Hyperelastic nature of the Hoek-Brown criterion

TL;DR

This paper introduces a hyperelastic elasto-plastic model linking the Hoek-Brown criterion to hyperbolic elasticity, demonstrating its advantages through simulations and highlighting its relevance for geotechnical material behavior.

Contribution

It proposes a novel hyperelastic elasto-plastic model that connects the Hoek-Brown criterion with hyperbolic elasticity, enhancing understanding of nonlinear material responses.

Findings

Nonlinear elastic behavior exhibits dilatancy saturation during cyclic loading.

The model shows improved fit for elasto-plastic responses in standard tests.

Finite element simulations confirm the model's numerical applicability.

Abstract

We propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or hyperelastic) behavior with plasticity obeying the associated flow rule. Interestingly, we find that a linear yield criterion on the thermodynamical force associated with plasticity results in a quadratic yield criterion in the stress space. This suggests a specific hyperelastic connection between Mohr-Coulomb and Hoek-Brown (or alternatively between Drucker-Prager and Pan-Hudson) yield criteria. We compare the elasto-plastic responses of standard tests for the Drucker-Prager yield criterion using either linear or the suggested hyperbolic elasticity. Notably, the nonlinear case stands out due to dilatancy saturation observed during cyclic loading in the triaxial compression test. We conclude this study with structural finite element simulations that clearly demonstrate the numerical applicability of the proposed model.