A selective smoothed finite element method with visco‐hyperelastic constitutive model for analysis of biomechanical responses of brain tissues

Abstract

AbstractBrain tissues are known for exhibiting complex nonlinear and time‐dependent properties, which require visco‐hyperelastic constitutive models for proper simulation. In this paper, a Total Lagrangian Explicit Selective Smoothed Finite Element Method (Selective S‐FEM) is formulated to analyze the dynamic behavior of incompressible brain tissues undergoing extremely large deformation. The proposed Selective S‐FEM deals with three‐dimensional problems using four‐node tetrahedron elements that can be automatically generated for geometrically complex soft tissues. It consists of the three key ingredients. (i) A visco‐hyperelastic constitutive model is developed within the framework of S‐FEM in the first time, allowing adequate modeling of the dynamic brain tissue behavior. (ii) Selective S‐FEM strategy is used for overcome the mesh distortion and the volumetric locking that often occurs in soft tissues. (iii) Total Lagrangian formulation is used in an explicit algorithm allowing rigorous simulation of extreme large deformation. (iv) A combined implementation of Selective S‐FEM with the visco‐hyperelastic constitutive model for dynamic simulations. The shear deformation is calculated by Face/Edge‐based S‐FEM, and the volume deformation is calculated by NS‐FEM. Numerical experiments show that Selective S‐FEM is a robust solver with good accuracy, and excellent ability to reduce element distortion effects in simulate time‐dependence behavior of bio‐tissues.