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The concept of strain is used to evaluate how much a given displacement differs locally from a rigid body displacement. [1] [8] [9] One of such strains for large deformations is the Lagrangian finite strain tensor, also called the Green-Lagrangian strain tensor or Green–St-Venant strain tensor, defined as
File:Lagrangian vs Eulerian [further explanation needed] Eulerian perspective of fluid velocity versus Lagrangian depiction of strain. In classical field theories, the Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time.
For infinitesimal deformations of a continuum body, in which the displacement gradient tensor (2nd order tensor) is small compared to unity, i.e. ‖ ‖, it is possible to perform a geometric linearization of any one of the finite strain tensors used in finite strain theory, e.g. the Lagrangian finite strain tensor, and the Eulerian finite strain tensor.
The concept of a continuum underlies the mathematical framework for studying large-scale forces and deformations in materials. Although materials are composed of discrete atoms and molecules, separated by empty space or microscopic cracks and crystallographic defects, physical phenomena can often be modeled by considering a substance distributed throughout some region of space.
Euler–Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams, and geometrically nonlinear beam deflection. Euler–Bernoulli beam theory does not account for the effects of transverse shear strain. As a result, it underpredicts deflections and overpredicts natural frequencies.
A two-dimensional flow that, at the highlighted point, has only a strain rate component, with no mean velocity or rotational component. In continuum mechanics, the strain-rate tensor or rate-of-strain tensor is a physical quantity that describes the rate of change of the strain (i.e., the relative deformation) of a material in the neighborhood of a certain point, at a certain moment of time.
The infinitesimal strain theory is used in the analysis of deformations of materials exhibiting elastic behavior, such as materials found in mechanical and civil engineering applications, e.g. concrete and steel. Large-displacement or large-rotation theory, which assumes small strains but large rotations and displacements.
Strain is a technical term with a precise technical dfinition, so in general Britannica may be right, but in technical discussion strain means something particular whereas "deformation" isn't well-defined (as far as I know). —Ben FrantzDale 14:43, 15 February 2007 (UTC) Deformation is the accumulation of strains.