Abstract
Deformation This chapter introduces the basic definitions of displacement and strain, establishes relations between these two field quantities, and investigates requirements to ensure single-valued, continuous displacement fields. As appropriate for linear elasticity, these kinematical results are developed under the conditions of small deformation theory. The study begins with the development of the basic field equations of elasticity theory by first investigating the kinematics of material deformation. As a result of applied loadings, elastic solids will change shape or deform, and these deformations can be quantified by knowing the displacements of material points in the body. The continuum hypothesis establishes a displacement field at all points within the elastic solid. Using appropriate geometry, the particular measures of deformation can be constructed leading to the development of the strain tensor. The strain components are related to the displacement field. Developments in this chapter lead to two fundamental sets of field equations: the strain-displacement relations and the compatibility equations.
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