A micro-mechanical model for the plasticity of porous granular media and link with the Cam clay model

Abstract

International audienceA micro-mechanical constitutive model for the plastic behavior of cohesive granular materials with hardening due to porosity changes is proposed. The plasticity model is based on a re-interpretation of a micro-mechanical strength model for cohesive frictional granular media. The hardening law by porosity changes explicitly stems from the homogenization process. The micro-macro plasticity model, analytical and fully explicit, depends only on two constant material parameters with a clear physical signification at the microscopic scale: the friction angle and the tensile strength of the grain to grain interfaces. The seminal ideas of critical state soil mechanics are retrieved: critical state line, state boundary surface in the stress/porosity space, hardening or softening due to change in porosity and ability to describe both dilatancy and contrac-tancy. The established micro-mechanical model is very similar to the phenomenological modified Cam clay model, providing to the latter a microstructural based interpretation

Micromechanics of elastoplastic porous polycrystals: Theory, algorithm, and application to osteonal bone

“…This may be seen as an interesting complement to the popular plastic homogenization approaches based on limit analysis and variational methods; considering, as a rule, microscopic strength criteria, equilibrium at the micro and macro-scale, maximization of dissipation, and sometimes associated plasticity. Corresponding recent developments are reported in (Cheng et al, 2014;Shen et al, 2015;Bignonnet et al, 2016).…”

On the thermodynamics consistency of Gurson’s model and its computational implications

“…For this reason, it is the rate of Lagrangian plastic porosity at time t (equation ( 35)) which will be consider in the following together with ḟ . Moreover, assuming that all the modifications for the volume of the RVE are irreversible, that is all the reversible parts of the volume change are neglected, the rates of Lagrangian and Eulerian porosities, in link with ( 22), are readily related by (see for instance also Bignonnet et al (2016)) Consequently, in this case, the intrinsic dissipation D, defined by (28), takes the form…”

“…To this end, we will take advantage of elastoplasticity theory for saturated porous media (see for instance Coussy (1995)) to incorporate in Gurson's model a pore fluid pressure. In such extension, it is well known that the state variable representing voids volume fraction and associated to the pore pressure is the Lagrangian porosity, instead of the Eulerian one (see Coussy (1995); Bignonnet et al (2016)). The formulation of the Gurson model in the context of generalized standard materials will be done in the linearized theory.…”

A micromechanics-based elastoplastic constitutive model for frozen sands based on homogenization theory

“…(2010) devoted to formulating a micromechanics-based constitutive model for granular materials under relatively low confining pressure and proposed new rigorous stress localization laws within the general framework of homogenization theory, and moreover established some local constitutive relations under the consideration of irreversible thermodynamics. Bignonnet et al. (2016) proposed a micromechanical constitutive model for the plastic behaviors of cohesive granular materials with strain hardening due to porosity changes stemming from the homogenization process on the basis of a reinterpretation of a micromechanical strength model.…”