An elastoviscoplastic constitutive model for geomaterials: Application to hydromechanical modelling of claystone response to drift excavation

A micromechanical inspired model for the coupled to damage elasto-plastic behavior of geomaterials under compression

“…From the mathematical point of view, e, p, s, and X are order 2 symmetrical tensors which can be identified with 3 Â 3 symmetrical matrices after the choice of an orthonormal basis. In other words, those tensors will be considered as elements of M 3 s . The plasticity (or yield) criterion is defined by giving the (closed with non-empty interior) convex set K of M 3 s where the thermodynamical forces X must lie.…”

“…(However, we will see in the next section that the image of this domain in the stress space evolves with the plastic strain.) In practice, the convex K is characterized by a convex function f : M 3 S ↦ ℝ so that the plasticity criterion reads as…”

“…Drucker-Prager criterion (or some variants like Mohr-Coulomb or Hoek-Brown criteria) is widely used in the modeling of the behavior of geomaterials under compression, see references [1,2,5]. In general, those criteria are used in a nonstandard context, i.e., with a nonassociative flow rule for the plasticity evolution, like in reference [3]. The main usual argument which is evoked to use a nonassociative flaw rule is that one overestimates the dilatancy effect with the normality rule associated with Drucker-Prager criterion.…”

“…The majority of these approaches is based on elasto-plastic formalism with some of them having resort to damage coupling. For instance, in soil or rock mechanics, one generally uses elasto-plastic or more generally (thermo)elasto-viscoplastic models without introducing damage variables [1][2][3], whereas it is generally admitted that one cannot reproduce the experimental results observed for concrete without considering a damage evolution law [4][5][6][7][8][9][10]. In all the cases the elasto-plastic models are based on a restricted choice of yield criteria (like Drucker-Prager one or some variants like Hoek-Brown criterion [1,2] or the cap model [11]), with common feature being the hypothesis of a nonassociative flow rule.…”

“…The previous properties suggest to search a response such that damage and plasticity evolve simultaneously. During this damage with plasticity stage, the strain and stress tensors are assumed to be of the form3 where p 0 remains constant and e z is a given function of time which is decreasing from its critical value given in reference (27). Relationship between Tr p and a. Inserting the form of the different tensors into the plasticity flow rule (which does not involve the damage state) gives…”