Integration along the path of loading in elastic‐plastic problems

Abstract

This paper considers the classical problem of the deformation of an elastic‐plastic body subjected to a prescribed history of loading. Attention is focused on the basis for the time discretization of the problem for numerical solution. It is suggested that this discretization can be achieved consistently by conceiving of the problem as a sequence of holonomic, or non‐linear elastic, problems. Complementary work bounds can be given, in special circumstances, for increasing numbers of time steps. The holonomic problem for a single time step is a non‐linear mathematical programming problem: it is shown that the conventional Newton‐Raphson algorithm used in elastic‐plastic finite element analysis can be interpreted as an iterative procedure for finding the least value of the holonomic potential work functional.

Citation

Martin, J.B. and Bird, W.W. (1988), "Integration along the path of loading in elastic‐plastic problems", Engineering Computations, Vol. 5 No. 3, pp. 217-223. https://doi.org/10.1108/eb023739