An efficient finite element of formulation for large deformation analysis of elastomers

A three-dimensional mixed finite element is formulated on the basis of a perturbed Lagrangian variational principle. The finite element equations are derived for both compressible and nearly incompressible materials. In order to improve the computational efficiency of nonlinear elasticity involving large strains and material incompressibility, a deformation-splitting process is employed to separate the deformation of elastomers into two distinct parts: isochoric and hydrostatic parts, respectively. In conjunction with this process, both the displacement and pressure fields are interpolated independently from a perturbed Lagrangian variational principle.