论文标题
Winkler的床垫模型用于薄弹性层的有效性：超越泊松比
Validity of Winkler's mattress model for thin elastomeric layers: Beyond Poisson's ratio
论文作者
论文摘要
Winkler的床垫模型通常被用作简化的模型，以了解在受分布式正常负载的约束时薄薄的弹性层如何变形：假定该层的变形与所施加的正常负载成正比。这种简单意味着Winkler模型已经发现了从软物质到地球物理学的广泛应用。但是，在不可压缩的弹性层的极限下，该模型预测了对变形的无限耐药性，因此破裂。由于应用中使用的许多薄层都是弹性的，因此接近不可压缩，我们考虑了何时适合此类层的Winkler模型的问题。我们正式得出了一个模型，该模型在薄弹性层之间在Winkler和不可压缩的限制之间进行了插值，并通过详细考虑了两个示例问题来说明此模型：涂层弹性体层的点凹痕和软弹性氢化动力学润滑的涂层弹性层和自我维持的升力。我们发现，Winkler模型的适用性（或其他方式）不是由泊松比的值决定，而是由将Poisson比与层的细长度相结合的可压缩参数确定，该参数取决于所考虑的问题。
Winkler's mattress model is often used as a simplified model to understand how a thin elastic layer, such as a coating, deforms when subject to a distributed normal load: the deformation of the layer is assumed proportional to the applied normal load. This simplicity means that the Winkler model has found a wide range of applications from soft matter to geophysics. However, in the limit of an incompressible elastic layer the model predicts infinite resistance to deformation, and hence breaks down. Since many of the thin layers used in applications are elastomeric, and hence close to incompressible, we consider the question of when the Winkler model is appropriate for such layers. We formally derive a model that interpolates between the Winkler and incompressible limits for thin elastic layers, and illustrate this model by detailed consideration of two example problems: the point indentation of a coated elastomeric layer and self-sustained lift in soft elastohydrodynamic lubrication. We find that the applicability (or otherwise) of the Winkler model is not determined by the value of the Poisson ratio alone, but by a compressibility parameter that combines the Poisson ratio with a measure of the layer's slenderness that depends on the problem under consideration.
