A finite strain model for multi-material, multi-component biomechanical analysis with total Lagrangian smoothed finite element method

In this paper, a Unified-Implementation of smoothed finite element method (UI-SFEM) is presented for analyzing large deformations of complex biological tissues using automatically generated linear triangles and tetrahedrons. Biological structures, including many multi-material, multi-component connected tissues, usually undergo finite deformation. Numerical method need to consider different numerical difficulties for different component or materials. In our method, the numerical integration domain can be constructed by combining arbitrary forms of smoothing domains based on gradient smoothing techniques according to the numerical characteristics of materials or components. In addition, the instantaneous hyperelasticity and time-dependent viscous behaviors commonly in biological tissues are considered. Numerical experiments, including fiber reinforced biological composites, the artery wall and cervical spine, show that the UI-SFEM possesses the following properties in simulating multi-material and multi-component biological tissues: (1) remarkably flexibility (2) high accuracy and computational efficiency. (3) insensitive to mesh distortion.