A simple robust numerical integration algorithm for a power-law visco-plastic model under both high and low rate-sensitivity

This note describes a simple and extremely robust algorithm for numerical integration of the power-law-type elasto-viscoplastic constitutive model discussed by Peric (Int. J. Num. Meth. Eng. 1993; 36: 1365–1393). As the rate-independent limit is approached with increasing exponents, the evolution equations of power-law-type models are known to become stiff. Under such conditions, the solution of the implicitly discretized viscoplastic evolution equation cannot be easily obtained by standard root-finding algorithms. Here, a procedure which proves to be remarkably robust under stiff conditions is obtained by means of a simple logarithmic mapping of the basic backward Euler time-discrete equation for the incremental plastic multiplier. The logarithm-transformed equation is solved by the standard Newton–Raphson scheme combined with a simple bisection procedure which ensures that the iterative guesses for the equation unknown (the incremental equivalent plastic strain) remain within the domain where the transformed equation makes sense. The resulting implementation can handle small and large (up to order 106) power-law exponents equally. This allows its effective use under any situation of practical interest, ranging from high rate-sensitivity to virtually rate-independent conditions. The robustness of the proposed scheme is demonstrated by numerical examples. Copyright © 2003 John Wiley & Sons, Ltd.

[1]  J. C. Simo,et al.  A CLASS OF MIXED ASSUMED STRAIN METHODS AND THE METHOD OF INCOMPATIBLE MODES , 1990 .

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

[3]  E. A. de Souza Neto,et al.  A model for elastoplastic damage at finite strains: algorithmic issues and applications , 1994 .

[4]  J. C. Rice,et al.  On numerically accurate finite element solutions in the fully plastic range , 1990 .

[5]  E. A. de Souza Neto,et al.  A new computational model for Tresca plasticity at finite strains with an optimal parametrization in the principal space , 1999 .

[6]  J. C. Simo,et al.  Geometrically non‐linear enhanced strain mixed methods and the method of incompatible modes , 1992 .

[7]  A. Needleman,et al.  A tangent modulus method for rate dependent solids , 1984 .

[8]  Peter M. Pinsky,et al.  Operator split methods for the numerical solution of the elastoplastic dynamic problem , 1983 .

[9]  J. C. Simo,et al.  A return mapping algorithm for plane stress elastoplasticity , 1986 .

[10]  Michael Ortiz,et al.  An analysis of a new class of integration algorithms for elastoplastic constitutive relations , 1986 .

[11]  D. Owen,et al.  Design of simple low order finite elements for large strain analysis of nearly incompressible solids , 1996 .

[12]  R. D. Krieg,et al.  Accuracies of Numerical Solution Methods for the Elastic-Perfectly Plastic Model , 1977 .

[13]  M. Ortiz,et al.  A material‐independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics , 1992 .

[14]  J. C. Simo,et al.  Non‐smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms , 1988 .

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

[16]  Djordje Peric,et al.  On a class of constitutive equations in viscoplasticity : formulation and computational issues , 1993 .

[17]  Sanjay Govindjee,et al.  Non‐linear B‐stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity , 1991 .