Extension of the unsymmetric 8‐node hexahedral solid element US‐ATFH8 to 3D hyper‐elastic finite deformation analysis

Abstract

This work extends the recent US-ATFH8 element to 3D hyper-elastic finite deformation analysis. Using two sets of shape functions, the new 3D element comprises of 8 nodes and 24 DOFs. The first set of shape functions represent the test functions that come from the conventional isoparametric interpolation, and the second set, representing the trial functions, are constructed from the homogenous solutions for linear elasticity governing equations, termed analytical trial functions (ATFs). This study considers finite deformation for hyper-elastic materials, but it is assumed that the analytical solutions associated with hyper-elastic materials can be updated to hold approximately in each incremental step. Moreover, the deformation information required for stress computation is updated by using the incremental deformation gradient, which is constructed from the updated ATFs. Numerical examples show that without additional pressure DOF, the element US-ATFH8 still behaves well in nearly incompressible hyper-elastic 3D problems with finite deformation, even when the meshes are extremely distorted.

Penalty hexahedral element formulation for flexoelectric solids based on consistent couple stress theory

“…The new element can be viewed as the extension and modification of the element model 36 developed for the CCST which is formulated within the framework of the penalty unsymmetric FEM. The unsymmetric FEM is essentially characteristic of independently or partially independently designing the element's test function and trial function 37–40 . In the present development, the C 1 requirement is satisfied in a weak sense by introducing an independent rotation field into the virtual work principle and using the penalty function method.…”

“…The unsymmetric FEM is essentially characteristic of independently or partially independently designing the element's test function and trial function. [37][38][39][40] In the present development, the C 1 requirement is satisfied in a weak sense by introducing an independent rotation field into the virtual work principle and using the penalty function method. Then, the element's test functions of the displacement, mechanical rotation and electric potential are formulated using the quadratic serendipity isoparametric interpolation function, from which the strain, curvature and electric field can be further derived.…”

An ANS/ATFs‐based unsymmetric solid‐shell finite element algorithm for high‐quality finite deformation analysis of hyper‐elastic shell

“…For material nonlinear analysis, the hyper-elastic formulations for elements US-ATFQ4 and US-ATFH8 were further developed based on the general UL approach. 42,43 These nonlinear unsymmetric formulations 39,40,42,43 still exhibit excellent performance and avoid the above locking problems.…”

Two 8‐node quadrilateral unsymmetric elements with different incompatible modes immune to severe distortion

“…Cen et al 31 proposed the unsymmetric 8‐node plane element US‐ATFQ8 by introducing an analytical trail function based on the basic Airy stress solutions. Later, Cen et al 32 produced a low‐order quadrilateral unsymmetric element named US‐ATFQ4, and then promoted it to a series of elements 33‐36 . Xie et al 30 developed unsymmetric 4‐node quadrilateral and 8‐node hexahedral elements with a skew coordinate by introducing the Trefftz stress solution to accomplish the trial function.…”

“…Later, Cen et al 32 produced a low-order quadrilateral unsymmetric element named US-ATFQ4, and then promoted it to a series of elements. [33][34][35][36] Xie et al 30 developed unsymmetric 4-node quadrilateral and 8-node hexahedral elements with a skew coordinate by introducing the Trefftz stress solution to accomplish the trial function.…”