Representing the stress and strain energy of elastic solids with initial stress and transverse texture anisotropy

Real-world solids, such as rocks, soft tissues and engineering materials, are often under some form of stress. Most real materials also, to degree, anisotropic due their microstructure, a characteristic called the ‘texture anisotropy’. This anisotropy can stem from preferential grain alignment in polycrystalline aligned micro-cracks or structural reinforcement, collagen bundles biological tissues, steel rods pre-stressed concrete reinforcing fibres composites. Here, we establish framework for initially stressed solids with transverse texture anisotropy. We consider that strain energy per unit mass reference is an explicit function elastic deformation gradient, initial stress tensor determine corresponding constitutive relations develop examples nonlinear energies depend explicitly on direction As application, then employ these models analyse distribution inflated cylinder tension welded metal plate. also deduce moduli needed describe linear elasticity example, show how measure small-amplitude shear waves.