An energy‐consistent material‐point method for dynamic finite deformation plasticity

Energy consistency for the material‐point method (MPM) is examined for thermodynamically consistent hyperelastic‐plastic materials. It is shown that MPM can be formulated with implicit, three‐ field variational, finite element algorithms which dissipate energy and conserve momentum for that class of material models. With a consistent mass matrix the resulting overall numerical method inherits the energy‐dissipative and momentum‐conserving properties of the mesh solution. Thus, the proposed MPM algorithm satisfies by construction a time‐discrete form of the second law of thermo‐ dynamics. Properties of the method are illustrated in numerical examples.