Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity models materials as
continua. Linear elasticity is a simplification of the more general
nonlinear theory of elasticity and is a branch of continuum mechanics. The fundamental "linearizing" assumptions of linear elasticity are:
infinitesimal strains or "small"
deformations (or strains) and linear relationships between the components of
stress and strain. In addition linear elasticity is valid only for stress states that do not produce
yielding. These assumptions are reasonable for many engineering materials and engineering design scenarios. Linear elasticity is therefore used extensively in
structural analysis and engineering design, often with the aid of
finite element analysis.