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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.
The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law.It deals with the case of linear elastic materials.Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
Orthotropic materials are a subset of anisotropic materials; their properties depend on the direction in which they are measured. Orthotropic materials have three planes/axes of symmetry. An isotropic material, in contrast, has the same properties in every direction. It can be proved that a material having two planes of symmetry must have a ...
Young's modulus represents the factor of proportionality in Hooke's law, which relates the stress and the strain. However, Hooke's law is only valid under the assumption of an elastic and linear response. Any real material will eventually fail and break when stretched over a very large distance or with a very large force; however, all solid ...
For small strains, the measure of stress that is used is the Cauchy stress while the measure of strain that is used is the infinitesimal strain tensor; the resulting (predicted) material behavior is termed linear elasticity, which (for isotropic media) is called the generalized Hooke's law. Cauchy elastic materials and hypoelastic materials are ...
The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: . Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),
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: = where σ is the applied stress;
Material failure theory is an interdisciplinary field of materials science and solid mechanics which attempts to predict the conditions under which solid materials fail under the action of external loads. The failure of a material is usually classified into brittle failure or ductile failure .