penalty method to alleviate the sharp material contrast between the initial failure region and the base material. The discrete frequency vectors are generalized to estimate the second and fourth order gradients such that the Gibbs effect near shape interfaces or jump conditions can be suppressed. Furthermore, a preconditioner is adopted to improve the convergence rate of the iterative linear solver. Three numerical experiments are used to systematically compare the performance of the FFT-based method in the multi-phase-field and high-order phase-field frameworks.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Columbia Univ., New York, NY (United States)

Sponsoring Organization:: USDOE; USDOE Office of Nuclear Energy (NE), Nuclear Energy University Program (NEUP)

Grant/Contract Number:: NE0008534

OSTI ID:: 1801240

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 362; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (80)

Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis Ortiz, M.; Pandolfi, A. International Journal for Numerical Methods in Engineering, Vol. 44, Issue 9 https://doi.org/10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7	journal	March 1999
A finite element method for crack growth without remeshing Mo�s, Nicolas; Dolbow, John; Belytschko, Ted International Journal for Numerical Methods in Engineering, Vol. 46, Issue 1 https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J	journal	September 1999
Effects of spatial heterogeneity and material anisotropy on the fracture pattern and macroscopic effective toughness of Mancos Shale in Brazilian tests Na, SeonHong; Sun, WaiChing; Ingraham, Mathew D. Journal of Geophysical Research: Solid Earth, Vol. 122, Issue 8 https://doi.org/10.1002/2016JB013374	journal	August 2017
Aspects of the computational testing of the mechanical properties of microheterogeneous material samples Zohdi, T. I.; Wriggers, P. International Journal for Numerical Methods in Engineering, Vol. 50, Issue 11 https://doi.org/10.1002/nme.146	journal	January 2001
Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations Miehe, C.; Welschinger, F.; Hofacker, M. International Journal for Numerical Methods in Engineering, Vol. 83, Issue 10 https://doi.org/10.1002/nme.2861	journal	August 2010
Multiscale method for characterization of porous microstructures and their impact on macroscopic effective permeability Sun, W. C.; Andrade, J. E.; Rudnicki, J. W. International Journal for Numerical Methods in Engineering, Vol. 88, Issue 12 https://doi.org/10.1002/nme.3220	journal	May 2011
A phase-field model for cohesive fracture: A PHASE-FIELD MODEL FOR COHESIVE FRACTURE Verhoosel, Clemens V.; de Borst, René International Journal for Numerical Methods in Engineering, Vol. 96, Issue 1 https://doi.org/10.1002/nme.4553	journal	July 2013
Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields: FOURIER-BASED SCHEMES WITH MODIFIED GREEN OPERATOR Willot, François; Abdallah, Bassam; Pellegrini, Yves-Patrick International Journal for Numerical Methods in Engineering, Vol. 98, Issue 7 https://doi.org/10.1002/nme.4641	journal	February 2014
Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy: PHASE-FIELD MODELING AND SIMULATION OF STRONGLY ANISOTROPIC FRACTURE Li, Bin; Peco, Christian; Millán, Daniel International Journal for Numerical Methods in Engineering, Vol. 102, Issue 3-4 https://doi.org/10.1002/nme.4726	journal	July 2014
Computational homogenization of elasticity on a staggered grid: COMPUTATIONAL HOMOGENIZATION OF ELASTICITY ON A STAGGERED GRID Schneider, Matti; Ospald, Felix; Kabel, Matthias International Journal for Numerical Methods in Engineering, Vol. 105, Issue 9 https://doi.org/10.1002/nme.5008	journal	October 2015
A nonlocal multiscale discrete-continuum model for predicting mechanical behavior of granular materials: A NONLOCAL MULTISCALE DISCRETE-CONTINUUM MODEL FOR GRANULAR MATERIALS Liu, Yang; Sun, WaiChing; Yuan, Zifeng International Journal for Numerical Methods in Engineering, Vol. 106, Issue 2 https://doi.org/10.1002/nme.5139	journal	November 2015
A study of the influence of REV variability in double-scale FEM ×DEM analysis: A study of the influence of REV variability in double-scale FEM ×DEM analysis Shahin, Ghassan; Desrues, Jacques; Pont, Stefano Dal International Journal for Numerical Methods in Engineering, Vol. 107, Issue 10 https://doi.org/10.1002/nme.5202	journal	February 2016
Mixed Arlequin method for multiscale poromechanics problems: Mixed Arlequin method for multiscale poromechanics problems Sun, WaiChing; Cai, Zhijun; Choo, Jinhyun International Journal for Numerical Methods in Engineering, Vol. 111, Issue 7 https://doi.org/10.1002/nme.5476	journal	February 2017
A finite element perspective on nonlinear FFT-based micromechanical simulations: A FINITE ELEMENT PERSPECTIVE ON NONLINEAR FFT-BASED SIMULATIONS Zeman, J.; de Geus, T. W. J.; Vondřejc, J. International Journal for Numerical Methods in Engineering, Vol. 111, Issue 10 https://doi.org/10.1002/nme.5481	journal	March 2017
An optimization-based phase-field method for continuous-discontinuous crack propagation: A phase-field method for continuous-discontinuous crack propagation Geelen, Rudy J. M.; Liu, Yingjie; Dolbow, John E. International Journal for Numerical Methods in Engineering, Vol. 116, Issue 1 https://doi.org/10.1002/nme.5911	journal	July 2018
A review on phase-field models of brittle fracture and a new fast hybrid formulation Ambati, Marreddy; Gerasimov, Tymofiy; De Lorenzis, Laura Computational Mechanics, Vol. 55, Issue 2 https://doi.org/10.1007/s00466-014-1109-y	journal	December 2014
Phase field modeling of brittle fracture for enhanced assumed strain shells at large deformations: formulation and finite element implementation Reinoso, J.; Paggi, M.; Linder, C. Computational Mechanics, Vol. 59, Issue 6 https://doi.org/10.1007/s00466-017-1386-3	journal	February 2017
Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials Nguyen, Thanh-Tung; Réthoré, Julien; Yvonnet, Julien Computational Mechanics, Vol. 60, Issue 2 https://doi.org/10.1007/s00466-017-1409-0	journal	April 2017
Spectral database constitutive representation within a spectral micromechanical solver for computationally efficient polycrystal plasticity modelling Eghtesad, Adnan; Zecevic, Miroslav; Lebensohn, Ricardo A. Computational Mechanics, Vol. 61, Issue 1-2 https://doi.org/10.1007/s00466-017-1413-4	journal	May 2017
The Variational Approach to Fracture Bourdin, Blaise; Francfort, Gilles A.; Marigo, Jean-Jacques Journal of Elasticity, Vol. 91, Issue 1-3 https://doi.org/10.1007/s10659-007-9107-3	journal	March 2008
A damage model for crack prediction in brittle and quasi-brittle materials solved by the FFT method Li, Jia; Tian, Xiao-Xiao; Abdelmoula, Radhi International Journal of Fracture, Vol. 173, Issue 2 https://doi.org/10.1007/s10704-011-9671-1	journal	January 2012
Experimental validation of a phase-field model for fracture Pham, K. H.; Ravi-Chandar, K.; Landis, C. M. International Journal of Fracture, Vol. 205, Issue 1 https://doi.org/10.1007/s10704-017-0185-3	journal	January 2017
A multiscale DEM-LBM analysis on permeability evolutions inside a dilatant shear band Sun, WaiChing; Kuhn, Matthew R.; Rudnicki, John W. Acta Geotechnica, Vol. 8, Issue 5 https://doi.org/10.1007/s11440-013-0210-2	journal	May 2013
Applications of semi-implicit Fourier-spectral method to phase field equations Chen, L. Q.; Shen, Jie Computer Physics Communications, Vol. 108, Issue 2-3 https://doi.org/10.1016/S0010-4655(97)00115-X	journal	February 1998
Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity Regueiro, Richard A.; Borja, Ronaldo I. International Journal of Solids and Structures, Vol. 38, Issue 21 https://doi.org/10.1016/S0020-7683(00)00250-X	journal	May 2001
Revisiting brittle fracture as an energy minimization problem Francfort, G. A.; Marigo, J. -J. Journal of the Mechanics and Physics of Solids, Vol. 46, Issue 8 https://doi.org/10.1016/S0022-5096(98)00034-9	journal	August 1998
A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua Feyel, Frédéric Computer Methods in Applied Mechanics and Engineering, Vol. 192, Issue 28-30 https://doi.org/10.1016/S0045-7825(03)00348-7	journal	July 2003
A numerical method for computing the overall response of nonlinear composites with complex microstructure Moulinec, H.; Suquet, P. Computer Methods in Applied Mechanics and Engineering, Vol. 157, Issue 1-2 https://doi.org/10.1016/S0045-7825(97)00218-1	journal	April 1998
Effective properties of composite materials with periodic microstructure: a computational approach Michel, J. C.; Moulinec, H.; Suquet, P. Computer Methods in Applied Mechanics and Engineering, Vol. 172, Issue 1-4 https://doi.org/10.1016/S0045-7825(98)00227-8	journal	April 1999
Generalized finite element methods for three-dimensional structural mechanics problems Duarte, C. A.; Babuška, I.; Oden, J. T. Computers & Structures, Vol. 77, Issue 2 https://doi.org/10.1016/S0045-7949(99)00211-4	journal	June 2000
N-site modeling of a 3D viscoplastic polycrystal using Fast Fourier Transform A. Lebensohn, R. Acta Materialia, Vol. 49, Issue 14 https://doi.org/10.1016/S1359-6454(01)00172-0	journal	August 2001
Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications Roters, F.; Eisenlohr, P.; Hantcherli, L. Acta Materialia, Vol. 58, Issue 4 https://doi.org/10.1016/j.actamat.2009.10.058	journal	February 2010
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement Hughes, T. J. R.; Cottrell, J. A.; Bazilevs, Y. Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 39-41 https://doi.org/10.1016/j.cma.2004.10.008	journal	October 2005
Isogeometric analysis of the Cahn–Hilliard phase-field model Gómez, Héctor; Calo, Victor M.; Bazilevs, Yuri Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 49-50 https://doi.org/10.1016/j.cma.2008.05.003	journal	September 2008
A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method Radovitzky, R.; Seagraves, A.; Tupek, M. Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 1-4 https://doi.org/10.1016/j.cma.2010.08.014	journal	January 2011
Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing Quey, R.; Dawson, P. R.; Barbe, F. Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 17-20 https://doi.org/10.1016/j.cma.2011.01.002	journal	April 2011
A multiscale mean-field homogenization method for fiber-reinforced composites with gradient-enhanced damage models Wu, L.; Noels, L.; Adam, L. Computer Methods in Applied Mechanics and Engineering, Vol. 233-236 https://doi.org/10.1016/j.cma.2012.04.011	journal	August 2012
A strong discontinuity approach on multiple levels to model solids at failure Linder, Christian; Raina, Arun Computer Methods in Applied Mechanics and Engineering, Vol. 253 https://doi.org/10.1016/j.cma.2012.07.005	journal	January 2013
A multiscale approach for modeling progressive damage of composite materials using fast Fourier transforms Spahn, J.; Andrä, H.; Kabel, M. Computer Methods in Applied Mechanics and Engineering, Vol. 268 https://doi.org/10.1016/j.cma.2013.10.017	journal	January 2014
An augmented-Lagrangian method for the phase-field approach for pressurized fractures Wheeler, M. F.; Wick, T.; Wollner, W. Computer Methods in Applied Mechanics and Engineering, Vol. 271 https://doi.org/10.1016/j.cma.2013.12.005	journal	April 2014
A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework Borden, Michael J.; Hughes, Thomas J. R.; Landis, Chad M. Computer Methods in Applied Mechanics and Engineering, Vol. 273 https://doi.org/10.1016/j.cma.2014.01.016	journal	May 2014
An integrated fast Fourier transform-based phase-field and crystal plasticity approach to model recrystallization of three dimensional polycrystals Chen, L.; Chen, J.; Lebensohn, R. A. Computer Methods in Applied Mechanics and Engineering, Vol. 285 https://doi.org/10.1016/j.cma.2014.12.007	journal	March 2015
Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model Lee, Sanghyun; Wheeler, Mary F.; Wick, Thomas Computer Methods in Applied Mechanics and Engineering, Vol. 305 https://doi.org/10.1016/j.cma.2016.02.037	journal	June 2016
Two-scale FE–FFT- and phase-field-based computational modeling of bulk microstructural evolution and macroscopic material behavior Kochmann, Julian; Wulfinghoff, Stephan; Reese, Stefanie Computer Methods in Applied Mechanics and Engineering, Vol. 305 https://doi.org/10.1016/j.cma.2016.03.001	journal	June 2016
A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects Borden, Michael J.; Hughes, Thomas J. R.; Landis, Chad M. Computer Methods in Applied Mechanics and Engineering, Vol. 312 https://doi.org/10.1016/j.cma.2016.09.005	journal	December 2016
A unified variational eigen-erosion framework for interacting brittle fractures and compaction bands in fluid-infiltrating porous media Wang, Kun; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 318 https://doi.org/10.1016/j.cma.2017.01.017	journal	May 2017
Sparse and scalable eigenstrain-based reduced order homogenization models for polycrystal plasticity Zhang, Xiang; Oskay, Caglar Computer Methods in Applied Mechanics and Engineering, Vol. 326 https://doi.org/10.1016/j.cma.2017.07.027	journal	November 2017
Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow Choo, Jinhyun; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 330 https://doi.org/10.1016/j.cma.2017.10.009	journal	March 2018
Fracture of solar-grade anisotropic polycrystalline Silicon: A combined phase field–cohesive zone model approach Paggi, M.; Corrado, M.; Reinoso, J. Computer Methods in Applied Mechanics and Engineering, Vol. 330 https://doi.org/10.1016/j.cma.2017.10.021	journal	March 2018
Computational thermomechanics of crystalline rock, Part I: A combined multi-phase-field/crystal plasticity approach for single crystal simulations Na, SeonHong; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 338 https://doi.org/10.1016/j.cma.2017.12.022	journal	August 2018
A multiscale multi-permeability poroplasticity model linked by recursive homogenizations and deep learning Wang, Kun; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 334 https://doi.org/10.1016/j.cma.2018.01.036	journal	June 2018
Cracking and damage from crystallization in pores: Coupled chemo-hydro-mechanics and phase-field modeling Choo, Jinhyun; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 335 https://doi.org/10.1016/j.cma.2018.01.044	journal	June 2018
Phase-field modeling of anisotropic brittle fracture including several damage mechanisms Bleyer, Jeremy; Alessi, Roberto Computer Methods in Applied Mechanics and Engineering, Vol. 336 https://doi.org/10.1016/j.cma.2018.03.012	journal	July 2018
A mixed-mode phase field fracture model in anisotropic rocks with consistent kinematics Bryant, Eric C.; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 342 https://doi.org/10.1016/j.cma.2018.08.008	journal	December 2018
An updated Lagrangian LBM–DEM–FEM coupling model for dual-permeability fissured porous media with embedded discontinuities Wang, Kun; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 344 https://doi.org/10.1016/j.cma.2018.09.034	journal	February 2019
Meta-modeling game for deriving theory-consistent, microstructure-based traction–separation laws via deep reinforcement learning Wang, Kun; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 346 https://doi.org/10.1016/j.cma.2018.11.026	journal	April 2019
A FFT solver for variational phase-field modeling of brittle fracture Chen, Yang; Vasiukov, Dmytro; Gélébart, Lionel Computer Methods in Applied Mechanics and Engineering, Vol. 349 https://doi.org/10.1016/j.cma.2019.02.017	journal	June 2019
FFT-based homogenization of hypoelastic plasticity at finite strains Ma, Ran; Truster, Timothy J. Computer Methods in Applied Mechanics and Engineering, Vol. 349 https://doi.org/10.1016/j.cma.2019.02.037	journal	June 2019
Phase field modeling of directional fracture in anisotropic polycrystals Clayton, J. D.; Knap, J. Computational Materials Science, Vol. 98 https://doi.org/10.1016/j.commatsci.2014.11.009	journal	February 2015
DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale Roters, F.; Diehl, M.; Shanthraj, P. Computational Materials Science, Vol. 158 https://doi.org/10.1016/j.commatsci.2018.04.030	journal	February 2019
Progressive damage analysis of 3D braided composites using FFT-based method Wang, Bing; Fang, Guodong; Liu, Shuo Composite Structures, Vol. 192 https://doi.org/10.1016/j.compstruct.2018.02.040	journal	May 2018
A phase field approach to simulate intralaminar and translaminar fracture in long fiber composite materials Quintanas-Corominas, A.; Reinoso, J.; Casoni, E. Composite Structures, Vol. 220 https://doi.org/10.1016/j.compstruct.2019.02.007	journal	July 2019
Formulation of nonlocal damage models based on spectral methods for application to complex microstructures Boeff, Martin; Gutknecht, Florian; Engels, Philipp S. Engineering Fracture Mechanics, Vol. 147 https://doi.org/10.1016/j.engfracmech.2015.06.030	journal	October 2015
Phase field modeling of fracture in anisotropic brittle solids Teichtmeister, S.; Kienle, D.; Aldakheel, F. International Journal of Non-Linear Mechanics, Vol. 97 https://doi.org/10.1016/j.ijnonlinmec.2017.06.018	journal	December 2017
Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory Miehe, Christian; Aldakheel, Fadi; Raina, Arun International Journal of Plasticity, Vol. 84 https://doi.org/10.1016/j.ijplas.2016.04.011	journal	September 2016
On micro-cracking, inelastic dilatancy, and the brittle-ductile transition in compact rocks: A micro-mechanical study Wei, Yujie; Anand, Lallit International Journal of Solids and Structures, Vol. 45, Issue 10 https://doi.org/10.1016/j.ijsolstr.2007.11.028	journal	May 2008
A numerical spectral approach for solving elasto-static field dislocation and g-disclination mechanics Berbenni, Stéphane; Taupin, Vincent; Djaka, Komlan Sénam International Journal of Solids and Structures, Vol. 51, Issue 23-24 https://doi.org/10.1016/j.ijsolstr.2014.08.009	journal	November 2014
Accelerating a FFT-based solver for numerical homogenization of periodic media by conjugate gradients Zeman, Jan; Vondřejc, Jaroslav; Novák, Jan Journal of Computational Physics, Vol. 229, Issue 21 https://doi.org/10.1016/j.jcp.2010.07.010	journal	October 2010
The role of interfaces in enhancing the yield strength of composites and polycrystals Aifantis, K. E.; Willis, J. R. Journal of the Mechanics and Physics of Solids, Vol. 53, Issue 5 https://doi.org/10.1016/j.jmps.2004.12.003	journal	May 2005
Crack kinking in a variational phase-field model of brittle fracture with strongly anisotropic surface energy Li, Bin; Maurini, Corrado Journal of the Mechanics and Physics of Solids, Vol. 125 https://doi.org/10.1016/j.jmps.2019.01.010	journal	April 2019
Ab initio study of the elastic properties of sodium chloride at high pressure Liu, Lei; Bi, Yan; Xu, Jian Physica B: Condensed Matter, Vol. 405, Issue 9 https://doi.org/10.1016/j.physb.2010.02.001	journal	May 2010
A phase field model of deformation twinning: Nonlinear theory and numerical simulations Clayton, J. D.; Knap, J. Physica D: Nonlinear Phenomena, Vol. 240, Issue 9-10 https://doi.org/10.1016/j.physd.2010.12.012	journal	April 2011
Connecting microstructural attributes and permeability from 3D tomographic images of in situ shear-enhanced compaction bands using multiscale computations: MICROSCALE AND IMPACT ON PERMEABILITY Sun, WaiChing; Andrade, José E.; Rudnicki, John W. Geophysical Research Letters, Vol. 38, Issue 10 https://doi.org/10.1029/2011GL047683	journal	May 2011
Weakening of rock salt by water during long-term creep Urai, Janos L.; Spiers, Christopher J.; Zwart, Hendrik J. Nature, Vol. 324, Issue 6097 https://doi.org/10.1038/324554a0	journal	December 1986
Transition between crack patterns in quenched glass plates Yuse, A.; Sano, M. Nature, Vol. 362, Issue 6418 https://doi.org/10.1038/362329a0	journal	March 1993
A fast numerical scheme for computing the response of composites using grid refinement Eyre, D. J.; Milton, G. W. The European Physical Journal Applied Physics, Vol. 6, Issue 1 https://doi.org/10.1051/epjap:1999150	journal	April 1999
Simulation of micromechanical behavior of polycrystals: finite elements versus fast Fourier transforms Prakash, A.; Lebensohn, R. A. Modelling and Simulation in Materials Science and Engineering, Vol. 17, Issue 6 https://doi.org/10.1088/0965-0393/17/6/064010	journal	August 2009
Necessary and sufficient elastic stability conditions in various crystal systems Mouhat, Félix; Coudert, François-Xavier Physical Review B, Vol. 90, Issue 22 https://doi.org/10.1103/PhysRevB.90.224104	journal	December 2014
Forbidden Directions for the Fracture of Thin Anisotropic Sheets: An Analogy with the Wulff Plot Takei, Atsushi; Roman, Benoît; Bico, José Physical Review Letters, Vol. 110, Issue 14 https://doi.org/10.1103/PhysRevLett.110.144301	journal	April 2013
FFT-based interface decohesion modelling by a nonlocal interphase Sharma, Luv; Peerlings, Ron H. J.; Shanthraj, Pratheek Advanced Modeling and Simulation in Engineering Sciences, Vol. 5, Issue 1 https://doi.org/10.1186/s40323-018-0100-0	journal	April 2018

Similar Records

Computational thermomechanics for crystalline rock. Part II: Chemo-damage-plasticity and healing in strongly anisotropic polycrystals

Journal Article · 2020 · Computer Methods in Applied Mechanics and Engineering · OSTI ID:1801242

Ma, Ran; Sun, WaiChing

Implementation and experimental validation of nonlocal damage in a large-strain elasto-viscoplastic FFT-based framework for predicting ductile fracture in 3D polycrystalline materials

Journal Article · 2023 · International Journal of Plasticity · OSTI ID:1922795

Cocke, Carter K.; Mirmohammad, H.; Zecevic, Miroslav; +4 more

A generalized massively parallel ultra-high order FFT-based Maxwell solver

Journal Article · 2019 · Computer Physics Communications · OSTI ID:1580963

Kallala, Haithem; Vay, Jean-Luc; Vincenti, Henri

Related Subjects

42 ENGINEERING
anisotropic cracks
fast Fourier transform
higher-order phase field fracture
multi-phase-field fracture
polycrystal
salt

Title: FFT-based solver for higher-order and multi-phase-field fracture models applied to strongly anisotropic brittle materials

Citation Formats

References (80)

Similar Records

Related Subjects