Quasistatic Evolution with Unstable Forces

TL;DR

This paper studies the well-posedness of load-controlled quasistatic evolution in a nonlocal continuum model related to peridynamics, establishing local existence, uniqueness, and energy balance for evolutions starting at stable critical points.

Contribution

It provides new mathematical results on the existence and uniqueness of quasistatic evolutions in nonlocal models, including energy balance, for load paths from stable states.

Findings

Proves local existence and uniqueness of quasistatic evolution.

Shows energy balance in load-controlled evolution.

Identifies conditions for stable critical points as starting states.

Abstract

We consider load controlled quasistatic evolution. Well posedness results for the nonlocal continuum model related to peridynamics are established. We show local existence and uniqueness of quasistatic evolution for load paths originating at stable critical points. These points can be associated with local energy minima among the convex set of deformations belonging to the strength domain of the material. The evolution of the displacements however is not constrained to lie inside the strength domain of the material. The load-controlled evolution is shown to exhibit energy balance.