Phase-field simulation of ductile fracture in shell structures

Abstract In this paper, a computational framework for simulating ductile fracture in multipatch shell structures is presented. A ductile fracture phase-field model at finite strains is combined with an isogeometric Kirchhoff–Love shell formulation. For the application to complex structures, we employ a penalty approach for imposing, at patch interfaces, displacement and rotational continuity and C 0 and C 1 continuity of the phase-field, the latter required if a higher-order phase-field formulation is adopted. We study the mesh dependency of the numerical model and we show that mesh refinement allows for capturing important features of ductile fracture such as cracking along shear bands. Therefore, we investigate the effectiveness of a predictor–corrector algorithm for adaptive mesh refinement based on LR NURBS. Thanks to the adoption of time- and space-adaptivity strategies, it is possible to simulate the failure of complex structures with a reasonable computational effort. Finally, we compare the predictions of the numerical model with experimental results.

[1]  J. F. Caseiro,et al.  On the Assumed Natural Strain method to alleviate locking in solid-shell NURBS-based finite elements , 2014 .

[2]  P. Wriggers,et al.  Isogeometric large deformation frictionless contact using T-splines , 2014 .

[3]  C. Miehe,et al.  Phase-field modelling of ductile fracture: a variational gradient-extended plasticity-damage theory and its micromorphic regularization , 2016, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[4]  Stefano Vidoli,et al.  Comparison of Phase-Field Models of Fracture Coupled with Plasticity , 2018 .

[5]  Marco Paggi,et al.  Phase field modeling of brittle fracture for enhanced assumed strain shells at large deformations: formulation and finite element implementation , 2017, Computational Mechanics.

[6]  H.-J. Christ,et al.  Numerical simulations of crack propagation in screws with phase-field modeling , 2015 .

[7]  Luigi Ambrosio,et al.  ON THE APPROXIMATION OF FREE DISCONTINUITY PROBLEMS , 1992 .

[8]  L. De Lorenzis,et al.  Phase-field simulation of interactive mixed-mode fracture tests on cement mortar with full-field displacement boundary conditions , 2017 .

[9]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multipli , 1988 .

[10]  Roland Wüchner,et al.  Isogeometric shell analysis with Kirchhoff–Love elements , 2009 .

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

[12]  Gianni Royer-Carfagni,et al.  Regularized variational theories of fracture: A unified approach , 2010 .

[13]  Xiaosheng Gao,et al.  Development of a phase field method for modeling brittle and ductile fracture , 2019, Computational Materials Science.

[14]  J. Marigo,et al.  Gradient Damage Models Coupled with Plasticity and Nucleation of Cohesive Cracks , 2014, Archive for Rational Mechanics and Analysis.

[15]  Les A. Piegl,et al.  The NURBS Book , 1995, Monographs in Visual Communication.

[16]  Alessandro Reali,et al.  Phase-field description of brittle fracture in plates and shells , 2016 .

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

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

[19]  Jean-Jacques Marigo,et al.  Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments , 2009 .

[20]  J. Marigo,et al.  Gradient damage models coupled with plasticity: Variational formulation and main properties , 2015 .

[21]  Thomas J. R. Hughes,et al.  A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects , 2016 .

[22]  Cristóbal Samaniego,et al.  A variational approach to the phase field modeling of brittle and ductile fracture , 2018, International Journal of Mechanical Sciences.

[23]  Ted Belytschko,et al.  Analysis of fracture in thin shells by overlapping paired elements , 2006 .

[24]  Odd Sture Hopperstad,et al.  On the resistance to penetration of stiffened plates, Part II: Numerical analysis , 2009 .

[25]  R. Müller,et al.  On phase field modeling of ductile fracture , 2016 .

[26]  Peter Wriggers,et al.  Computational Contact Mechanics with the Finite Element Method , 2017 .

[27]  L. Lorenzis,et al.  Phase-field modeling of brittle and ductile fracture in shells with isogeometric NURBS-based solid-shell elements , 2016 .

[28]  A. Atkins,et al.  Out-of-plane stretching and tearing fracture in ductile sheet materials , 1997 .

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

[30]  Ralf Müller,et al.  On degradation functions in phase field fracture models , 2015 .

[31]  Trond Kvamsdal,et al.  Isogeometric analysis using LR B-splines , 2014 .

[32]  Jacques Besson,et al.  Continuum Models of Ductile Fracture: A Review , 2010 .

[33]  Michael C. H. Wu,et al.  Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials , 2015 .

[34]  J. Marigo,et al.  Gradient Damage Models and Their Use to Approximate Brittle Fracture , 2011 .

[35]  Roger A. Sauer,et al.  Adaptive local surface refinement based on LR NURBS and its application to contact , 2017, ArXiv.

[36]  Jean-Jacques Marigo,et al.  Crack nucleation in variational phase-field models of brittle fracture , 2018 .

[37]  Michael Kaliske,et al.  A phase-field crack model based on directional stress decomposition , 2018, Computational Mechanics.

[38]  Michael M. Khonsari,et al.  Validation simulations for the variational approach to fracture , 2015 .

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

[40]  Josef Kiendl,et al.  A framework for efficient isogeometric computations of phase-field brittle fracture in multipatch shell structures , 2020 .

[41]  Jørgen Amdahl,et al.  On the resistance to penetration of stiffened plates, Part I – Experiments , 2009 .

[42]  Thomas J. R. Hughes,et al.  A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework , 2014 .

[43]  K. Ravi-Chandar,et al.  Experimental validation of a phase-field model for fracture , 2017, International Journal of Fracture.

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

[45]  Roger A. Sauer,et al.  An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS , 2019, Computational Mechanics.

[46]  Peter Wriggers,et al.  Variational phase-field formulation of non-linear ductile fracture , 2018, Computer Methods in Applied Mechanics and Engineering.

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

[48]  Ming-Chen Hsu,et al.  Penalty coupling of non-matching isogeometric Kirchhoff–Love shell patches with application to composite wind turbine blades , 2019, Computer Methods in Applied Mechanics and Engineering.

[49]  Christian Miehe,et al.  Phase Field Modeling of Fracture in Plates and Shells , 2012 .

[50]  I. Ashcroft,et al.  Phase-field modelling of brittle fracture in thin shell elements based on the MITC4+ approach , 2020, Computational Mechanics.

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

[52]  Christian Miehe,et al.  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 , 2015 .

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

[54]  Michael Kaliske,et al.  A ductile phase-field model based on degrading the fracture toughness: Theory and implementation at small strain , 2020 .

[55]  Josef Kiendl,et al.  Isogeometric Kirchhoff–Love shell formulation for elasto-plasticity , 2018, Computer Methods in Applied Mechanics and Engineering.

[56]  A. A. Griffith.  The Phenomena of Rupture and Flow in Solids , 1921 .

[57]  S. Klinkel,et al.  Phase-field model of brittle fracture in Reissner–Mindlin plates and shells , 2021 .

[58]  Pablo J. Sánchez,et al.  A phase-field/gradient damage model for brittle fracture in elastic–plastic solids , 2015 .

[59]  R. Sauer,et al.  Isogeometric continuity constraints for multi-patch shells governed by fourth-order deformation and phase field models , 2020, Computer Methods in Applied Mechanics and Engineering.