Analytical solutions of the simple shear problem for micromorphic models and other generalized continua

To draw conclusions as regards the stability and modelling limits of the investigated continuum, we consider a family of infinitesimal isotropic generalized continuum models (Mindlin-Eringen micromorphic, relaxed micromorphic continuum, Cosserat, micropolar, microstretch, microstrain, microvoid, indeterminate couple stress, second gradient elasticity, etc.) and solve analytically the simple shear problem of an infinite stripe. A qualitative measure characterizing the different generalized continuum moduli is given by the shear stiffness mu*. This stiffness is in general length-scale dependent. Interesting limit cases are highlighted, which allow to interpret some of the appearing material parameter of the investigated continua.

Automated summary

The stability and modeling limits of investigated continuum are examined by considering a family of infinitesimal isotropic generalized continuum models and solving the simple shear problem analytically. The shear stiffness mu* serves as a qualitative measure characterizing different generalized continuum moduli, which is generally dependent on length-scale. Interesting limit cases are highlighted to interpret material parameters in the investigated continua.