Local transmitting boundaries for the generalized interpolation material point method

Abstract

SummaryThe boundary‐value problems of mechanics can be solved using the material point method with explicit solver formulations. In explicit formulations, even quasi‐static problems are solved as if dynamic, which means that waves are reflected at computational boundaries, generating spurious oscillations in the solution to the boundary‐value problem. Such oscillations can be reduced to a level such that they are barely noticeable with the use of transmitting boundaries. Current implementations of transmitting boundaries in the material point method are limited to the standard viscous boundary. The absence of any stiffness component in the standard viscous boundary may lead to an undesirable finite rigid‐body motion over time. This motion can be minimized through the adoption of the transmitting cone boundary that approximates the stiffness of the unbounded domain. This paper lays out the implementation of the transmitting cone boundary for the generalized interpolation material point method. The cone boundary reflection‐canceling tractions can be applied to either the edges or the centroids of material points; this paper discusses the implications of both approaches.