Numerical analysis of hyper-elasto-plastic solid shells via VDQ method

Abstract

This article presents an efficient numerical framework for solving problems in hyper-elasto-plasticity under finite deformations. The main novelty of the current study lies in the first-time extension of the Variational Differential Quadrature (VDQ) method to finite-strain elasto-plasticity, addressing challenges such as large nonlinear deformations, path-dependent material behavior, and post-critical instability. The general tensorial equations of 3D hyper-elasto-plasticity are first derived and then reformulated into compact vector-matrix forms suitable for computational purposes. The proposed grid-based VDQ method is locking-free, simple to implement, and shows fast convergence. To evaluate the accuracy and efficiency of the method, several benchmark problems involving solid-shell structures with complex geometries are analyzed. The results demonstrate the capability of the proposed approach to reliably capture large deformation responses in elasto-plastic solids, offering a robust alternative to conventional finite element methods. © 2025