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Real-world solids, such as rocks, soft tissues, and engineering materials,are often under some form of stress. Most real materials are also, to somedegree, anisotropic due to their microstructure, a characteristic often calledthe `texture anisotropy'. This anisotropy can stem from preferential grainalignment in polycrystalline materials, aligned micro-cracks, or structuralreinforcement, such as collagen bundles in biological tissues, steel rods inprestressed concrete and reinforcing fibres in composites. Here we establish aframework for initially stressed solids with transverse texture anisotropy. Weconsider that the strain energy per unit mass of the reference is an explicitfunction of the elastic deformation gradient, the initial stress tensor, andthe texture anisotropy. We determine the corresponding constitutive relationsand develop examples of nonlinear strain energies which depend explicitly onthe initial stress and direction of texture anisotropy. As an application, wethen employ these models to analyse the stress distribution of an inflatedinitially stressed cylinder with texture anisotropy, and the tension of awelded metal plate. We also deduce the elastic moduli needed to describe linearelasticity from stress reference with transverse texture anisotropy. As anexample we show how to measure the stress with small-amplitude shear waves.

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