Simplified impact analysis in FEniCS using hertz contact law

Abstract

The interaction of two bodies during and after impact results in complex behavior. Modelling such behaviour can be simplified by introducing a closed-form law, e.g. the Hertz law for frictionless contact. Such a model significantly reduces implementation challenges because the kinematic constraint of impenetrability is replaced by nonlinear force. This paper investigates such impact models focusing mainly on implementation details in the nowadays popular finite element solver FEniCS. This solver provides a high level of abstraction for PDEs description and solution techniques. The process of matrix assembling and localization is automated by the solver. The contribution shows usability of the FEniCS for Hertz law implementation and investigates the influence of the boundary conditions. Although the contribution focuses mostly on implementation details, example models correspond to real problem of glass plates subjected to low-velocity impact and are validated by experimentally obtained results.