论文标题
胶片/底物双层屈曲的精制模型
A refined model for the buckling of film/substrate bilayers
论文作者
论文摘要
膜/底物双层的经典还原模型是膜由Euler-Bernoulli束方程支配的膜，底物被弹簧阵列（所谓的Winkler Foundation假设）取代。我们得出了一个精致的模型，其中胶片底部的正常和剪切段用相应的水平和垂直位移表示，而半空间的响应由确切的理论描述。精制模型的自矛盾是通过证明其产生的（在不可压缩的情况下）或六个期（在可压缩的情况下）扩展的临界菌株的六个期（在不可压缩的情况下）的自一度，这与确切理论的扩展相符。
The classical reduced model for a film/substrate bilayer is one in which the film is governed by the Euler-Bernoulli beam equation and the substrate is replaced by an array of springs (the so-called Winkler foundation assumption). We derive a refined model in which the normal and shear tractions at the bottom of the film are expressed in terms of the corresponding horizontal and vertical displacements, and the response of the half-space is described by the exact theory. The self-consistency of the refined model is confirmed by showing that it yields a four-term (in the incompressible case) or six-term (in the compressible case) expansion for the critical strain that agrees with the expansion given by the exact theory.
