A new uniformly valid asymptotic integration algorithm for elasto‐plastic creep and unified viscoplastic theories including continuum damage

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Abstract
A new scheme to integrate a system of stiff differential equations for both the elasto‐plastic‐creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code, through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self‐adaptive forward Euler method are made.