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Brain tissues are known for exhibiting complex non-linear 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 Total Lagrangian Explicit Selective S-FEM deals with three-dimensional (3D) problems using four-node tetrahedron (T4) elements that can be automatically generated for geometrically complex soft tissues. It consists of the three key ingredients. 1) 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. 2) Selective S-FEM strategy is used for overcome the mesh distortion related issues and the volumetric locking that often occurs in soft tissues; 3) Total Lagrangian formulation is used in an explicit algorithm allowing rigorous simulation of extreme large deformation, and a combined implementation of the Selective S-FEM with the visco-hyperelastic constitutive model for dynamic simulations. Selective S-FEM is found mesh insensitive to mesh distortion and incompressibility of soft tissues, which are often encountered in the standard FEM modeling using T4 elements. This is attributed to the use of selective strain smoothing in SFEM, which provide proper “softening” effects from the Node-based Smooth Finite Element Method (NS-FEM). The deformation of brain tissue is split into shear part and volumetric part in Selective S-FEM. The shear deformation is calculated by Face-based S-FEM or Edgebased S-FEM, and the volume deformation is calculated by NS-FEM. In order to accurately simulate the large deformation and stress relaxation characteristics of brain tissue, viscohyperelastic constitutive model with strain energy format is used and effective constitutive iterative algorithm for the convolution integral is accomplished. Numerical experiments show that Selective-SFEM is a robust solver with good accuracy, and excellent ability to reduce element distortion effects in simulate time-dependence behavior of bio-tissues.