Editing Infinitesimal strain theory (section)

{{Short description|Mathematical model for describing material deformation under stress}}
{{More footnotes needed|date=August 2023}}
{{Continuum mechanics|cTopic=solid}}
In [[continuum mechanics]], the '''infinitesimal strain theory''' is a mathematical approach to the description of the [[deformation (mechanics)|deformation]] of a solid body in which the [[Displacement (vector)|displacements]] of the material [[particle]]s are assumed to be much smaller (indeed, [[infinitesimally]] smaller) than any relevant dimension of the body; so that its geometry and the constitutive properties of the material (such as [[density]] and [[stiffness]]) at each point of space can be assumed to be unchanged by the deformation.

With this assumption, the equations of continuum mechanics are considerably simplified. This approach may also be called '''small deformation theory''', '''small displacement theory''', or '''small displacement-gradient theory'''. It is contrasted with the [[finite strain theory]] where the opposite assumption is made.

The infinitesimal strain theory is commonly adopted in civil and mechanical engineering for the [[stress analysis]] of structures built from relatively stiff [[elasticity (physics)|elastic]] materials like [[concrete]] and [[steel]], since a common goal in the design of such structures is to minimize their deformation under typical [[Structural load|loads]]. However, this approximation demands caution in the case of thin flexible bodies, such as rods, plates, and shells which are susceptible to significant rotations, thus making the results unreliable.<ref>{{Cite book |last=Boresi, Arthur P. (Arthur Peter), 1924– |title=Advanced mechanics of materials |date=2003 |publisher=John Wiley & Sons |others=Schmidt, Richard J. (Richard Joseph), 1954– |isbn=1601199228 |edition=6th |location=New York |page=62 |oclc=430194205}}</ref>