Elasticity

Abstract

The theory of elasticity models rate-independent material behaviour without hysteresis. An elastic material is distinguished by the property that the current state of stress depends only on the current state of deformation, so that the memory part G in the reduced form (7.27) and (7.28) vanishes identically. A memory going back to past deformation processes does not exist; the most general constitutive equation in the theory of elasticity reads

$$\tilde{T} = g\left( C \right)$$

(9.1)

or

$$\tilde T = g\left( E \right)$$

(9.2)

Here, g(·): fym (V³) → fym(V³) is a symmetric tensor-valued function of the Cauchy-Green tensor C or Green strain tensor E.