A total Lagrangian selective smoothed finite element method for three-dimensional multi-body contact dynamics of biological soft tissue

Abstract

In this article, a total Lagrangian selective smoothed finite element method (Selective S-FEM) is proposed for 3D multi-body contact dynamic analysis of biological soft tissues. A time-dependent total Lagrangian explicit algorithm is formulated in the proposed Selective S-FEM to calculate nonlinear large deformation of soft materials, considering incompressible, hyperelastic, and visco-hyperelastic behaviors. To overcome the incompressibility, the shear deformation is evaluated using the Edge/Face-based S-FEM and volumetric deformation is handled via Node-based S-FEM. A multi-body contact algorithm is also implemented in our Selective S-FEM model using master–slave surface-based node-to-surface algorithms, together with the penalty function method. The contact algorithm enables multi-component, multi-material complex contact between soft-hard materials, as well as the hybrid contacts, such as knee joint contact and skull-brain contact resulted from impact. The proposed Selective S-FEM uses the four-node tetrahedral (T4) that can be generated automatically, and numerical examples have shown that the results are insensitive to large mesh distortion, robust in handling various contacts, and produces accurate stress solution.