Local and nonlocal energy-based coupling models

TL;DR

This paper explores two energy-based methods for coupling local and nonlocal operators, proving existence and uniqueness of solutions, and extends these ideas to local/nonlocal elasticity models.

Contribution

It introduces two novel energy-based coupling strategies for local and nonlocal operators and applies them to elasticity models, establishing theoretical solution properties.

Findings

Proved existence and uniqueness of solutions for both coupling models.

Developed a direct minimization approach for the energy functionals.

Extended coupling methods to local/nonlocal elasticity models.

Abstract

In this paper we study two different ways of coupling a local operator with a nonlocal one in such a way that the resulting equation is related to an energy functional. In the first strategy the coupling is given via source terms in the equation and in the second one a flux condition in the local part appears. For both models we prove existence and uniqueness of a solution that is obtained via direct minimization of the related energy functional. In the second part of this paper we extend these ideas to deal with local/nonlocal elasticity models in which we couple classical local elasticity with nonlocal peridynamics.