In the present study, the effect of material microstructure on the mechanical response of a two-dimensional elastic layer perfectly bonded to a substrate is examined under surface loadings. In the current model, the substrate is treated as an elastic half plane as opposed to a rigid base, and this enables its applications in practical cases when the modulus of the layer (e.g., the coating material) and substrate (e.g., the coated surface) are comparable. The material microstructure is modeled using the generalized continuum theory of couple stress elasticity. The boundary value problems are formulated in terms of the displacement field and solved in an analytical manner via the Fourier transform and stiffness matrix method. The results demonstrate the capability of the present continuum theory to efficiently model the size-dependency of the response of the material when the external and internal length scales are comparable. Furthermore, the results indicated that the material mismatch and substrate stiffness play a crucial role in the predicted elastic field. Specifically, the study also addresses significant discrepancy of the response for the case of a layer resting on a rigid substrate.

在本研究中，在表面载荷下检查了材料微观结构对完美结合到基材上的二维弹性层的机械响应的影响。在当前模型中，基材被视为与刚性基材相对的弹性半平面，这使得它可以在实际情况下（例如涂层材料）和基材（例如涂层表面）的模量进行应用）具有可比性。使用耦合应力弹性的广义连续理论对材料的微观结构进行建模。边界值问题是根据位移场来表示的，并通过傅立叶变换和刚度矩阵方法以解析方式进行求解。结果表明，当外部长度尺度和内部长度尺度可比时，本连续理论能够有效地对材料响应的尺寸依赖性进行建模。此外，结果表明，材料失配和基底刚度在预测的弹性场中起着至关重要的作用。具体而言，该研究还解决了在刚性基板上放置一层的情况下响应的显着差异。