This paper is concerned with a theory of elastic materials with voids where the second gradient of deformation and the second gradient of volume fraction field are added to the set of independent constitutive variables. First, we establish the nonlinear theory and study the continuous dependence of solutions upon initial state and body loads. Then, we derive the linear theory and establish a uniqueness theorem with no definiteness assumption on the constitutive coefficients. We present the equations for homogeneous and isotropic solids and establish a counterpart of the Boussinesq‐Somigliana‐Galerkin solution in the classical elastostatics. The effects of concentrated body loads acting in an infinite space are investigated.

中文翻译：

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多孔弹性固体的梯度理论

本文涉及具有空隙的弹性材料的理论，其中将第二变形梯度和体积分数场的第二梯度添加到一组独立的本构变量中。首先，我们建立非线性理论，研究溶液对初始状态和体载荷的连续依赖性。然后，我们推导出线性理论，并建立了本构系数没有确定性假设的唯一性定理。我们提出了均质和各向同性固体的方程，并建立了经典弹性静力学中的Boussinesq-Somigliana-Galerkin解的对应项。研究了在无限空间中集中的人体载荷的作用。