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Hooke's law states that the force required to deform elastic objects should be directly proportional to the distance of deformation, regardless of how large that distance becomes. This is known as perfect elasticity , in which a given object will return to its original shape no matter how strongly it is deformed.
Elastomers and shape memory metals such as Nitinol exhibit large elastic deformation ranges, as does rubber. However, elasticity is nonlinear in these materials. Normal metals, ceramics and most crystals show linear elasticity and a smaller elastic range. Linear elastic deformation is governed by Hooke's law, which states:
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
Compatibility conditions are mathematical conditions that determine whether a particular deformation will leave a body in a compatible state. [2] In the context of infinitesimal strain theory, these conditions are equivalent to stating that the displacements in a body can be obtained by integrating the strains.
Expressed in terms of components with respect to a rectangular Cartesian coordinate system, the governing equations of linear elasticity are: [1]. Equation of motion: , + = where the (), subscript is a shorthand for () / and indicates /, = is the Cauchy stress tensor, is the body force density, is the mass density, and is the displacement.
This phenomenon is called elastic deformation. This behavior in materials is described by Hooke's Law. Materials behave elastically until the deforming force increases beyond the elastic limit, which is also known as the yield stress. At that point, the material is permanently deformed and fails to return to its original shape when the force is ...
The first two make use of analytical formulations which apply mostly simple linear elastic models, leading to closed-form solutions, and can often be solved by hand. The finite element approach is actually a numerical method for solving differential equations generated by theories of mechanics such as elasticity theory and strength of materials.
Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials. [1] (Note however, the work done by a stretched rubber band is not an example of elastic energy. [citation needed] It is an example of entropic elasticity.) The elastic potential energy equation is used in calculations of positions of mechanical ...