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In this thesis, the constitutive equation for incompressible, anisotropic materials with finite strains is developed on convected coordinate system. A general form of the constitutive equation for anisotropic materials, where the principal directions are curvilinear, is derived. This derivation is b...

In this thesis, the constitutive equation for incompressible, anisotropic materials with finite strains is developed on convected coordinate system. A general form of the constitutive equation for anisotropic materials, where the principal directions are curvilinear, is derived. This derivation is based on hyperelastic theory of the material and represented theorem of invariant. Also adequate finite element formulation with the same coordinate systems is developed. The formulation is based on hyperelastic theory of the material and mixed finite element method. To demonstrate the applicability of the developed constitutive equation, derivation of specific forms of the constitutive equation for specific types of material anisotropy is discussed. Particularly for transversely isotropic case, it is shown that an explicit form of the equation can be systematically derived by the method presented in this thesis. The present work could be effectively used in the analysis of the structures of composites such as biological tissues and reinforced rubber-like composite materials.

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