Modelling contacts with a total Lagrangian material point method - de Vaucorbeil, Alban; Nguyen, Vinh Phu (Computer methods in applied mechanics and engineering, 2021)
The total Lagrangian Material Point Method (TLMPM) is an efficient formulation of the well known Material Point Method (MPM). Unlike the MPM, it is not subject to cell-crossing instabilities or numerical failure, and features better quadrature. However, the TLMPM is unable to model (no-slip) contacts seamlessly as the standard updated Lagrangian MPM. This paper presents a contact algorithm for the TLMPM able to model contacts with or without friction. Its performance is tested and compared to the standard MPM using five different tests that are popular problems from the MPM literature. Even when using simple hat weighting functions, and unlike in the MPM, the stress field in the TLMPM is fairly smooth and with this algorithm, there is no gap between two surfaces in contact. Moreover, there are less energy losses, and less error in the predicted forces. •Derivation of a contact algorithm for the total Lagrangian Material Point Method.•This contact algorithm allows for contacts with or without friction.•Contacts occur without gaps unlike in the Material Point Method.•The total Lagrangian MPM presents smoother stress fields than the MPM.•There are less energy losses with the total Lagrangian MPM than the MPM.•Better contact force predictions are obtained with the total Lagrangian MPM.