Geometrical foundations of plasticity yield criteria: A unified theory

TL;DR

This paper introduces a unified theoretical framework for plasticity yield criteria using differential geometry and group theory, enabling better modeling of material behavior including anisotropy and complex stress dependencies.

Contribution

It develops a novel mathematical model that unifies classical and anomalous yield criteria through tensor functions and series expansions, enhancing understanding of plasticity.

Findings

Accurately describes classical yield criteria like Tresca and Von Mises.

Predicts new stress-dependent behaviors in metals such as aluminium.

Provides a flexible, symmetry-aware framework for material plasticity analysis.

Abstract

A new model for elucidating the mathematical foundation of plasticity yield criteria is proposed. The proposed ansatz uses differential geometry and group theory concepts in addition to elementary hypotheses based on well-established experimental evidence. Its theoretical development involves the analysis of tensor functions and provides a series expansion which allows the functional stress-dependence of plasticity yield criteria to be predicted. The theoretical framework for the model includes a series of spatial coefficients that provide a more flexible theory for in-depth examination of symmetry and anisotropy in compact solid materials. It describes the classical yield criteria (like those of Tresca, Von Mises, Hosford, Hill, etc) and accurately describes the anomalous behaviour of metals such as aluminium, which was elucidated by Hill (1979). Further, absolutely new instances of stress-dependence are predicted; this makes it highly useful for fitting experimental data with a view to studying the phenomena behind plasticity.