The simplest relationship between stress and strain is known as linear elastic behaviour in which strain is directly proportional to the stress applied.
Linear elasticity :
Linear elasticity is a mathematical model that describes how solid objects deform and become internally stressed as a result of specific loading conditions. It is a branch of continuum mechanics and a simplified version of the more general nonlinear theory of elasticity. 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.
A linear elastic boundary value problem is governed by three tensor partial differential equations for linear momentum balance and six infinitesimal strain-displacement relations. A set of linear algebraic constitutive relations completes the system of differential equations.
Elastostatics :
Elastostatics is the study of linear elasticity under the conditions of equilibrium, in which all forces on the elastic body sum to zero, and the displacements are not a function of time.
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