Modified midpoint integration rule for the trilinear element in large deformation elasticity

TL;DR

This paper introduces two modified one-point Gauss integration rules for trilinear elements in large deformation elasticity, improving stability and accuracy, especially on distorted elements and near incompressible conditions.

Contribution

The paper proposes novel modified integration rules that stabilize hourglass modes and enhance accuracy for distorted elements in large deformation elasticity simulations.

Findings

Modified rules stabilize hourglass modes.

Enhanced accuracy on severely distorted elements.

Effective handling of near incompressible situations.

Abstract

In this paper we suggest two modified one-point Gauss integration rules for the Q1 bi- or trilinear element. The modifications both stabilize the hourglass modes of the one-point rule, and one of them is accurate also on severely distorted elements. We investigate the performance of the integration rules for the hexahedron element, and combine standard one-point integration of the volumetric terms with the modified rules for the isochoric terms to handle near incompressible situations.