Stress channelling in extreme couple-stress materials Part II: Localized folding vs faulting of a continuum in single and cross geometries

TL;DR

This paper investigates how extreme anisotropic Cosserat elastic materials exhibit localized stress channelling, folding, and faulting phenomena, governed by wave propagation conditions rather than ellipticity, revealing behaviors absent in classical elastic materials.

Contribution

It introduces the role of wave propagation in governing localized phenomena in extreme Cosserat materials, highlighting behaviors like folding and faulting not seen in traditional elasticity.

Findings

Localized stress channelling occurs in extreme Cosserat materials.

Folding involves finite jumps in displacement gradients.

Faulting shows finite displacement discontinuities.

Abstract

The antiplane strain Green's functions for an applied concentrated force and moment are obtained for Cosserat elastic solids with extreme anisotropy, which can be tailored to bring the material in a state close to an instability threshold such as failure of ellipticity. It is shown that the wave propagation condition (and not ellipticity) governs the behavior of the antiplane strain Green's functions. These Green's functions are used as perturbing agents to demonstrate in an extreme material the emergence of localized (single and cross) stress channelling and the emergence of antiplane localized folding (or creasing, or weak elastostatic shock) and faulting (or elastostatic shock) of a Cosserat continuum, phenomena which remain excluded for a Cauchy elastic material. During folding some components of the displacement gradient suffer a finite jump, whereas during faulting the displacement itself displays a finite discontinuity.