×

Fourth-order phase-field modeling for brittle fracture in piezoelectric materials. (English) Zbl 07912638

MSC:

74S22 Isogeometric methods applied to problems in solid mechanics
74R10 Brittle fracture
74F15 Electromagnetic effects in solid mechanics

Software:

COMSOL
Full Text: DOI

References:

[1] Gao, C. F.; Fan, W. X., Exact solutions for the plane problem in piezoelectric materials with an elliptic or a crack, International Journal of Solids and Structures, 36, 2527-2540, 1999 · Zbl 0955.74024 · doi:10.1016/S0020-7683(98)00120-6
[2] Chen, W. Q.; Ding, H. J., A penny-shaped crack in a transversely isotropic piezoelectric solid: modes II and III problems, Acta Mechanica Sinica, 15, 52-58, 1999 · doi:10.1007/BF02487900
[3] Wang, B. L.; Noda, N., Exact thermoelectroelasticity solution for a penny-shaped crack in piezoelectric materials, Journal of Thermal Stresses, 27, 241-251, 2004 · doi:10.1080/01495730490271018
[4] Zhou, Z. G.; Chen, Z. T., A 3-D rectangular permeable crack or two 3-D rectangular permeable cracks in a piezoelectric material, Archive of Applied Mechanics, 81, 641-668, 2011 · Zbl 1271.74403 · doi:10.1007/s00419-010-0441-8
[5] Chen, H.; Wei, W.; Liu, J.; Fang, D., Propagation of a semi-infinite conducting crack in piezoelectric materials: mode-I problem, Journal of the Mechanics and Physics of Solids, 68, 77-92, 2014 · Zbl 1328.74038 · doi:10.1016/j.jmps.2014.03.010
[6] Bhargava, R. R.; Sharma, K., A study of finite size effects on cracked 2-D piezoelectric media using extended finite element method, Computational Materials Science, 50, 1834-1845, 2011 · doi:10.1016/j.commatsci.2011.01.026
[7] Mishra, R.; Burela, R. G., Thermo-electro-mechanical fatigue crack growth simulation in piezoelectric solids using XFEM approach, Theoretical and Applied Fracture Mechanics, 104, 102388, 2019 · doi:10.1016/j.tafmec.2019.102388
[8] Schlüter, A.; Willenbücher, A.; Kuhn, C.; Müller, R., Phase field approximation of dynamic brittle fracture, Computational Mechanics, 54, 1141-1161, 2014 · Zbl 1311.74106 · doi:10.1007/s00466-014-1045-x
[9] Rabczuk, T.; Belytschko, T., Cracking particles: a simplified meshfree method for arbitrary evolving cracks, International Journal for Numerical Methods in Engineering, 61, 2316-2343, 2004 · Zbl 1075.74703 · doi:10.1002/nme.1151
[10] Rabczuk, T.; Belytschko, T., A three-dimensional large deformation meshfree method for arbitrary evolving cracks, Computer Methods in Applied Mechanics and Engineering, 196, 2777-2799, 2007 · Zbl 1128.74051 · doi:10.1016/j.cma.2006.06.020
[11] Rabczuk, T.; Zi, G.; Bordas, S.; Hung, N., A simple and robust three-dimensional cracking-particle method without enrichment, Computer Methods in Applied Mechanics and Engineering, 199, 2437-2455, 2010 · Zbl 1231.74493 · doi:10.1016/j.cma.2010.03.031
[12] Francfort, G. A.; Marigo, J. J., Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, 46, 1319-1342, 1998 · Zbl 0966.74060 · doi:10.1016/S0022-5096(98)00034-9
[13] Bourdin, B.; Francfort, G. A.; Marigo, J. J., Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, 48, 797-826, 2000 · Zbl 0995.74057 · doi:10.1016/S0022-5096(99)00028-9
[14] Miehe, C.; Welschinger, F.; Hofacker, M., Thermodynamically consistent phase-field models of fracture: variational principles and multi-field FE implementations, International Journal for Numerical Methods in Engineering, 83, 1273-1311, 2010 · Zbl 1202.74014 · doi:10.1002/nme.2861
[15] Kuhn, C.; Müller, R., A continuum phase field model for fracture, Engineering Fracture Mechanics, 77, 3625-3634, 2010 · doi:10.1016/j.engfracmech.2010.08.009
[16] Pham, K.; Amor, H.; Marigo, J.; Maurini, C., Gradient damage models and their use to approximate brittle fracture, International Journal of Damage Mechanic, 20, 618, 2011 · doi:10.1177/1056789510386852
[17] Wu, J. Y., A unified phase-field theory for the mechanics of damage and quasi-brittle failure, Journal of the Mechanics and Physics of Solids, 103, 72-99, 2017 · doi:10.1016/j.jmps.2017.03.015
[18] Wu, J. Y.; Nguyen, V., A length scale insensitive phase-field damage model for brittle fracture, Journal of the Mechanics and Physics of Solids, 119, 20-42, 2018 · doi:10.1016/j.jmps.2018.06.006
[19] Zhou, S.; Rabczuk, T.; Zhuang, X., Phase field modeling of quasi-static and dynamic crack propagation: COMSOL implementation and case studies, Advances in Engineering Software, 122, 31-49, 2018 · doi:10.1016/j.advengsoft.2018.03.012
[20] Ambati, M.; Kruse, R.; De Lorenzis, L., A phase-field model for ductile fracture at finite strains and its experimental verification, Computational Mechanics, 57, 149-167, 2016 · Zbl 1381.74181 · doi:10.1007/s00466-015-1225-3
[21] Rodriguez, P.; Ulloa, J.; Samaniego, C.; Samaniego, E., A variational approach to the phase field modeling of brittle and ductile fracture, International Journal of Mechanical Sciences, 144, 502, 2018 · doi:10.1016/j.ijmecsci.2018.05.009
[22] Khalil, Z.; Elghazouli, A. Y.; Martínez-Pañeda, E., A generalised phase field model for fatigue crack growth in elastic-plastic solids with an efficient monolithic solver, Computer Methods in Applied Mechanics and Engineering, 388, 114286, 2022 · Zbl 1507.74081 · doi:10.1016/j.cma.2021.114286
[23] Hao, S.; Chen, Y.; Cheng, J.; Shen, Y., A phase field model for high-speed impact based on the updated Lagrangian formulation, Finite Elements in Analysis and Design, 199, 103652, 2022 · doi:10.1016/j.finel.2021.103652
[24] Du, C.; Cui, H.; Zhang, H.; Cai, Z.; Zhai, W., Phase field modeling of thermal fatigue crack growth in elastoplastic solids and experimental verification, Mechanics of Materials, 188, 104839, 2024 · doi:10.1016/j.mechmat.2023.104839
[25] Zhou, S.; Zhuang, X.; Rabczuk, T., A phase-field modeling approach of fracture propagation in poroelastic media, Engineering Geology, 240, 189-203, 2018 · doi:10.1016/j.enggeo.2018.04.008
[26] Zhang, Y.; Wang, J.; Zhang, T., The jumping dielectric breakdown behavior induced by crack propagation in ferroelectric materials: a phase field study, Journal of the Mechanics and Physics of Solids, 169, 105088, 2022 · doi:10.1016/j.jmps.2022.105088
[27] Ye, J.; Zhang, L., Damage evolution of polymer-matrix multiphase composites under coupled moisture effects, Computer Methods in Applied Mechanics and Engineering, 388, 114213, 2022 · Zbl 1507.74369 · doi:10.1016/j.cma.2021.114213
[28] Li, D.; Li, P.; Li, W.; Zhou, K., Three-dimensional phase-field modeling of temperature-dependent thermal shock-induced fracture in ceramic materials, Engineering Fracture Mechanics, 268, 108444, 2022 · doi:10.1016/j.engfracmech.2022.108444
[29] Tan, Y.; Liu, C.; Zhao, J.; He, Y.; Li, P.; Li, X., Phase field model for brittle fracture in multiferroic materials, Computer Methods in Applied Mechanics and Engineering, 414, 116193, 2023 · Zbl 1539.74387 · doi:10.1016/j.cma.2023.116193
[30] Miehe, C.; Welschinger, F.; Hofacker, M., A phase field model of electromechanical fracture, Journal of the Mechanics and Physics of Solids, 58, 1716-1740, 2010 · Zbl 1200.74123 · doi:10.1016/j.jmps.2010.06.013
[31] Abdollahi, A.; Arias, I., Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions, Journal of the Mechanics and Physics of Solids, 60, 2100-2126, 2012 · doi:10.1016/j.jmps.2012.06.014
[32] Wilson, Z. A.; Borden, M. J.; Landis, C. M., A phase-field model for fracture in piezoelectric ceramics, International Journal of Fracture, 183, 135-153, 2013 · doi:10.1007/s10704-013-9881-9
[33] Mohanty, S.; Kumbhar, P. Y.; Swaminathan, N.; Annabattula, R., A phase-field model for crack growth in electro-mechanically coupled functionally graded piezo ceramics, Smart Materials and Structures, 29, 045005, 2020 · doi:10.1088/1361-665X/ab7145
[34] Wu, J. Y.; Chen, W. X., Phase-field modeling of electromechanical fracture in piezoelectric solids: analytical results and numerical simulations, Computer Methods in Applied Mechanics and Engineering, 387, 114125, 2021 · Zbl 1507.74428 · doi:10.1016/j.cma.2021.114125
[35] Tan, Y.; He, Y.; Liu, C.; Li, X., Phase field fracture model of transversely isotropic piezoelectric materials with thermal effect, Engineering Fracture Mechanics, 268, 108479, 2022 · doi:10.1016/j.engfracmech.2022.108479
[36] Tan, Y.; He, Y.; Li, X., Phase field fracture modeling of transversely isotropic piezoelectric material with anisotropic fracture toughness, International Journal of Solids and Structures, 248, 111615, 2022 · doi:10.1016/j.ijsolstr.2022.111615
[37] Tan, Y.; He, Y.; Li, X.; Kang, G., A phase field model for fatigue fracture in piezoelectric solids: a residual controlled staggered scheme, Computer Methods in Applied Mechanics and Engineering, 399, 115459, 2022 · Zbl 1507.74421 · doi:10.1016/j.cma.2022.115459
[38] Dan, S.; Tarafder, P.; Ghosh, S., Adaptive wavelet-enhanced cohesive zone phase-field FE model for crack evolution in piezoelectric composites, Computer Methods in Applied Mechanics and Engineering, 392, 114636, 2022 · Zbl 1507.74142 · doi:10.1016/j.cma.2022.114636
[39] Tarafder, P.; Dan, S.; Ghosh, S., Cohesive zone phase field model for electromechanical fracture in multiphase piezoelectric composites, Journal of Composite Materials, 57, 531-543, 2023 · doi:10.1177/00219983231151396
[40] Behera, A. K.; Unnikrishna Pillai, A.; Rahaman, M. M., A phase-field model for electro-mechanical fracture with an open-source implementation of it using Gridap in Julia, Mathematics and Mechanics of Solids, 28, 1877-1908, 2023 · doi:10.1177/10812865221133860
[41] Kiran, R.; Nguyen-Thanh, N.; Zhou, K., Adaptive isogeometric analysis-based phase-field modeling of brittle electromechanical fracture in piezoceramics, Engineering Fracture Mechanics, 274, 108738, 2022 · doi:10.1016/j.engfracmech.2022.108738
[42] Kiran, R.; Nguyen-Thanh, N.; Yu, H.; Zhou, K., Adaptive isogeometric analysis-based phase-field modeling of interfacial fracture in piezoelectric composites, Engineering Fracture Mechanics, 288, 10918, 2023 · doi:10.1016/j.engfracmech.2023.109181
[43] Borden, M. J.; Hughes, T. J R.; Landis, C. M.; Verhoosel, C. V., A higher-order phase-field model for brittle fracture: formulation and analysis within the isogeometric analysis framework, Computer Methods in Applied Mechanics and Engineering, 273, 100, 2014 · Zbl 1296.74098 · doi:10.1016/j.cma.2014.01.016
[44] Goswami, S.; Anitescu, C.; Rabczuk, T., Adaptive fourth-order phase field analysis for brittle fracture, Computer Methods in Applied Mechanics and Engineering, 361, 112808, 2020 · Zbl 1442.74202 · doi:10.1016/j.cma.2019.112808
[45] Makvandi, R.; Duczek, S.; Juhre, D., A phase-field fracture model based on strain gradient elasticity, Engineering Fracture Mechanics, 220, 106648, 2020 · doi:10.1016/j.engfracmech.2019.106648
[46] Chen, L.; Li, B.; De-Borst, R., Adaptive isogeometric analysis for phase-field modeling of anisotropic brittle fracture, International Journal for Numerical Methods in Engineering, 121, 4630, 2020 · Zbl 1540.74120 · doi:10.1002/nme.6457
[47] Nguyen-Thanh, N.; Li, W.; Huang, J.; Zhou, K., Adaptive higher-order phase-field modeling of anisotropic brittle fracture in 3D polycrystalline materials, Computer Methods in Applied Mechanics and Engineering, 372, 113434, 2020 · Zbl 1506.74363 · doi:10.1016/j.cma.2020.113434
[48] Goswami, S.; Anitescu, C.; Rabczuk, T., Adaptive fourth-order phase field analysis using deep energy minimization, Theoretical and Applied Fracture Mechanics, 107, 102527, 2020 · doi:10.1016/j.tafmec.2020.102527
[49] Sridhar, A.; Keip, M. A., A phase-field model for anisotropic brittle fracturing of piezoelectric ceramics, International Journal of Fracture, 220, 221-242, 2019
[50] Park, S.; Sun, C. T., Fracture criteria for piezoelectric ceramics, Journal of the American Ceramic Society, 78, 1475-1480, 1995 · doi:10.1111/j.1151-2916.1995.tb08840.x
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.