Accurate asymptotic solutions are presented for axisymmetric deformation of thin layers constrained by either two rigid plates or two rigid spheres. Those solutions are developed using Saint-Venant’s principle and the layer thinness as the only assumptions. The solutions are valid in the entire range of Poisson’s ratios, and allow one to distinguish among compressible, nearly incompressible, and incompressible layers. That classification involves both material and geometric parameters.

中文翻译：

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两个刚性表面之间可压缩，几乎不可压缩和不可压缩的薄层的轴对称变形

提出了由两个刚性板或两个刚性球约束的薄层的轴对称变形的精确渐近解。这些解决方案是使用Saint-Venant原理开发的，并且仅将层薄度作为假设。这些解决方案在整个泊松比范围内都是有效的，并且允许人们区分可压缩层，几乎不可压缩层和不可压缩层。该分类涉及材料和几何参数。