Hyperelastic nature of Hoek-Brown criterion

Ilaria Fontana (1, 2, 3) , Kyrylo Kazymyrenko (2, 3) , Daniele Di Pietro (1)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 IMSIA - UMR 9219 - Institut des Sciences de la mécanique et Applications industrielles
3 EDF R&D ERMES - ElectRotechnique et MEcanique des Structures

We analyze the influence of hyperelasticity on the plastic behavior of materials. A specific class of what we call hyperbolic elasticity arises from theoretical considerations as straight consequence of plastic invariance of elastic domain. The latter property of fixed residual plasticity is observed experimentally for many geomaterials. We superimpose hyperelastic effects on the plastic Drucker-Prager constitutive relation, widely used in geoscience. Curiously, we found that the hyperbolic nonlinearity, introduced through the Standard Generalized Material formalism, curves the initially linear surface to a quadratic one, that is assimilated to the generalized Hoek-Brown criterion. We conclude than that one possible justification of the empirical Hoek-Brown fit is the material's hyperlastic nature.

Mots clés: hyperelasticity; elasto-plastic model; Hoek-Brown criterion; constitutive relation; Drucker-Prager criterion; Fairhurst criterion

Domaines: Sciences de l'ingénieur [physics]

Ilaria Fontana, Kyrylo Kazymyrenko, Daniele Di Pietro. Hyperelastic nature of Hoek-Brown criterion. 2021. ⟨hal-03501788v1⟩