Modeling Imperfect Interfaces in the Material Point Method using Multimaterial Methods

The “multimaterial” version of the material point method (MPM) extrapolates each material to its own velocity field on a background grid. By reconciling momenta on nodes interacting with two or more materials, MPM is able to automatically handle contact without any need for special contact elements. This paper extends multimaterial MPM to automatically handle imperfect interfaces between materials as well. The approach is to evaluate displacement discontinuity on multimaterial nodes and then add internal forces and interfacial energy determined by an imperfect interface traction law. The concept is simple, but implementation required numerous corrections to make the analysis mesh independent, to work for any stiffness interfaces, and to find the interfacial normal vector. Several examples illustrated the need and demonstrated the validity of the various corrections. A composite mechanics problem found the bulk modulus of a particulate filled composite as a function interface quality. This calculation revealed a scaling effect — interfaces in nanoparticle composites must be better than interfaces in the corresponding microparticle composites for the nanocomposite mechanical properties to be as good as the conventional composite properties. keyword: Material point method, MPM, Imperfect interfaces, multimaterial, contact, nanocomposites