Simulating penetration problems in incompressible materials using the material point method

This paper presents a methodology for computing the response of a rigid strip footing in incompressible Tresca soil when loaded to large settlements. The numerical simulations were performed using the generalized interpolation material point method (GIMP). For efficiency, a block-structured rectilinear irregular grid was used that moves and compresses as the footing advances. Volumetric locking was prevented using the non-linear extension to the B-bar method. The paper addresses the modifications required for the implementation of the B-bar method in GIMP and demonstrates its efficacy in mitigating locking using two benchmark problems: the Cook?s membrane problem and the limit bearing capacity of a footing in a Tresca soil at small settlements. The response of the footing when loaded to large settlements under both quasi-static and dynamic loads is then presented. A comparison of the solutions obtained using the proposed methodology with other numerical solutions available in the literature illustrates the efficacy of the proposed method.