Spatial Elasticity Tensor in Eulerian Rate Type Constitutive Equations

In finite deformation analysis¡ the use of constitutive equations in rate form is often required. In a spatial setting¡ elastic modulus tensor relates some objective rate of a spatial stress tensor to the rate of deformation. It is important to know that¡ the spatial elastic modulus tensors of a material in different constitutive equations differ and relation between them may be interest for some researchers. In this paper¡ a general explicit formulation between the spatial elastic modulus tensors of some constitutive equations expressed. This formulation is a function of left Cauchy-Green tensor and its eigenvectors.