# Deformation problem for glued elastic bodies and an alternative iteration method

## TL;DR

This paper models the deformation of glued elastic bodies using linear elasticity with adhesive forces, proving solution existence, analyzing an iterative solution method, and numerically validating convergence.

## Contribution

It introduces a variational framework for the deformation problem and demonstrates the convergence of an alternating energy minimization method.

## Key findings

- Unique existence of weak solutions established.
- Alternating iteration method shown to be an energy minimization process.
- Numerical results confirm convergence of the proposed methods.

## Abstract

We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence of a weak solution based on it. Furthermore, we also consider an alternating iteration method and show that it is nothing but an alternating minimizing method of the total energy. The convergence of a monolithic formulation and the alternating iteration method are numerically studied with the finite element method.