Homogenization and global responses of inhomogeneous spherical nonlinear elastic shells. (English) Zbl 1094.74046

Summary: Homogenization of radially inhomogeneous spherical nonlinear elastic shells subject to internal pressure is studied. The equivalent homogeneous material is defined in such a way that it gives rise to exactly the same global response to the pressure load as that of the inhomogeneous shell. For a shell with general strain-energy function and inhomogeneity, the strain-energy function of the equivalent homogeneous material is determined explicitly. The resulting formula is used to study layered composite shells. The equivalent homogeneous material for an infinitely fine layered composite shell is examined, and is found to give not only the same global response, but also the same average stress field as the composite shell does.


74Q15 Effective constitutive equations in solid mechanics
74K25 Shells
74E30 Composite and mixture properties
74B20 Nonlinear elasticity
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