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, threefield 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 thermodynamics. Properties of the method are illustrated in numerical examples