Thermoelastic-Plastic Flow Equations in General Coordinates

TL;DR

This paper generalizes thermoelastic-plastic flow equations for isotropic solids from Cartesian to arbitrary coordinate systems, facilitating applications based on symmetry considerations in spherical, cylindrical, and spheroidal coordinates.

Contribution

It introduces coordinate-invariant equations for thermoelastic-plastic flow applicable in various geometries, extending previous Cartesian-only formulations.

Findings

Equations are explicitly evaluated in spherical coordinates.

Formulations are provided for cylindrical and spheroidal coordinates.

The generalized equations enable symmetry-based analysis of solid flow.

Abstract

The equations governing the thermoelastic-plastic flow of isotropic solids in the Prandtl-Reuss and small anisotropy approximations in Cartesian coordinates are generalized to arbitrary coordinate systems. In applications the choice of coordinates is dictated by the symmetry of the solid flow. The generally invariant equations are evaluated in spherical, cylindrical (including uniaxial), and both prolate and oblate spheroidal coordinates.