Strength of a matrix with elliptic criterion reinforced by rigid inclusions with imperfect interfaces

• We consider the imperfect bounding of rigid inclusions in a matrix with elliptic strength.
• Three interface strength cases are studied: perfect, Tresca, Mohr–Coulomb.
• Closed form effective criteria are derived using micro-mechanics.
• Effective criteria are made of part of ellipses corresponding to active/inactive interfaces.
• Activation of interface mechanisms is controlled by macrosc. strain triaxiality ratio.

Elliptic effective strength criteria in the mean-deviatoric stress plane are encountered in porous media for a granular material made of rigid grains with cohesive frictional interfaces or a material with pores in a Drucker–Prager matrix. The macroscopic strength criterion of a heterogeneous material comprising a matrix with elliptic strength criterion reinforced by rigid inclusions with perfect or imperfect interfaces is studied. Considered imperfect interfaces follow either a Tresca or a Mohr–Coulomb strength criterion. Derived macroscopic criteria are shown to be a combination of a larger ellipse, which corresponds to the criterion for perfectly bounded interfaces, conditionally truncated by a smaller ellipse resulting from the activation of interfacial mechanisms. The activation of the interfacial mechanisms depends on the matrix and interfaces strength properties, inclusions concentration, as well as the macroscopic strain triaxiality ratio.