A Penalty Function Method for Modelling Frictional Contact in MPM

Abstract

Frictional contact is commonly represented in the Material Point Method (MPM) by algorithms based on multi-velocity fields, in which the correction is performed at the background computational mesh. Typically for applications of various stiffness values, these algorithms show a non-physical variation in the contact stresses along the interface surface. The lack of a smoothening function in the detection procedure, which is essential in explicit finite element algorithms, contributes to the stress oscillation and causes a gap between the bodies in contact. For MPM versions with a finite particle size, like Convected Particle Domain Interpolation method (CPDI), the effect of the last shortcoming becomes more pronounced. Results can be improved by using denser mesh, however, the computational cost will increase considerably.In the present paper, the boundary of a continuum object is discretised separately from the MPM discretisation and traced accurately during the solution advancement. Therefore, contact forces among different boundaries are evaluated using a penalty function method commonly implemented in Lagrangian analyses. These forces are then mapped to the computational mesh, where the momentum equation is solved, as an external force. The suggested approach is validated with a benchmark problem, where the closed-form solution is available, and compared to the classical MPM contact algorithm. Furthermore, an application of two bodies collision with large deformation is demonstrated.