Collisions between two nonlinear deformable bodies stated within Continuum Mechanics

The study of the interaction between two deformable bodies that collide is of great interest since desired effects, as a stable contact, or undesired ones, as the failure of a mechanical part, can be predicted. In this work, a Signorini type contact model with impact considering large rotations and deformations is addressed. The problem is stated using the Continuum Mechanics formulation in two and three dimensions with the Lagrangian description employing the two Piola–Kirchhoff stress tensors with linear or non-linear constitutive equations. The governing equations are solved through a general purpose software oriented to solve partial differential equations by means of a finite element discretization. The impact of a deformable body over a rigid boundary or over other deformable body is tackled. Also a three-dimensional problem is addressed (i.e. a spheric ball impacting on a rigid surface). Numerical illustrations include parametric studies on the energy, the impulse forces and the time of contact for different initial conditions and materials. A comparison among the models is shown. Additionally the problem of the impact of two deformable solid balls is solved and contrasted with simpler models developed by other authors.