The material point method in simulating rocking problems

Sofianos C.D., Koumousis V.K. (2021). The material point method in simulating rocking problems. in Proceedings of the 10th International Congress on Computational Mechanics (GRACM 2021), 5-7 July, 2021, Athens, Greece (virtual event).

Abstract | In this work the Material Point Method (MPM) is employed to study the behavior of rocking structures. In the MPM the body is discretized into a number of material points that hold all the variables of the system such as stress, strain, velocities etc. The method employs a background grid, and the various variables are mapped to the nodes of the grid using shape functions similar to the Finite Element Method. The equations of conservation of momentum and conservation of energy are solved at the grid nodes and the updated state variables are again mapped back to the material points updating their positions and velocities. Mass conservation is automatically satisfied since every material point holds its mass during the analysis. The background grid is only used to solve the governing equations at the end of each computational step and after that, it is reverted back to its original undeformed configuration. The method employs a single velocity field for all material points, that results in an Inherent no-slip, no-penetration contact algorithm. This means that collisions and contact are automatically resolved. The method is examined at its original formulation, and its capability of resolving the contacts and simulating the rocking behavior of a rigid block is assessed. Furthermore, the MPM is extended using linear ground springs to simulate the contact surface at the edges of the block. The problem examined is Housner’s original rigid block problem (Housner, 1963) where a rigid block is subjected to horizontal ground acceleration for which certain assumptions are made and a governing equation is established in differential form. Results are compared with the analytical results and other already published results.