COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Commun. Numer. Meth. Engng 2004; 20:1–17 (DOI: 10.1002/cnm.648) A simple robust numerical integration algorithm for a power-law visco-plastic model under both high and low rate-sensitivity E. A. de Souza Neto ∗; † Civil and Computational Engineering Centre; University of Wales Swansea; U.K. SUMMARY This note describes a simple and extremely robust algorithm for numerical integration of the power- law-type elasto-viscoplastic constitutive model discussed by Peri c(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 sti. Under such conditions, the solution of the implicitly discretized viscoplastic evolution equation cannot be easily obtained by standard root- nding algorithms. Here, a procedure which proves to be remarkably robust under sti 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 10 6 ) power-law exponents equally. This allows its eective 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. KEY WORDS: viscoplasticity; power law; return mapping 1. INTRODUCTION Over the last three decades, the numerical treatment of elasto-plasticity and elasto-visco- plasticity in the context of nite element simulations has been thoroughly investigated by a large number of authors [1–6]. As a result, a wide range of sophisticated material models based on both elasto-plasticity and elasto-viscoplasticity is currently available in standard com- mercial nite-element codes. Some of these material models are capable of representing rather ∗ Correspondence to: E. A. de Souza Neto, Department of Civil Engineering, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K. † E-mail: cgneto@swansea.ac.uk; e.desouzaneto@swansea.ac.uk Received 22 May 2002 Copyright ? 2003 John Wiley & Sons, Ltd. Accepted 24 March 2003