Symmetry groups of non-stationary planar ideal plasticity

TL;DR

This paper analyzes the Lie symmetry groups of a system modeling non-stationary planar ideal plastic flow, classifies subalgebras, and derives invariant solutions using symmetry reduction.

Contribution

It provides a detailed classification of symmetry subalgebras and applies symmetry reduction to find invariant solutions for the system.

Findings

Classification of Lie algebra subalgebras for the system

Derivation of invariant solutions via symmetry reduction

Identification of symmetry generators for different force types

Abstract

This paper is a study of the Lie groups of point symmetries admitted by a system describing a non-stationary planar flow of an ideal plastic material. For several types of forces involved in the system, the infinitesimal generators which generate the Lie algebra of symmetries have been obtained. In the case of a monogenic force, the classification of one- and two- dimensional subalgebras into conjugacy classes under the action of the group of automorphisms has been accomplished. The method of symmetry reduction is applied for certain subalgebra classes in order to obtain invariant solutions.