Constitutive Model for (Geological) Materials

TLDR

The authors propose a polynomial‑expansion framework for the yield function of isotropic, hardening materials, enabling the development of material models from laboratory data and suggesting extensions to non‑associative behavior, pore pressure, and anisotropy. The framework employs associated plasticity, expanding the yield function in stress‑tensor invariants, and defines hardening functions from cubical specimen tests by relating plastic strain trajectories to the deviatoric‑to‑total strain ratio, with predictions validated against multiple stress paths. The resulting model accurately reproduces stress‑strain and volumetric strain responses for various stress paths, demonstrating its suitability for evolving material models from experimental results.

Abstract

A general procedure based on polynomial expansion of yield function in terms of invariants of the stress tensor is proposed in the context of associated plasticity for isotropic materials undergoing isotropic hardening. The procedure can be used to evolve one or more models for a material by using appropriate laboratory test results. One of the functions showing invariance at ultimate and a single function to describe continuous yield and ultimate yield behavior is investigated in detail. Based on comprehensive series of bests on cubical specimens for different (geological) materials, a hardening or growth function is defined in terms of the trajectory of plastic strain and the ratio of deviatoric to total plastic strain. The predictions of the proposed model are verified with respect to the observed results from tests with different stress paths. The model provides highly satisfactory predictions for both stress‐strain and volumetric strain responses from various stress paths. The proposed model shows potential for incorporating other characteristics such as nonassociative rule, pore water pressure effect, and induced anisotropy.