A block-coupled Finite Volume methodology for problems of large strain and large displacement

TL;DR

This paper introduces a nonlinear block-coupled Finite Volume method tailored for large strain and displacement problems, enabling more accurate and efficient simulations by extending existing linear elasticity frameworks.

Contribution

The paper presents a novel nonlinear block-coupled Finite Volume methodology that can be easily adapted from linear elasticity to finite strains, improving accuracy and convergence.

Findings

Significantly reduced errors compared to segregated procedures

Higher convergence rates demonstrated in 2-D benchmark cases

Method applicable to large displacement and large strain regimes

Abstract

A nonlinear block-coupled Finite Volume methodology is developed for large displacement and large strain regime. The new methodology uses the same normal and tangential face derivative discretisations found in the original fully coupled cell-centred Finite Volume solution methodology for linear elasticity, meaning that existing block-coupled implementations may easily be extended to include finite strains. Details are given of the novel approach, including use of the Newton-Raphson procedure on a residual functional defined using the linear momentum equation. A number of 2-D benchmark cases have shown that, compared with a segregated procedure, the new approach exhibits errors with many orders of magnitude smaller and a much higher convergence rate.