Yield criteria for quasibrittle and frictional materials

TL;DR

This paper introduces a versatile, convex yield function capable of modeling the inelastic behavior of various pressure-sensitive, frictional, and ductile materials, capturing transitions between different material classes and fitting diverse experimental data.

Contribution

It proposes a new, unified yield/damage function that generalizes multiple classical criteria and models material behavior transitions during hardening or damage.

Findings

The yield function accurately fits experimental data for soils, concrete, rocks, metals, and polymers.

It encompasses well-known criteria like von Mises, Drucker-Prager, and Tresca as special cases.

Convexity of the function is rigorously proved and can be used to generate other yield functions.

Abstract

A new yield/damage function is proposed for modelling the inelastic behaviour of a broad class of pressure-sensitive, frictional, ductile and brittle-cohesive materials. The yield function allows the possibility of describing a transition between the shape of a yield surface typical of a class of materials to that typical of another class of materals. This is a fundamental key to model the behaviour of materials which become cohesive during hardening (so that the shape of the yield surface evolves from that typical of a granular material to that typical of a dense material), or which decrease cohesion due to damage accumulation. The proposed yield function is shown to agree with a variety of experimental data relative to soil, concrete, rock, metallic and composite powders, metallic foams, porous metals, and polymers. The yield function represents a single, convex and smooth surface in stress space approaching as limit situations well-known criteria and the extreme limits of convexity in the deviatoric plane. The yield function is therefore a generalization of several criteria, including von Mises, Drucker-Prager, Tresca, modified Tresca, Coulomb-Mohr, modified Cam-clay, and --concerning the deviatoric section-- Rankine and Ottosen. Convexity of the function is proved by developing two general propositions relating convexity of the yield surface to convexity of the corresponding function. These propositions are general and therefore may be employed to generate other convex yield functions.