A generalized approach to formulate the consistent tangent stiffness in plasticity with application to the GLD porous material model

Abstract It has been shown that the use of the consistent tangent moduli is crucial for preserving the quadratic convergence rate of the global Newton iterations in the solution of the incremental problem. In this paper, we present a general method to formulate the consistent tangent stiffness for plasticity. The robustness and efficiency of the proposed approach are examined by applying it to the isotropic material with J2 flow plasticity and comparing the performance and the analysis results with the original implementation in the commercial finite element program ABAQUS. The proposed approach is then applied to an anisotropic porous plasticity model, the Gologanu–Leblond–Devaux model. Performance comparison between the consistent tangent stiffness and the conventional continuum tangent stiffness demonstrates significant improvement in convergence characteristics of the overall Newton iterations caused by using the consistent tangent matrix.

[1]  Thomas Pardoen,et al.  An extended model for void growth and coalescence - application to anisotropic ductile fracture , 2000 .

[2]  Thomas Pardoen,et al.  Micromechanics-based model for trends in toughness of ductile metals , 2003 .

[3]  V. Tvergaard.  On localization in ductile materials containing spherical voids , 1982, International Journal of Fracture.

[4]  Pierre Suquet,et al.  Continuum Micromechanics , 1997, Encyclopedia of Continuum Mechanics.

[5]  John W. Hutchinson,et al.  A computational approach to ductile crack growth under large scale yielding conditions , 1995 .

[6]  N. Aravas.  On the numerical integration of a class of pressure-dependent plasticity models , 1987 .

[7]  Claudio Ruggieri,et al.  Numerical modeling of ductile crack growth in 3-D using computational cell elements , 1996 .

[8]  E. P. Popov,et al.  Accuracy and stability of integration algorithms for elastoplastic constitutive relations , 1985 .

[9]  J. H. Lee,et al.  On the numerical integration of a class of pressure‐dependent plasticity models with mixed hardening , 1991 .

[10]  Jean-Baptiste Leblond,et al.  Approximate models for ductile metals containing non-spherical voids—Case of axisymmetric prolate ellipsoidal cavities , 1993 .

[11]  W. Brocks,et al.  On the numerical integration of a class of pressure-dependent plasticity models including kinematic hardening , 2003 .

[12]  Viggo Tvergaard,et al.  An analysis of ductile rupture modes at a crack tip , 1987 .

[13]  Jean-Baptiste Leblond,et al.  Approximate Models for Ductile Metals Containing Nonspherical Voids—Case of Axisymmetric Oblate Ellipsoidal Cavities , 1994 .

[14]  Zhiliang Zhang,et al.  Explicit consistent tangent moduli with a return mapping algorithm for pressure-dependent elastoplasticity models , 1995 .

[15]  Jean-Baptiste Leblond,et al.  Recent extensions of Gurson's model for porous ductile metals , 1997 .

[16]  J. C. Simo,et al.  Consistent tangent operators for rate-independent elastoplasticity☆ , 1985 .

[17]  Xiaosheng Gao,et al.  Cell model for nonlinear fracture analysis – I. Micromechanics calibration , 1998 .

[18]  A. Gurson.  Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media , 1977 .

[19]  Xiaosheng Gao,et al.  Cell model for nonlinear fracture analysis – II. Fracture- process calibration and verification , 1998 .

[20]  Jean-Baptiste Leblond,et al.  Theoretical models for void coalescence in porous ductile solids. II. Coalescence “in columns” , 2001 .

[21]  Robert H. Dodds,et al.  Ductile tearing in part-through cracks: experiments and cell-model predictions , 1998 .