Isotropic Materials
For a linear isotropic material subjected only to compressive (i.e. normal) forces, the deformation of a material in the direction of one axis will produce a deformation of the material along the other axis in three dimensions. Thus it is possible to generalize Hooke's Law (for compressive forces) into three dimensions:
or
where
- , and are strain in the direction of, and axis
- , and are stress in the direction of, and axis
- is Young's modulus (the same in all directions:, and for isotropic materials)
- is Poisson's ratio (the same in all directions:, and for isotropic materials)
These equations will hold in the general case which includes shear forces as well as compressive forces, and the full generalization of Hooke's law is given by:
where is the Kronecker delta and
Read more about this topic: Poisson's Ratio
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