High-performance unsymmetric 8-node hexahedral element in modeling nearly-incompressible soft tissues

Abstract

In biomechanics problems, the biological soft tissues are usually treated as anisotropic nearly incompressible hyperelastic materials, but such complicated nonlinear material models often cause challenging problems of severe volumetric locking and instabilities in numerical simulations. In this paper, the recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with different test and analytical trial functions (ATFs) is modified for the analysis of the anisotropic nearly-incompressible hyperelastic soft tissues. Unlike the original formulation, the linear analytical general solutions for anisotropic elasticity and the consistent tangent modulus are firstly employed for formulating the trial functions, and are used to construct the incremental displacement fields that result in the incremental deformation gradient. The total deformation gradient is obtained by multiplying the incremental deformation gradient by the deformation gradient, after which the Cauchy stresses can be directly calculated from a total-form constitutive equation relating to the deformation gradient. Numerical tests, including commonly used benchmarks and cardiac examples, demonstrate attractive properties of the proposed finite element formulation in modeling nearly-incompressible anisotropic hyperelastic materials. It is free of various locking and quite insensitive to mesh distortions, and provides high accuracy with faster convergence rates when compared with other existing models.