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.

提出了一种基于连续介质力学的模型来描述具有微结构的材料之间弱化界面的机械行为。弱化界面由附着在两侧的表面弹性介质模拟，体弹性连续体表现出具有约束旋转的 Cosserat 材料的行为。在一般框架不变性考虑下，表明表面连续体的变形状态完全由延伸和旋转矢量指定，其中后者与表面连续体相切。与这些变形量共轭的是表面力和表面力偶，它们与作用在其连接表面上的体连续体的减小的力牵引力和减小的力偶牵引力处于局部平衡。描述小变形线性弹性背景下表面连续体力学行为的本构方程有五种关系，它们将表面力的每个分量线性相关，并耦合到延伸和旋转矢量的相应分量。可以说，表面连续体代表了弹簧型界面，因为它的行为可以看作是厚度消失的线性弹簧和扭转弹簧在其表面上连续分布。然后，使用所提出的模型研究弱化界面对嵌入无界基体中的球形不均匀性周围应力集中的影响，无界基体均由旋转受限的 Cosserat 材料组成。