A coupled implicit MPM-FEM approach for brittle fracture and fragmentation

Abstract

A new approach has been developed that couples the Material Point Method (MPM) with the Finite Element Method (FEM). The introduced coupling method is achieved by utilizing a bond element to connect the material points to the finite elements, and employing the penalty approach to prevent slippage. Moreover, the developed approach deals with the contact between MPM and FEM. The contact is regulated by introducing additional conditions. When these conditions are met, the bond elements become active and prevent penetration. The coupling is monolithic, meaning that one system of equations is built for both MPM and FEM, and solved simultaneously. Additionally, an automated conversion of finite elements to material points is presented, which is controlled by the eigenfracture approach that splits the finite elements into intact and eroded sets. Eroded finite elements are then converted to material points. Numerical examples are reported to express the novelty of the developed approach.