TABLE OF CONTENTS The constitutive law of the material is an essential ingredient in any structural design analysis. It provides the indispensable relation between strains and stresses, a linear relation in the case of elastic analyses (Hooke's law), and a much more complex non-linear relation in inelastic analyses, involving time and additional internal variables.
This book is limited to the traditional continuous medium approach, i.e. the representative volume element (RVE) of the material is considered under quasi-uniform macroscopic strain or stress. This continuous medium hypothesis amounts to neglecting the local heterogenity of stresses and strains within the RVE, by working on averaged quantities, the effects of the heterogenities operating only indirectly through a certain number of internal variables. Furthermore, within the framework of the local state method of thermo-mechanics of continuous media, it is assumed that the state of a material point (or of its immediate neighborhood in the sense of RVE) is independent of the state of the neighboring material point, and that the stress or strain gradients do not operate in the constitutive equations. This hypothesis is obviously questioned in recent theories on the mechanics of generalized continuous media, which will not be addressed here.
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This entire study is limited to quasi-static movements, which are considered to be sufficiently slow, within the framework of small perturbations (small strains, less than 20% for example). Furthermore, the indicated laws will be formulated without introducing the influence of temperature (though it can be very significant in some cases). In other words,...
