Linear elasticity: Difference between revisions

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{{Multiplemergefrom|[[Elastic wave]] and [[3-D elasticity]]|date=June 2007}}

'''Linear elasticity''' is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions. Linear elasticity relies upon the continuum hypothesis and is applicable at macroscopic (and sometimes microscopic) length scales. 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: "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is only valid for stress states that do not produce [[Yield (engineering) |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 through the aid of [[finite element analysis]]. This article presents a summary of some of the basic equations used to describe linear elasticity mathematically in tensor notation. For an alternative presentation using engineering notation, see the article on [[3-D elasticity]].

'''Linear elasticity''' models the macroscopic mechanical properties of solids assuming "small" deformations.

It is a key part of [[3-D elasticity|elasticity theory]], which described the initial part

of [[Deformation|deformation of solids]] under an external [[Stress (physics)|stress]].

Linear elasticity has a well-defined mathematical theory which describes well a wide

range of [[solids]].

The current page summarizes some of the basic equations used to describe linear elasticity

mathematically in tensor notation. For an alternative notation to describe

linear elasticity, see the article on [[3-D elasticity]].

== Basic equations ==