Mean stress dependent nonlinear hyperelasticity coupled with damage stiffness degradation. A thermodynamical approach

• We couple damage stiffness degradation with stress dependent nonlinear elasticity.
• Two families of damage models based on different assumptions are compared.
• Increase of intact matrix stiffness with mean stress may counterbalance damage effects.

Porous materials, such as geomaterials, exhibit a behaviour dependent on the confining pressure. The aim of this paper is to study the degradation of the elastic stiffness of mean stress dependent materials, due to the deterioration of the microstructure during loading.Continuum damage mechanics offers a framework to model this rigidity deterioration. In addition to the concept of effective stress, a choice has to be made between two widely used hypotheses, the principle of strain equivalence and the principle of equivalent elastic energy, in order to build a complete modelling framework.A mean stress dependent hyperelastic formulation is used to ensure a conservative behaviour, and associated to the two previous damage modelling assumptions, whose effects are compared. This allows for mean stress dependent elasticity to be reproduced, with elastic moduli increasing with mean stress while decreasing with damage.