Combining coupled, staggered and uncoupled solution methods for phase-field-based fracture analysis

References

• T. Rabczuk, Computational methods for fracture in brittle and quasi-brittle solids: state-of-the-art review and future perspectives, Int. Schol. Res. Not., vol. 2013, pp. 1–38, 2013. DOI: 10.1155/2013/849231.
   Google Scholar
• S. P. Bordas, et al., Strain smoothing in fem and xfem, Computers & Structures., vol. 88, no. 23-24, pp. 1419–1443, 2010. DOI: 10.1016/j.compstruc.2008.07.006.
   Web of Science ®Google Scholar
• J. Dujc, and B. Brank, Modeling fracture in elasto-plastic solids by embedded-discontinuity stress-hybrid finite element formulation, Mech. Adv. Mater. Struct., pp. 1–17, 2020. DOI: 10.1080/15376494.2020.1786755.
   Web of Science ®Google Scholar
• J. Dujc, B. Brank, and A. Ibrahimbegovic, Quadrilateral finite element with embedded strong discontinuity for failure analysis of solids, Comput. Model. Eng. Sci., vol. 69, no. 3, pp. 223–260, 2010a.
   Web of Science ®Google Scholar
• J. Dujc, B. Brank, and A. Ibrahimbegovic, Stress-hybrid quadrilateral finite element with embedded strong discontinuity for failure analysis of plane stress solids, Int. J. Numer. Meth. Eng., vol. 94, no. 12, pp. 1075–1098, 2013. DOI: 10.1002/nme.4475.
   Web of Science ®Google Scholar
• J. Dujc, B. Brank, A. Ibrahimbegovic, and D. Brancherie, An embedded crack model for failure analysis of concrete solids, Comput. Concr., vol. 7, no. 4, pp. 331–346, 2010b. DOI: 10.12989/cac.2010.7.4.331.
   Web of Science ®Google Scholar
• M. Jukić, B. Brank, and A. Ibrahimbegović, Embedded discontinuity finite element formulation for failure analysis of planar reinforced concrete beams and frames, Eng. Struct., vol. 50, pp. 115–125, 2013. DOI: 10.1016/j.engstruct.2012.07.028.
   Web of Science ®Google Scholar
• M. Jukić, B. Brank, and A. Ibrahimbegović, Failure analysis of reinforced concrete frames by beam finite element that combines damage, plasticity and embedded discontinuity, Eng. Struct., vol. 75, pp. 507–527, 2014. DOI: 10.1016/j.engstruct.2014.06.017.
   Web of Science ®Google Scholar
• A. Stanić, B. Brank, and D. Brancherie, Fracture of quasi-brittle solids by continuum and discrete-crack damage models and embedded discontinuity formulation, Eng. Fract. Mech., vol. 227, no. 106924, pp. 106924, 2020. DOI: 10.1016/j.engfracmech.2020.106924.
   Google Scholar
• A. Stanić, B. Brank, A. Ibrahimbegovic, and H. Matthies, Crack propagation simulation without crack tracking algorithm: embedded discontinuity formulation with incompatible modes, Comput Method Appl M., vol. 386, pp. 114090, 2021.
   Google Scholar
• A. A. Griffith, Vi. the phenomena of rupture and flow in solids, Philos. Trans. R..Soc. London. Ser A: Contain Papers Math Phys Charact., vol. 221, no. 582-593, pp. 163–198, 1921.
   Google Scholar
• G. A. Francfort, and J.-J. Marigo, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, vol. 46, no. 8, pp. 1319–1342, 1998. DOI: 10.1016/S0022-5096(98)00034-9.
   Web of Science ®Google Scholar
• B. Bourdin, Numerical implementation of the variational formulation for quasi-static brittle fracture, Interfaces Free Bound., vol. 9, no. 3, pp. 411–430, 2007. DOI: 10.4171/IFB/171.
   Web of Science ®Google Scholar
• B. Bourdin, G. A. Francfort, and J.-J. Marigo, Numerical experiments in revisited brittle fracture, J. Mech. Phys. Solids, vol. 48, no. 4, pp. 797–826, 2000. DOI: 10.1016/S0022-5096(99)00028-9.
   Web of Science ®Google Scholar
• B. Bourdin, G. A. Francfort, and J.-J. Marigo, The variational approach to fracture, J. Elast., vol. 91, no. 1–3, pp. 5–148, 2008. DOI: 10.1007/s10659-007-9107-3.
   Web of Science ®Google Scholar
• M. Ambati, T. Gerasimov, and L. De Lorenzis, A review on phase-field models of brittle fracture and a new fast hybrid formulation, Comput. Mech., vol. 55, no. 2, pp. 383–405, 2015b. DOI: 10.1007/s00466-014-1109-y.
   Web of Science ®Google Scholar
• H. Amor, J.-J. Marigo, and C. Maurini, Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments, J. Mech. Phys. Solids, vol. 57, no. 8, pp. 1209–1229, 2009. DOI: 10.1016/j.jmps.2009.04.011.
   Web of Science ®Google Scholar
• M. J. Borden, T. J. Hughes, C. M. Landis, and C. V. Verhoosel, A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework, Comput. Methods Appl. Mech. Eng.., vol. 273, pp. 100–118, 2014. DOI: 10.1016/j.cma.2014.01.016.
   Web of Science ®Google Scholar
• M. J. Borden, C. V. Verhoosel, M. A. Scott, T. J. Hughes, and C. M. Landis, A phase-field description of dynamic brittle fracture, Comput. Methods Appl. Mech. Eng., vol. 217, pp. 77–95, 2012.
   Web of Science ®Google Scholar
• F. Freddi, and G. Royer-Carfagni, Regularized variational theories of fracture: a unified approach, J. Mech. Phys. Solids, vol. 58, no. 8, pp. 1154–1174, 2010. DOI: 10.1016/j.jmps.2010.02.010.
   Web of Science ®Google Scholar
• Y. Kriaa, H. Hentati, and B. Zouari, Applying the phase-field approach for brittle fracture prediction: Numerical implementation and experimental validation, Mech. Adv. Mater. Struct., pp. 1–12, 2020. DOI: 10.1080/15376494.2020.1795957.
   Web of Science ®Google Scholar
• C. Kuhn, and R. Müller, A continuum phase field model for fracture, Eng. Fract. Mech., vol. 77, no. 18, pp. 3625–3634, 2010. DOI: 10.1016/j.engfracmech.2010.08.009.
   Web of Science ®Google Scholar
• G. Lancioni, and G. Royer-Carfagni, The variational approach to fracture mechanics. a practical application to the french panthéon in paris, J. Elast., vol. 95, no. 1-2, pp. 1–30, 2009. DOI: 10.1007/s10659-009-9189-1.
   Web of Science ®Google Scholar
• A. Mesgarnejad, B. Bourdin, and M. Khonsari, Validation simulations for the variational approach to fracture, Comput. Methods Appl. Mech. Eng., vol. 290, pp. 420–437, 2015. DOI: 10.1016/j.cma.2014.10.052.
   Web of Science ®Google Scholar
• C. Miehe, M. Hofacker, and F. Welschinger, A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Comput. Methods Appl. Mech. Eng.., vol. 199, no. 45–48, pp. 2765–2778, 2010. DOI: 10.1016/j.cma.2010.04.011.
   Web of Science ®Google Scholar
• C. Miehe, F. Welschinger, and M. Hofacker, Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field fe implementations, Int. J. Numer. Meth. Engng. ., vol. 83, no. 10, pp. 1273–1311, 2010. DOI: 10.1002/nme.2861.
   Web of Science ®Google Scholar
• K. Pham, H. Amor, J.-J. Marigo, and C. Maurini, Gradient damage models and their use to approximate brittle fracture, Int. J. Damage Mech., vol. 20, no. 4, pp. 618–652, 2011. DOI: 10.1177/1056789510386852.
   Web of Science ®Google Scholar
• J.-Y. Wu, and V. P. Nguyen, A length scale insensitive phase-field damage model for brittle fracture, J. Mech. Phys. Solids, vol. 119, pp. 20–42, 2018. DOI: 10.1016/j.jmps.2018.06.006.
   Web of Science ®Google Scholar
• J.-Y. Wu, V. P. Nguyen, H. Zhou, and Y. Huang, A variationally consistent phase-field anisotropic damage model for fracture, Comput. Methods Appl. Mech. Eng., vol. 358, no. 112629, pp. 112629, 2020. DOI: 10.1016/j.cma.2019.112629.
   Google Scholar
• R. Alessi, M. Ambati, T. Gerasimov, S. Vidoli, and L. De Lorenzis. Comparison of phase-field models of fracture coupled with plasticity. In Advances in Computational Plasticity, Springer, Cham, pp. 1–21, 2018.
   Google Scholar
• R. Alessi, J.-J. Marigo, and S. Vidoli, Gradient damage models coupled with plasticity: variational formulation and main properties, Mech. Mater., vol. 80, pp. 351–367, 2015. DOI: 10.1016/j.mechmat.2013.12.005.
   Web of Science ®Google Scholar
• M. Ambati, T. Gerasimov, and L. De Lorenzis, Phase-field modeling of ductile fracture, Comput. Mech., vol. 55, no. 5, pp. 1017–1040, 2015a. DOI: 10.1007/s00466-015-1151-4.
   Web of Science ®Google Scholar
• M. J. Borden, T. J. Hughes, C. M. Landis, A. Anvari, and I. J. Lee, A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects, Comput. Methods Appl. Mech. Eng., vol. 312, pp. 130–166, 2016. DOI: 10.1016/j.cma.2016.09.005.
   Web of Science ®Google Scholar
• F. P. Duda, A. Ciarbonetti, P. J. Sánchez, and A. E. Huespe, A phase-field/gradient damage model for brittle fracture in elastic–plastic solids, Int. J. Plast., vol. 65, pp. 269–296, 2015. DOI: 10.1016/j.ijplas.2014.09.005.
   Web of Science ®Google Scholar
• C. Miehe, F. Aldakheel, and A. Raina, Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory, Int. J. Plast., vol. 84, pp. 1–32, 2016. DOI: 10.1016/j.ijplas.2016.04.011.
   Web of Science ®Google Scholar
• C. Miehe, M. Hofacker, L.-M. Schänzel, and F. Aldakheel, Phase field modeling of fracture in multi-physics problems. part ii. coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic–plastic solids, Comput. Methods Appl. Mech. Eng., vol. 294, pp. 486–522, 2015. DOI: 10.1016/j.cma.2014.11.017.
   Web of Science ®Google Scholar
• M. Ambati and L. De Lorenzis, Phase-field modeling of brittle and ductile fracture in shells with isogeometric nurbs-based solid-shell elements, Comput. Methods Appl. Mech. Eng.., vol. 312, pp. 351–373, 2016. DOI: 10.1016/j.cma.2016.02.017.
   Web of Science ®Google Scholar
• F. Amiri, D. Millán, Y. Shen, T. Rabczuk, and M. Arroyo, Phase-field modeling of fracture in linear thin shells, Theor. Appl. Fract. Mech., vol. 69, pp. 102–109, 2014. DOI: 10.1016/j.tafmec.2013.12.002.
   Web of Science ®Google Scholar
• P. Areias, T. Rabczuk, and M. Msekh, Phase-field analysis of finite-strain plates and shells including element subdivision, Comput. Methods Appl. Mech. Eng., vol. 312, pp. 322–350, 2016. DOI: 10.1016/j.cma.2016.01.020.
   Web of Science ®Google Scholar
• D. H. Doan, T. Van Do, P. M. Pham, and N. D. Duc, Validation simulation for free vibration and buckling of cracked mindlin plates using phase-field method, Mech. Adv. Mater. Struct., vol. 26, no. 12, pp. 1018–1027, 2019. DOI: 10.1080/15376494.2018.1430262.
   Web of Science ®Google Scholar
• T. Guillén-Hernández, J. Reinoso, and M. Paggi, Phase field model for fracture analysis of functionally graded power-based shell structures, Mech. Adv. Mater. Struct., pp. 1–11, 2020. DOI: 10.1080/15376494.2020.1751354.
   Web of Science ®Google Scholar
• J. Kiendl, M. Ambati, L. De Lorenzis, H. Gomez, and A. Reali, Phase-field description of brittle fracture in plates and shells, Comput. Methods Appl. Mech. Eng., vol. 312, pp. 374–394, 2016. DOI: 10.1016/j.cma.2016.09.011.
   Web of Science ®Google Scholar
• J. Reinoso, M. Paggi, and C. Linder, Phase field modeling of brittle fracture for enhanced assumed strain shells at large deformations: formulation and finite element implementation, Comput. Mech. ., vol. 59, no. 6, pp. 981–1001, 2017. DOI: 10.1007/s00466-017-1386-3.
   Web of Science ®Google Scholar
• H. Ulmer, M. Hofacker, and C. Miehe, Phase field modeling of fracture in plates and shells, Proc. Appl. Math. Mech. ., vol. 12, no. 1, pp. 171–172, 2012. DOI: 10.1002/pamm.201210076.
   Google Scholar
• L. De Lorenzis, and T. Gerasimov, 2020. Numerical implementation of phase-field models of brittle fracture. In Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids, Pages, Springer, pp. 75–101.
   Google Scholar
• M. Artina, M. Fornasier, S. Micheletti, and S. Perotto, Anisotropic mesh adaptation for crack detection in brittle materials, SIAM J. Sci. Comput., vol. 37, no. 4, pp. B633–B659, 2015. DOI: 10.1137/140970495.
   Web of Science ®Google Scholar
• S. Burke, C. Ortner, and E. Süli, An adaptive finite element approximation of a variational model of brittle fracture, SIAM J. Numer. Anal., vol. 48, no. 3, pp. 980–1012, 2010. DOI: 10.1137/080741033.
   Web of Science ®Google Scholar
• S. Burke, C. Ortner, and E. Süli, An adaptive finite element approximation of a generalized ambrosio–tortorelli functional, Math. Models Methods Appl. Sci., vol. 23, no. 09, pp. 1663–1697, 2013. DOI: 10.1142/S021820251350019X.
   Google Scholar
• T. Heister, M. F. Wheeler, and T. Wick, A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach, Comput. Methods Appl. Mech. Eng.., vol. 290, pp. 466–495, 2015. DOI: 10.1016/j.cma.2015.03.009.
   Web of Science ®Google Scholar
• M. Klinsmann, D. Rosato, M. Kamlah, and R. M. McMeeking, An assessment of the phase field formulation for crack growth, Comput. Methods Appl. Mech. Eng., vol. 294, pp. 313–330, 2015. DOI: 10.1016/j.cma.2015.06.009.
   Web of Science ®Google Scholar
• S. Nagaraja, M. Elhaddad, M. Ambati, S. Kollmannsberger, L. De Lorenzis, and E. Rank, Phase-field modeling of brittle fracture with multi-level hp-fem and the finite cell method, Comput. Mech. ., vol. 63, no. 6, pp. 1283–1300, 2019. DOI: 10.1007/s00466-018-1649-7.
   Web of Science ®Google Scholar
• T. Wick, Goal functional evaluations for phase-field fracture using pu-based dwr mesh adaptivity, Comput. Mech., vol. 57, no. 6, pp. 1017–1035, 2016. DOI: 10.1007/s00466-016-1275-1.
   Web of Science ®Google Scholar
• T. Gerasimov, and L. De Lorenzis, A line search assisted monolithic approach for phase-field computing of brittle fracture, Comput. Methods Appl. Mech. Eng., vol. 312, pp. 276–303, 2016. DOI: 10.1016/j.cma.2015.12.017.
   Web of Science ®Google Scholar
• T. Wick, An error-oriented newton/inexact augmented lagrangian approach for fully monolithic phase-field fracture propagation, SIAM J. Sci. Comput., vol. 39, no. 4, pp. B589–B617, 2017a. DOI: 10.1137/16M1063873.
   Web of Science ®Google Scholar
• T. Wick, Modified newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation, Comput. Methods Appl. Mech. Eng., vol. 325, pp. 577–611, 2017b. DOI: 10.1016/j.cma.2017.07.026.
   Web of Science ®Google Scholar
• P. Farrell, and C. Maurini, Linear and nonlinear solvers for variational phase-field models of brittle fracture, Int. J. Numer. Meth. Eng., vol. 109, no. 5, pp. 648–667, 2017. DOI: 10.1002/nme.5300.
   Web of Science ®Google Scholar
• P. K. Kristensen, and E. Martínez-Pañeda, Phase field fracture modelling using quasi-newton methods and a new adaptive step scheme, Theor. Appl. Fract. Mech., vol. 107, pp. 102446, 2020. DOI: 10.1016/j.tafmec.2019.102446.
   Web of Science ®Google Scholar
• F. Aldakheel, B. Hudobivnik, A. Hussein, and P. Wriggers, Phase-field modeling of brittle fracture using an efficient virtual element scheme, Comput. Methods Appl. Mech. Eng., vol. 341, pp. 443–466, 2018. DOI: 10.1016/j.cma.2018.07.008.
   Web of Science ®Google Scholar
• C. Bilgen, and K. Weinberg, On the crack-driving force of phase-field models in linearized and finite elasticity, Comput. Methods Appl. Mech. Eng., vol. 353, pp. 348–372, 2019. DOI: 10.1016/j.cma.2019.05.009.
   Web of Science ®Google Scholar
• A. Ibrahimbegovic. Nonlinear Solid Mechanics:Theoretical Formulations and Finite Eeement Solution Methods, Springer Science & Business Media, vol. 160, 2009.
   Google Scholar
• J. Korelc, 2021. Acegen, acefem, acegen - manual, and acefem - manual. http://symech.fgg.uni-lj.si/.
   Google Scholar
• Wolfram Research, Inc. Mathematica, version 12.3.1, Champaign, IL, 2021. https://www.wolfram.com/mathematica.
   Google Scholar
• J. Korelc, Automation of primal and sensitivity analysis of transient coupled problems, Comput. Mech., vol. 44, no. 5, pp. 631–649, 2009. DOI: 10.1007/s00466-009-0395-2.
   Web of Science ®Google Scholar
• J. Korelc, and P. Wriggers, Automation of Finite Element Methods, Springer, Cham, 2016..
   Google Scholar
• J. N. Reddy, Nonlinear Finite Element Analysis, Oxford University Press, New York, 2004.
   Google Scholar
• A. Kopaničáková, and R. Krause, A recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture, Comput. Methods Appl. Mech. Eng., vol. 360, no. 112720, pp. 112720, 2020. DOI: 10.1016/j.cma.2019.112720.
   Google Scholar
• K. Pham, K. Ravi-Chandar, and C. Landis, Experimental validation of a phase-field model for fracture, Int. J. Fract., vol. 205, no. 1, pp. 83–101, 2017. DOI: 10.1007/s10704-017-0185-3.
   Web of Science ®Google Scholar
• J. Schmidt, A. Zemanová, J. Zeman, and M. Šejnoha, Phase-field fracture modelling of thin monolithic and laminated glass plates under quasi-static bending, Materials, vol. 13, no. 22, pp. 5153, 2020. DOI: 10.3390/ma13225153.
   PubMed Web of Science ®Google Scholar
• X. Zhang, C. Vignes, S. W. Sloan, and D. Sheng, Numerical evaluation of the phase-field model for brittle fracture with emphasis on the length scale, Comput. Mech., vol. 59, no. 5, pp. 737–752, 2017. DOI: 10.1007/s00466-017-1373-8.
   Web of Science ®Google Scholar
• F. Freddi, Fracture energy in phase field models, Mech. Res. Commun., vol. 96, pp. 29–36, 2019. DOI: 10.1016/j.mechrescom.2019.01.009.
   Web of Science ®Google Scholar
• M. Lavrenčič, and B. Brank, Hybrid-mixed shell quadrilateral that allows for large solution steps and is low-sensitive to mesh distortion, Comput. Mech., vol. 65, no. 1, pp. 177–192, 2020. DOI: 10.1007/s00466-019-01759-3.
   Web of Science ®Google Scholar
• A. Stanić, B. Brank, and J. Korelc, On path-following methods for structural failure problems, Comput. Mech., vol. 58, no. 2, pp. 281–306, 2016. DOI: 10.1007/s00466-016-1294-y.
   Web of Science ®Google Scholar
• P. Jäger, P. Steinmann, and E. Kuhl, Modeling three-dimensional crack propagation – A comparison of crack path tracking strategies, Int. J. Numer. Meth. Eng., vol. 76, no. 9, pp. 1328–1352, 2008. DOI: 10.1002/nme.2353.
   Web of Science ®Google Scholar
• H. G. Matthies, T. Gerasimov, U. Römer, A. Stanić, J. Vondřejc, and L. D. Lorenzis, 2021. Expressing behavioural non-uniqueness by stochastic solutions. In A. Ibrahimbegovic and M. Nikolić editors, ECCOMAS 2021 5th International Conference on Multi-Scale Computational Methods for Solids and Fluids, pp. 19–21
   Google Scholar
• T. Gerasimov, U. Römer, J. Vondřejc, H. G. Matthies, and L. De Lorenzis, Stochastic phase-field modeling of brittle fracture: computing multiple crack patterns and their probabilities, Comput. Methods Appl. Mech. Eng., vol. 372, pp. 113353, 2020. DOI: 10.1016/j.cma.2020.113353.
   Web of Science ®Google Scholar