Error estimation and adaptivity in flow formulation for forming problems

TLDR

A simple and reliable error estimator has recently been developed for linear elasticity problems. This study extends that estimator to incompressible plastic flow of metals or polymers using a flow‑formulation approach. The method predicts required h‑mesh refinement for a given accuracy, employs a suitable mesh generator for efficient adaptivity, and is tested on steady‑state extrusion and more complex upsetting problems. The estimator performs well across various scenarios, yielding an economical adaptive process.

Abstract

Abstract A very simple and reliable error estimator has recently been developed for problems of linear elasticity. 1 This leads naturally toa predication of an h ‐mesh refinement required for a given accuracy and with a suitable mesh generator 2 for an efficient adaptive process. In this paper we extend the methodology developed previously to incompresible plastic flow of metals or polymers using the ‘flow formulation’ approach. 3 The examples of application include steady state extrusion problems for which exact solutions are available and hence allow the efficiency of the error estimates to be tested as well as more complex problems of upsetting in which the mesh is updated. It is found that the estimator performs well under various circumstances and provides an economical adaptive process.