Hypo-Elastic Problems

Abstract

This thesis consists of five chapters. In chapter I, the problem of initial stress has been analysed. The limitations of the existing theories of isotropic elasticity gave rise to the need for an altogether new approach to the problem. Consequently hypo-elasticity, a new theory of elastic response based on time rates, was proposed in 1955 by Truesdell (14). Details of its formulation are given here to show that the theory is dynamical sound. Its main features have also been described. the relations of hypo elasticity to other theories of elasticity and plasticity have been shown. That this new theory in some cases predicts yield without assuming an yield condition indicates its strength and potentials relevance. Later in this chapter, we have described fluent bodies recently introduced by Walter Noll (18) as a special type of 'hygrosteric materials. The diagram to show various specials cases, especially hypo- elastic bodies is also attached. In Chapter II, we have discussed the problem of hypoelastic flexure for hypo elastic materials of grade zero. The exact solution of the constitutive equations, consistent with the equations of mass and motion and the boundary conditions, has been obtained without assuming any particular from of the stress strain relation. When compared with those obtained by seth (34) after assuming the linear stress-strain relation and with those obtained by Erickson (35) after using the strain energy function, our results happen to be similar to theirs. In hypo elasticity no particular form of the stress strain relation is assumed. It is rather the outcome of definite assumption regarding the motion. It depends on the manner in which the stress is applied in time.