New material point method contact algorithms for improved accuracy, large-deformation problems, and proper null-space filtering

Abstract

The material point method (MPM) is increasingly being used in multimaterial contact problems. Despite MPM’s advantages for such problems, some aspects of current contact methods are prone to instabilities. The main causes of instabilities are errors in the methods used to calculate normal vector and material separation. This paper presents new methods for these tasks by applying logistic regression to material point clouds contributing to each contact node. The new logistic regression process determines the most probable plane between two materials and finds their separation. The separation calculation explicitly accounts for particle deformation for increased accuracy in large deformation problems. Another improvement to multimaterial MPM is to do contact mechanics corrections twice each time step — first after initial velocity extrapolation to the grid and second after updating grid momenta. Two corrections are needed to find the correct acceleration when updating particle velocities and to extend methods that filter null-space noise to account for contact mechanics. Several examples validate the new methods and demonstrate their advantages over prior methods.