This work aims at studying the interfacial behavior of functionally graded coatings (FGCs) on different substrates, here modeled as asymmetric double cantilever beams, in line with the experimental tests. An enhanced beam theory (EBT) is proposed to treat the mixed-mode phenomena in such specimens, whose interface is considered as an assembly of two components of the coating/substrate system bonded together partially by an elastic interface. This last one is modeled as a continuous distribution of elastic–brittle springs acting along the tangential and/or normal direction depending on the interfacial mixed-mode condition. Starting with the Timoshenko beam theory, we determine the differential equations of the problem directly expressed in terms of the unknown interfacial stresses, both in the normal and tangential directions. Different distribution laws are implemented to define the functional graduation of the material in the thickness direction of the specimens, whose variation is demonstrated numerically to affect both the local and global response in terms of interfacial stresses, internal actions, energy quantities and load–displacement curves. The good accuracy of the proposed method is verified against predictions by a classical single beam theory (SBT), with interesting results that could serve as reference solutions for more expensive experimental investigations on the topic.

这项工作旨在研究功能梯度涂层（FGC）在不同基材上的界面行为，这里建模为不对称双悬臂梁，与实验测试一致。提出了增强梁理论（EBT）来处理此类样本中的混合模式现象，其界面被认为是涂层/基材系统的两个组件通过弹性界面部分粘合在一起的组件。最后一个模型被建模为根据界面混合模式条件沿切线和/或法线方向作用的弹性脆性弹簧的连续分布。从 Timoshenko 梁理论开始，我们确定了直接用未知界面应力（法向和切向方向）表示的问题的微分方程。采用不同的分布定律来定义材料在样本厚度方向上的功能分级，并通过数值证明其变化会影响界面应力、内部作用、能量和载荷-位移曲线方面的局部和全局响应。该方法的良好准确性通过经典单束理论（SBT）的预测得到了验证，有趣的结果可以作为该主题更昂贵的实验研究的参考解决方案。