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1.1 Content The characterization of materials behaviour is of importance in many research fields. From an analytical point of view, the mechanical behaviour of materials could be described either by using empirical laws based on experimental observations or by using a framework to develop constitutive laws. In the latter case, the thermodynamic of irreversible processes could be used as the framework. These constitutive laws are generally dedicated to complex problems and are thus developed in a three-dimensional context. Materials behave in different ways under loading but, under specific conditions, they all will generally exhibit instantaneous and time-dependant deformations. Instantaneous deformation could be elastic, plastic and so forth, while time-dependant deformation generally refers to the viscosity of the material. Moreover, as for the Navier-Stokes equation in fluid mechanics which is only valid for Newtonian fluids, constitutive laws are developed considering the nature of the materials. Hence, in this chapter, targeted materials are isotropic granular materials such as concrete, carbon block materials and ramming paste (Sorlie and Oye, 2010). Contrary to metals, this implies that the tensile behaviour is different from the compressive one. Models are also meant to represent various phenomena such as creep and relaxation, which are mainly those of interest in this chapter. The upcoming sections will give a brief overview of the mechanical deformations such as creep/relaxation that are involved in viscoelasticity. Some basic principles governing the development of constitutive law modelling within a thermodynamic framework will be discussed, as well.

Three-Dimensional Constitutive Viscoelastic Model for Isotropic Materials