An n-sided polygonal selective smoothed finite element method for nearly incompressible visco-hyperelastic soft materials

In this article, an n-sided polygonal smoothed finite element (nSFEM) is formulated for dynamic analyses of nonlinear problems of visco-hyperelastic materials undergoing large deformations. Two types of smoothing domains are constructed for mesh of n-sided polygonal elements. Using the gradient smoothing technique, the calculation of the strain-displacement matrix requires only the shape function values rather than the derivatives of shape function. The simple averaging point interpolation technique is used to calculate the values of the shape functions on the boundary of different smoothing domains. The Total Lagrangian formulation is used to deal with the nonlinear dynamic analysis of soft materials with finite strain. The polygonal FEM with Wachspress coordinate is also implemented for comparison. To overcome volumetric locking, selective smoothing domain scheme is used to calculate the smoothing nodal internal force. To analyze the time-dependent mechanical behavior of soft materials, a constitutive update algorithm for explicit time-integration is implemented based on the generalized Maxwell visco-hyperelastic model. A number of numerical examples are presented to demonstrate the high precision and super convergence, and robustness of the present nS-FEM for incompressible visco-hyperelastic problems.