Adaptive phase field method using novel physics based refinement criteria

Abstract Amongst the available methods to model fracture processes, the phase field approach has proved to be efficient and has received extensive attention. However, the approach is computationally demanding as it requires a very high resolution, both in space and time to resolve the fracture characteristics . In this paper, a novel adaptive phase field method is proposed for modelling quasi-static crack propagation in brittle materials . The adaptive refinement is based on the stability analysis which is combined with the quadtree decomposition. The stability analysis is based on a linear perturbation method that is used herein to determine the onset of fracture initiation on the fly. Three standard benchmark problems are solved to show the efficiency and the robustness of the proposed method. It is shown that the proposed framework does not require any post processing technique for adaptive refinement and yet is effective.

[1]  Hirshikesh,et al.  Adaptive phase field method for quasi-static brittle fracture using a recovery based error indicator and quadtree decomposition , 2019, Engineering Fracture Mechanics.

[2]  Haim Waisman,et al.  Fracture of viscoelastic solids modeled with a modified phase field method , 2019, Computer Methods in Applied Mechanics and Engineering.

[3]  Francesco Freddi,et al.  Phase-field modelling of failure in hybrid laminates , 2017 .

[4]  B. K. Mishra,et al.  A local moving extended phase field method (LMXPFM) for failure analysis of brittle materials , 2018, Computer Methods in Applied Mechanics and Engineering.

[5]  H. Waisman,et al.  Onset of shear band localization by a local generalized eigenvalue analysis , 2015 .

[6]  Marco Paggi,et al.  Strength prediction of notched thin ply laminates using finite fracture mechanics and the phase field approach , 2017 .

[7]  Laura De Lorenzis,et al.  A review on phase-field models of brittle fracture and a new fast hybrid formulation , 2015 .

[8]  H. Waisman,et al.  Thermal-conductivity degradation across cracks in coupled thermo-mechanical systems modeled by the phase-field fracture method , 2020 .

[9]  Haim Waisman,et al.  A coupled phase field shear band model for ductile–brittle transition in notched plate impacts , 2016 .

[10]  Thomas Wick,et al.  Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation , 2017 .

[11]  M. Floater.  Mean value coordinates , 2003, Computer Aided Geometric Design.

[12]  Ratna Kumar Annabattula,et al.  Modeling crack propagation in variable stiffness composite laminates using the phase field method , 2019, Composite Structures.

[13]  B. Bourdin,et al.  Numerical experiments in revisited brittle fracture , 2000 .

[14]  Rolf Mahnken,et al.  Goal‐oriented adaptive refinement for phase field modeling with finite elements , 2013 .

[15]  Indra Vir Singh,et al.  An adaptive multiscale phase field method for brittle fracture , 2018 .

[16]  Cv Clemens Verhoosel,et al.  A phase-field description of dynamic brittle fracture , 2012 .

[17]  Xiaoying Zhuang,et al.  Adaptive phase field simulation of quasi-static crack propagation in rocks , 2018, Underground Space.

[18]  Yi-long Bai.  Thermo-plastic instability in simple shear , 1982 .

[19]  Tymofiy Gerasimov,et al.  A line search assisted monolithic approach for phase-field computing of brittle fracture , 2016 .

[20]  Emilio Mart'inez-Paneda,et al.  Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme , 2019, Theoretical and Applied Fracture Mechanics.

[21]  Mary F. Wheeler,et al.  A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach , 2015 .

[22]  Gilles A. Francfort,et al.  Revisiting brittle fracture as an energy minimization problem , 1998 .

[23]  Marco Paggi,et al.  Modeling complex crack paths in ceramic laminates: A novel variational framework combining the phase field method of fracture and the cohesive zone model , 2018 .

[24]  Emilio Mart'inez-Paneda,et al.  A phase field formulation for hydrogen assisted cracking , 2018, Computer Methods in Applied Mechanics and Engineering.

[25]  Timon Rabczuk,et al.  Fracture properties prediction of clay/epoxy nanocomposites with interphase zones using a phase field model , 2017 .

[26]  Fucheng Tian,et al.  A hybrid adaptive finite element phase‐field method for quasi‐static and dynamic brittle fracture , 2019, International Journal for Numerical Methods in Engineering.

[27]  H. Waisman,et al.  Stability analysis of the phase-field method for fracture with a general degradation function and plasticity induced crack generation , 2018 .

[28]  Chongmin Song,et al.  Adaptive phase-field modeling of brittle fracture using the scaled boundary finite element method , 2019, Computer Methods in Applied Mechanics and Engineering.

[29]  Ratna Kumar Annabattula,et al.  A FEniCS implementation of the phase field method for quasi-static brittle fracture , 2018, Frontiers of Structural and Civil Engineering.

[30]  Timon Rabczuk,et al.  An h-adaptive thermo-mechanical phase field model for fracture , 2018 .

[31]  A. Raina,et al.  Phase field modeling of ductile fracture at finite strains: A variational gradient-extended plasticity-damage theory , 2016 .

[32]  Thomas Wick,et al.  Mesh adaptivity for quasi‐static phase‐field fractures based on a residual‐type a posteriori error estimator , 2019, GAMM-Mitteilungen.

[33]  Jonathan B. Russ,et al.  Rupture of 3D-printed hyperelastic composites: Experiments and phase field fracture modeling , 2020 .

[34]  L. Lorenzis,et al.  Phase-field modeling of ductile fracture , 2015, Computational Mechanics.

[35]  Ralf Müller,et al.  Phase field simulation of thermomechanical fracture , 2009 .

[36]  Julien Yvonnet,et al.  A phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography , 2016 .

[37]  A. M. Lyapunov.  The general problem of the stability of motion , 1992 .

[38]  Christian Miehe,et al.  A phase-field model for fracture in biological tissues , 2016, Biomechanics and modeling in mechanobiology.

[39]  M. Kaliske,et al.  Fracture simulation of viscoelastic polymers by the phase-field method , 2020, Computational Mechanics.

[40]  T. Rabczuk,et al.  Phase-field modeling of fracture in linear thin shells , 2014 .

[41]  Christian Miehe,et al.  Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations , 2010 .

[42]  L. Anand,et al.  Onset of shear localization in viscoplastic solids , 1987 .

[43]  Laura De Lorenzis,et al.  A phase-field model for ductile fracture at finite strains and its experimental verification , 2016 .

[44]  Patrick E. Farrell,et al.  Linear and nonlinear solvers for variational phase‐field models of brittle fracture , 2015, 1511.08463.

[45]  H. Waisman,et al.  A unified model for metal failure capturing shear banding and fracture , 2015 .

[46]  Christian Miehe,et al.  A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits , 2010 .

[47]  Timon Rabczuk,et al.  Phase-field analysis of finite-strain plates and shells including element subdivision , 2016 .

[48]  Zhanli Liu,et al.  Study the dynamic crack path in brittle material under thermal shock loading by phase field modeling , 2017, International Journal of Fracture.

[49]  Ernst Rank,et al.  Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method , 2018, Computational Mechanics.

[50]  Haim Waisman,et al.  Multidimensional stability analysis of the phase-field method for fracture with a general degradation function and energy split. , 2018 .