Analytical solutions of the simple shear problem for certain types of micromorphic continuum models -- including full derivations

Abstract

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 ${\mu }^{\ast }$. 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.

23 pages, 6 figures

References in corpus (4)

• A reduced micromorphic model for multiscale materials and its applications in wave propagation
• A new view on boundary conditions in the Grioli-Koiter-Mindlin-Toupin indeterminate couple stress model
• Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)
• Identification of second-gradient elastic materials from planar hexagonal lattices. Part II: Mechanical characteristics and model validation