On Hashin’s Hollow Cylinder and Sphere Assemblages in Anisotropic Nonlinear Elasticity

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.