On geometric conditions for reduction of the Moreau sweeping process to the Prandtl-Ishlinskii operator

TL;DR

This paper investigates the specific geometric conditions under which the complex Moreau sweeping process can be simplified to the Prandtl-Ishlinskii operator, facilitating easier analysis of elastoplastic systems.

Contribution

It identifies the geometric conditions that allow reduction of the sweeping process to the Prandtl-Ishlinskii model, even with complex spring topologies.

Findings

Reduction conditions depend on specific geometric configurations

Complex topologies can be simplified to Prandtl-Ishlinskii under certain conditions

The results facilitate analysis of elastoplastic systems

Abstract

The sweeping process was proposed by J. J. Moreau as a general mathematical formalism for quasistatic processes in elastoplastic bodies. This formalism deals with connected Prandtl's elastic-ideal plastic springs, which can form a system with an arbitrarily complex topology. The model describes the complex relationship between stresses and elongations of the springs. On the other hand, the Prandtl-Ishlinskii model assumes a very simple connection of springs. This model results in an input-output operator, which has many good mathematical properties. It turns out that the sweeping processes can be reducible to the Prandtl-Ishlinskii operator even if the topology of the system of springs is complex. In this work, we analyze the conditions for such reducibility.