Modified midpoint integration rule for the trilinear element in large deformation elasticity
This work addresses the need for accurate and stable low-order finite elements in large deformation elasticity, particularly for hexahedral elements prone to hourglassing and distortion issues.
The paper proposes two modified one-point Gauss integration rules for the Q1 trilinear element that stabilize hourglass modes and improve accuracy on distorted elements, with one rule performing well even under severe distortion. The methods are combined with standard one-point integration for volumetric terms to handle near-incompressibility in large deformation elasticity.
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.