The 3é hyperelastic model applied to the modeling of 3D impact problems

Lainé et al. [Nonlinear isotropic constitutive laws: choice of the three invariants, convex potentials and constitutive inequalities, Int. J. Eng. Sci. 37 (1999) 1927–1941.] have proposed a new third order hyperelastic model, named here the 3é model. The present paper is devoted to the modeling of finite deformations of hyperelastic bodies described by the 3é model under contact/impact conditions. A total Lagrangian formulation is adopted to describe the geometrically nonlinear behavior. A first order algorithm is applied to integrate the equations of motion. For the finite element implementation, an explicit expression of the tangent operator is derived. Efficiency and accuracy of the resulting method are illustrated on a numerical example.