The tangential stiffness matrix of Mooney-Rivlin model strain energy function-based rubber material in finite element method

The tangential constitutive matrix is derived in the paper for the nonlinear finite element computation of rubber material as the strain energy function is expressed by Mooney-Rivlin model. The stress and strain of constitutive relation are separately expressed by Piola-Kirchhoff stress and Green strain with Lagrange description. As the incompressibility considered, the strain energy function is decoupled into volume -preserving and dilatational parts. The tangential stiffness matrix is then attained by use of the tangential constitutive matrix. The stiffness matrix is developed to nonlinear finite element computation of hyperelastic material.