Search results
Results From The WOW.Com Content Network
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.
In homogeneous and isotropic materials, these define Hooke's law in 3D, = + (), where σ is the stress tensor, ε the strain tensor, I the identity matrix and tr the trace function. Hooke's law may be written in terms of tensor components using index notation as σ i j = 2 μ ε i j + λ δ i j ε k k , {\displaystyle \sigma _{ij}=2\mu ...
In mechanics, strain is defined as relative deformation, compared to a reference position configuration. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered.
The index n usually lies between the values of 2, for fully strain hardened materials, and 2.5, for fully annealed materials. It is roughly related to the strain hardening coefficient in the equation for the true stress-true strain curve by adding 2. [1] Note, however, that below approximately d = 0.5 mm (0.020 in) the value of n can surpass 3.
These include the Boltzmann constant, which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant, which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless).
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 other words, the Pockels effect is the basis of the operation of Pockels cells. By controlling the refractive index, the optical retardance of the crystal is altered so the polarization state of incident light beam is changed. Therefore, Pockels cells are used as voltage-controlled wave plates as well as other photonics applications.
Secondly, the strain history of all the material elements must be controlled and known. Thirdly, the strain rates and strain levels must be high enough to stretch the polymeric chains beyond their normal radius of gyration, requiring instrumentation with a large range of deformation rates and a large travel distance. [8] [9]