Comparison of a phase‐field model and of a thick level set model for brittle and quasi‐brittle fracture

Summary This paper provides a comparison between one particular phase-field damage model and a thick level set (TLS) damage model for the simulation of brittle and quasi-brittle fractures. The TLS model is recasted in a variational framework, which allows comparison with the phase-field model. Using this framework, both the equilibrium equations and the damage evolution laws are guided by the initial choice of the potential energy. The potentials of the phase-field model and of the TLS model are quite different. TLS potential enforces a priori a bound on damage gradient whereas the phase-field potential does not. The TLS damage model is defined such that the damage profile fits to the one of the phase-field model for a beam of infinite length. The model parameters are calibrated to obtain the same surface fracture energy. Numerical results are provided for unidimensional and bidimensional tests for both models. Qualitatively, similar results are observed, although TLS model is observed to be less sensible to boundary conditions. Copyright © 2015 John Wiley & Sons, Ltd.

[1]  Nicolas Triantafyllidis,et al.  A gradient approach to localization of deformation. I. Hyperelastic materials , 1986 .

[2]  Paul A. Wawrzynek,et al.  Quasi-automatic simulation of crack propagation for 2D LEFM problems , 1996 .

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

[4]  J. Mazars.  APPLICATION DE LA MECANIQUE DE L'ENDOMMAGEMENT AU COMPORTEMENT NON LINEAIRE ET A LA RUPTURE DU BETON DE STRUCTURE , 1984 .

[5]  Nicolas Moës,et al.  Damage growth modeling using the Thick Level Set (TLS) approach: Efficient discretization for quasi-static loadings , 2012 .

[6]  Milan Jirásek,et al.  Nonlocal integral formulations of plasticity and damage : Survey of progress , 2002 .

[7]  E. Riks.  The Application of Newton's Method to the Problem of Elastic Stability , 1972 .

[8]  F. Dufour,et al.  Stress-based nonlocal damage model , 2011 .

[9]  N. Chevaugeon,et al.  A level set based model for damage growth: The thick level set approach , 2011 .

[10]  René de Borst,et al.  Gradient-dependent plasticity: formulation and algorithmic aspects , 1992 .

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

[12]  Jean-Jacques Marigo,et al.  From Gradient Damage Laws to Griffith’s Theory of Crack Propagation , 2013 .

[13]  S. Andrieux,et al.  A variational formulation for nonlocal damage models , 1999 .

[14]  Cv Clemens Verhoosel,et al.  Phase-field models for brittle and cohesive fracture , 2014 .

[15]  Mgd Marc Geers,et al.  A critical comparison of nonlocal and gradient-enhanced softening continua , 2001 .

[16]  Claudia Comi,et al.  Computational modelling of gradient‐enhanced damage in quasi‐brittle materials , 1999 .

[17]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[18]  Gilles Pijaudier-Cabot,et al.  Boundary effect on weight function in nonlocal damage model , 2009 .

[19]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[20]  Gilles Pijaudier-Cabot,et al.  From damage to fracture mechanics and conversely: A combined approach , 1996 .

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

[22]  E. Aifantis.  On the Microstructural Origin of Certain Inelastic Models , 1984 .

[23]  Mgd Marc Geers,et al.  Strain-based transient-gradient damage model for failure analyses , 1998 .

[24]  Nicolas Moës,et al.  A new model of damage: a moving thick layer approach , 2012, International Journal of Fracture.

[25]  Marc G. D. Geers,et al.  An integrated continuous-discontinuous approach towards damage engineering in sheet metal forming processes , 2006 .

[26]  Rhj Ron Peerlings,et al.  Gradient enhanced damage for quasi-brittle materials , 1996 .

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

[28]  Jean-Jacques Marigo,et al.  The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models , 2011 .

[29]  Kyrylo Kazymyrenko,et al.  Convergence of a gradient damage model toward a cohesive zone model , 2011 .

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

[31]  L. J. Sluys,et al.  From continuous to discontinuous failure in a gradient-enhanced continuum damage model , 2003 .

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

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

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

[35]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .