Discrete dynamics of complex bodies with substructural dissipation: variational integrators and convergence

TL;DR

This paper develops variational integrators for the linearized dynamics of complex bodies with substructural dissipation, proving their convergence using BV estimates and accounting for unique inertia and dissipation effects.

Contribution

It introduces a novel variational integrator framework for complex bodies with substructural effects and provides a rigorous convergence proof.

Findings

Successful construction of variational integrators for complex bodies

Proof of convergence using BV estimates on rate fields

Inclusion of substructural inertia and dissipation in the model

Abstract

For the linearized setting of the dynamics of complex bodies we construct variational integrators and prove their convergence by making use of BV estimates on the rate fields. We allow for peculiar substructural inertia and internal dissipation, all accounted for by a d'Alembert-Lagrange-type principle.