Weakened interfaces in Cosserat bi-materials with constrained rotation

Abstract

A continuum mechanics–based model is proposed to describe the mechanical behavior of a weakened interface lying between materials with microstructure. The weakened interface is simulated by a surface elastic medium adhering on either side with bulk elastic continua exhibiting behavior of Cosserat materials with constrained rotation. Under general frame invariance considerations, it is shown that the deformation state of the surface continuum is completely specified by an extension and a rotation vector with the latter being tangential to the surface continuum. Conjugate to these deformation quantities are a surface force and a surface couple being in local equilibrium with the reduced force traction and the reduced couple traction of the bulk continua acting on their connected surfaces. The constitutive equations describing the mechanical behavior of the surface continuum within the context of linear elasticity of small deformation are five relationships that linearly relate each component of the surface force and couple to the corresponding component of the extension and rotation vector. It can be said that the surface continuum represents a spring-type interface since its behavior can been seen as that of linear and torsional springs of vanishing thickness distributed continuously over its surface. Then, the proposed model is used to investigate the effect of a weakened interface on the stress concentration around a spherical inhomogeneity embedded in an unbounded matrix both of which consist of Cosserat materials with constrained rotation.