Performance of a vertex-centred block-coupled finite volume methodology for small-strain static elastoplasticity

This article assesses the performance of a vertex-centred block-coupled finite volume methodology for static small-strain elastoplasticity based on a Newton-Raphson algorithm. The proposed coupled solution algorithm is compared with vertex-centred and cell-centred segregated solution procedures in terms of accuracy, efficiency and robustness for quasi-static problems. This coupled methodology is then verified on four test cases: a patch test to check its ability to reproduce first-order polynomials; the method of manufactured solutions to check the order of convergence of displacement and stress; a 2-D perforated plate and a 3-D narrow T-member under elastoplastic conditions to examine the accuracy of the solutions on non-trivial test cases. The proposed methodology demonstrates high accuracy and a computational efficiency of up to 28× speedups over the standard cell-centred segregated approach.