Search results
Results from the WOW.Com Content Network
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.
See the main article on constitutive relations for a fuller description. [15]: 44–45 For materials without polarization and magnetization, the constitutive relations are (by definition) [9]: 2 =, =, where ε 0 is the permittivity of free space and μ 0 the permeability of free space. Since there is no bound charge, the total and the free ...
For an isotropic material the Cauchy stress tensor can be expressed as a function of the left Cauchy-Green tensor =.The constitutive equation may then be written: = (). In order to find the restriction on which will ensure the principle of material frame-indifference, one can write:
The hyperelastic material is a special case of a Cauchy elastic material. For many materials, linear elastic models do not accurately describe the observed material behaviour. The most common example of this kind of material is rubber, whose stress-strain relationship can be defined as non-linearly elastic, isotropic and incompressible.
Materials where either pair of fields is not parallel are called anisotropic. In bi-isotropic media, the electric and magnetic fields are coupled. The constitutive relations are = + = + D, E, B, H, ε and μ are corresponding to usual electromagnetic qualities.
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.
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 ...
Such materials are conservative and the stresses in the material can be derived by a scalar elastic potential, more commonly known as the Strain energy density function. The constitutive relation between the stress and strain can be expressed in different forms based on the chosen stress and strain forms.