A family of metric strains and conjugate stresses, prolonging usual material laws from small to large transformations

A new family of simple generalized strains and conjugate stresses based on the material metric (right Cauchy–Green) tensor is proposed. It includes an interesting quasilinear pair. It is a close approximation of the Seth–Hill family, with the advantage of being easier to calculate. It extends the realm of application of the classical theories of linear elasticity and perfect plasticity from small to large transformations for isotropic and anisotropic materials without any modification.