Optimal control problems for stress tensor in plastic plane medium

TL;DR

This paper integrates mechanics, PDEs, and control theory to formulate and analyze optimal control problems for stress tensors in plastic deformation, revealing insights into the physical behavior of such materials.

Contribution

It introduces a novel optimal control framework for stress tensors constrained by equilibrium equations in plastic media, transforming classical variational problems into control problems.

Findings

Confirmation of physical features of plastic deformation

Derivation of integrability conditions from control constraints

Natural split of constraints leading to new insights

Abstract

This paper joins some concepts from Mechanics, Partial Differential Equations and Control Theory in order to solve bi-time optimization problems related to stress tensor in plastic deformations. The main goal is to analyze some optimal control problems constrained by the equilibrium equations of the stress tensor in perfect plastic plane medium. As consequence of this approach, a natural split of the constraints arises, leading to integrability conditions and changes a classical variational problem into an optimal control one. The final outcomes confirm all the expectations related to the physical features of plastic deformations phenomenon.