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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.
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:
The constant is called the modulus of elasticity (or just modulus) while its reciprocal is called the modulus of compliance (or just compliance). There are three postulates that define the ideal elastic behaviour: (1) the strain response to each level of applied stress (or vice versa) has a unique equilibrium value;
The elastic components, as previously mentioned, can be modeled as springs of elastic constant E, given the formula: = where σ is the stress, E is the elastic modulus of the material, and ε is the strain that occurs under the given stress, similar to Hooke's law.
In continuum mechanics, a compatible deformation (or strain) tensor field in a body is that unique tensor field that is obtained when the body is subjected to a continuous, single-valued, displacement field.
This is known as perfect elasticity, in which a given object will return to its original shape no matter how strongly it is deformed. This is an ideal concept only; most materials which possess elasticity in practice remain purely elastic only up to very small deformations, after which plastic (permanent) deformation occurs.
In physics and continuum mechanics, deformation is the change in the shape or size of an object. It has dimension of length with SI unit of metre (m). It is quantified as the residual displacement of particles in a non-rigid body, from an initial configuration to a final configuration, excluding the body's average translation and rotation (its rigid transformation). [1]
The elastic modulus of an object is defined as the slope of its stress–strain curve in the elastic deformation region: [1] A stiffer material will have a higher elastic modulus. An elastic modulus has the form: =