We introduce the surface viscoelasticity under finite deformations. The theory is straightforward generalization of the Gurtin–Murdoch model to materials with fading memory. Surface viscoelasticity may reflect some surface related creep/stress relaxation phenomena observed at small scales. Discussed model could also describe thin inelastic coatings or thin interfacial layers. The constitutive equations for surface stresses are proposed. As an example we discuss propagation shear (anti-plane) waves in media with surface stresses taking into account viscoelastic effects. Here we analysed surface waves in an elastic half-space with viscoelastic coatings. Dispersion relations were derived.

我们引入有限变形下的表面粘弹性。该理论是古廷-默多克模型对记忆衰退材料的直接推广。表面粘弹性可以反映在小尺度下观察到的一些与表面相关的蠕变/应力松弛现象。讨论的模型还可以描述薄的非弹性涂层或薄的界面层。提出了表面应力的本构方程。作为一个例子，我们讨论在具有表面应力的介质中传播剪切（反平面）波，并考虑粘弹性效应。在这里，我们分析了具有粘弹性涂层的弹性半空间中的表面波。导出了色散关系。