From Boussinesq-Love contact to impact between hyperelastic bodies

This article is devoted to the modeling of finite deformations of hyperelastic bodies 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. The contact problem is solved by the bi-potential method. For the finite element implementation, an explicit expression of the tangent operator for the 36 hyperelastic model is derived. The classical Boussinesq-Love contact problem is first investigated numerically. A second example concerns the impact between two hyperelastic bodies in three-dimension.