We generalize Hashin’s nonlinear isotropic hollow cylinder and sphere assemblages to nonlinear anisotropic solids. More specifically, we find the effective hydrostatic constitutive equation of nonlinear transversely isotropic hollow sphere assemblages with radial material preferred directions. We also derive the effective constitutive equations of finite and infinitely-long hollow cylinder assemblages made of incompressible orthotropic solids with axial, radial, and circumferential material preferred directions. In both sphere and cylinder assemblages the spherical and cylindrical shells can be radially inhomogeneous as long as Hashin’s definition of similar shells is properly generalized.

我们将 Hashin 的非线性各向同性空心圆柱体和球体组合推广到非线性各向异性固体。更具体地说，我们找到了具有径向材料优选方向的非线性横向各向同性空心球组合的有效流体静力本构方程。我们还推导出了由具有轴向、径向和圆周材料优先方向的不可压缩正交各向异性固体制成的有限和无限长空心圆柱组合的有效本构方程。在球体和圆柱体组合中，球体和圆柱体壳可以在径向上不均匀，只要 Hashin 对相似壳的定义被适当地概括。