Separately Global Solutions to Rate-Independent Processes in Large-Strain Inelasticity

TL;DR

This paper introduces a new concept of separately global solutions for large-strain rate-independent systems, providing existence results for models with complex nonlinearities and couplings, advancing the mathematical understanding of large-strain inelasticity.

Contribution

It develops a novel solution framework for large-strain inelasticity models, extending theories from small strain to more complex large deformation scenarios.

Findings

Established existence of solutions for large-strain damage models.

Handled non-convex energies and prevented interpenetration of matter.

Extended solution concepts to nonlinear couplings with Eulerian and Lagrangian terms.

Abstract

In this paper, we introduce the notion of separately global solutions for large-strain rate-independent systems, and we provide an existence result for a model describing bulk damage. Our analysis covers non-convex energies blowing up for extreme compressions, yields solutions excluding interpenetration of matter, and allows to handle nonlinear couplings of the deformation and the internal variable featuring both Eulerian and Lagrangian terms. In particular, motivated by the theory developed in [49] in the small strain setting, and for separately convex energies we provide a solution concept suitable for large strain inelasticity.