Abaqus implementation of monolithic and staggered schemes for quasi-static and dynamic fracture phase-field model

Abstract The phase-field model for fractures regularizes crack diffusion using a length-scale parameter. The displacement fields and the phase-field in a coupled system can be solved as either fully coupled “monolithic” or sequentially coupled “staggered” fields. In this paper, we employ the commercial finite-element software Abaqus to solve the monolithic and staggered phase-field models using a user-defined element (UEL) and user-defined material (UMAT/VUMAT) subroutines in two- and three-dimensions for quasi-static and dynamic fractures. We present the implementation procedures for both strategies, and make a detailed comparison using different applications. By comparing the phase-field model as a diffusive crack model and the extended finite-element method (XFEM) as a discrete crack model, we obtain good agreement. We investigate the influence of the model-regularization parameter based on experimental results. We adopt the thread-parallel execution and mutexes of Abaqus solvers.

[1]  Christian Miehe,et al.  Algorithms for computation of stresses and elasticity moduli in terms of Seth–Hill's family of generalized strain tensors , 2001 .

[2]  Timon Rabczuk,et al.  Abaqus implementation of phase-field model for brittle fracture , 2015 .

[3]  Cv Clemens Verhoosel,et al.  A phase‐field model for cohesive fracture , 2013 .

[4]  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 .

[5]  Ted Belytschko,et al.  A three-dimensional impact-penetration algorithm with erosion , 1987 .

[6]  Hung Nguyen-Xuan,et al.  A Phantom-Node Method with Edge-Based Strain Smoothing for Linear Elastic Fracture Mechanics , 2013, J. Appl. Math..

[7]  Jacob Fish,et al.  The rs‐method for material failure simulations , 2008 .

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

[9]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[10]  Y. R. Rashid,et al.  Ultimate strength analysis of prestressed concrete pressure vessels , 1968 .

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

[12]  A. Karma,et al.  Phase-field model of mode III dynamic fracture. , 2001, Physical review letters.

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

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

[15]  Herbert Levine,et al.  Dynamic instabilities of fracture under biaxial strain using a phase field model. , 2004, Physical review letters.

[16]  B. Bourdin.  Numerical implementation of the variational formulation for quasi-static brittle fracture , 2007 .

[17]  Francisco Armero,et al.  Finite elements with embedded branching , 2009 .

[18]  C. Miehe,et al.  Phase Field Modeling of Brittle and Ductile Fracture , 2013 .

[19]  Ralf Müller,et al.  A continuum phase field model for fracture , 2010 .

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

[21]  Adrian Willenbücher,et al.  Phase field approximation of dynamic brittle fracture , 2014 .

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

[23]  G. R. Johnson,et al.  Eroding interface and improved tetrahedral element algorithms for high-velocity impact computations in three dimensions , 1987 .

[24]  Joško Ožbolt,et al.  Dynamic fracture of concrete compact tension specimen: Experimental and numerical study , 2013 .

[25]  Stéphane Bordas,et al.  On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM) , 2011 .

[26]  Guirong Liu,et al.  Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth , 2012 .

[27]  Xiaopeng Xu,et al.  Numerical simulations of fast crack growth in brittle solids , 1994 .

[28]  M. Ortiz,et al.  Computational modelling of impact damage in brittle materials , 1996 .

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

[30]  Christian Hesch,et al.  Thermodynamically consistent algorithms for a finite‐deformation phase‐field approach to fracture , 2014 .

[31]  Ted Belytschko,et al.  Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions , 2010 .

[32]  Joško Ožbolt,et al.  Dynamic fracture of concrete – compact tension specimen , 2011 .

[33]  Christian Miehe,et al.  A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns , 2013 .

[34]  Luigi Cedolin,et al.  Finite element modeling of crack band propagation , 1983 .

[35]  Eugenio Giner,et al.  An Abaqus implementation of the extended finite element method , 2009 .

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

[37]  T. Belytschko,et al.  A comparative study on finite element methods for dynamic fracture , 2008 .

[38]  Ted Belytschko,et al.  Dynamic fracture with meshfree enriched XFEM , 2010 .

[39]  Ted Belytschko,et al.  A regularized phenomenological multiscale damage model , 2014 .

[40]  I. Babuska,et al.  GENERALIZED FINITE ELEMENT METHODS — MAIN IDEAS, RESULTS AND PERSPECTIVE , 2004 .

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