Exact closed‐form solution of the return mapping algorithm in plane stress elasto‐viscoplasticity

Abstract

In Simo and Taylor, the classical radial return algorithm of Wilkins and Krieg and Key for plane strain and three‐dimensional J2‐flow theory, is extended to the case of plane stress. In three dimensions (or plane strain), enforcement of the discrete consistency condition reduces to a simple radial scaling of the trial stress onto the yield surface; i.e., the return map is radial. In plane stress, on the other hand, the return map, that restores the trial stress back to the yield surface, is constrained to remain in the plane stress subspace, and thus no longer reduces to a simple radial scaling. The determination of the final stress point from the trial stress now involves the solution by Newton's method of a non‐linear scalar equation, referred to as the discrete consistency equation in what follows, that yields the discrete consistency parameter λn+>0. The requirement that λn+>1 be positive is a direct consequence of the discrete Kuhn‐Tucker optimality conditions.

Citation

Simo, J.C. and Govindjee, S. (1988), "Exact closed‐form solution of the return mapping algorithm in plane stress elasto‐viscoplasticity", Engineering Computations, Vol. 5 No. 3, pp. 254-258. https://doi.org/10.1108/eb023744