An Asynchronous Variational Integrator for Contact Problems Involving Elastoplastic Solids

Simulations of contact problems involving at least one plastic solid may be costly due to their strong nonlinearity and requirements of stability. In this work, we develop an explicit asynchronous variational integrator (AVI) for inelastic non-frictional contact problems involving a plastic solid. The AVI assigns each element in the mesh an independent time step and updates the solution at the elements and nodes asynchronously. This asynchrony makes the AVI highly efficient in solving such bi-material problems. Taking advantage of the AVI, the constitutive update is locally performed in one element at a time, and contact constraints are also enforced on only one element. The time step of the contact element is subdivided into multiple segments, and the fields are updated accordingly. During a contact event, only one element involving a few degrees of freedom is considered, leading to high efficiency. The proposed formulation is first verified with a pure elastodynamics benchmark and further applied to a contact problem involving an elastoplastic solid with non-associative volumetric hardening. The numerical results indicate that the AVI exhibits excellent energy behaviors and has high computational efficiency.