Most solid bodies are porous and in such bodies we expect the material properties to vary with porosity and hence with the density. Such bodies whose properties depend on the density cannot be described by the classical linearized elastic constitutive relation when they are undergoing small deformations, as the material moduli cannot depend on density. A constitutive relation which is valid in the small displacement gradient range wherein the material moduli are dependent on the density can be developed by linearizing implicit constitutive relations for describing elastic bodies introduced recently by Rajagopal [1]. In this paper, we determine the stress concentration due to a hole in a slab that is subject to biaxial loading in a body described by such a constitutive relation. We find that the stress concentration can be much as 147% higher than that for classical linearized elasticity for the range of loadings considered in the study.

中文翻译：

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带孔多孔弹性体板双轴变形引起的应力集中

大多数固体都是多孔的，在这些实体中，我们预计材料属性会随着孔隙率和密度而变化。这种性质取决于密度的物体在经历小变形时不能用经典的线性弹性本构关系来描述，因为材料的模量不能取决于密度。在小位移梯度范围内有效的本构关系，其中材料模量取决于密度，可以通过线性化隐式本构关系来开发，用于描述 Rajagopal 最近引入的弹性体 [1]。在本文中，我们确定了由于承受双轴载荷的板坯中的孔而引起的应力集中，该孔由这种本构关系描述。