ABSTRACT
The ultimate objective of ‘Modeling and Computing’ is to predict the deformation response of a geotechnical system subjected to loading. It is evident that the global behavior of a soil system is intimately related to the behavior of all the small elements of the soil. Thus, in order to evaluate the global deformation response, we must first formulate a constitutive model (i.e. stress-strain relationship) for an element of soil. In the initial stage of shearing, before the soil begins to yield, the stress-strain relationship is observed to be reversible which can be modeled by an ‘elastic constitutive law’. Furthermore, if the stress-strain relationship is linear then linear elasticity may be used as a model within a rather small range of strains.
An elastic material is defined as one for which the current stress depends only on the current strain without being influenced by the past history. If the stresses are considered as the derivatives of the ‘strain energy density function’ with respect to strains, then the resulting models are called the Green-elastic or the hyper-elastic models. In this chapter, we consider only this type of elastic model where the essential stress-strain relationships in the framework of ‘linear elasticity’ are presented.
