Abstract
The previous two chapters established elasticity field equations related to the kinematics of small deformation theory and the equilibrium of the associated internal stress field. Based on these physical concepts, six strain–displacement relations and three equilibrium equations were developed for the general three-dimensional case. Nine field equations have now been developed. The unknowns in these equations include three displacement components, six components of strain, and six stress components, yielding a total of 15 unknowns. Thus, the nine equations are not sufficient to solve for the 15 unknowns, and additional field equations are needed. This result should not be surprising since up to this point we have not considered the material response. We now wish to complete our general formulation by specializing to a particular material model that provides reasonable characterization of materials under small deformations. The model we use is that of a linear elastic material, a name that categorizes the entire theory. This chapter presents the basics of the elastic model for the special case of homogeneous and isotropic materials.
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