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In this section the basic expressions and notations for strain in cubic crystalline solids are established. A more detailed analysis can be found in textbooks [Bir74,Kittel96,Singh93]. Starting point for the definition of strain in a system is a set of orthonormal vectors and embedded in an unstrained solid. These vectors are distorted to , and under the influence of a uniform deformation
(3.1) |
For a uniform deformation of a body point originally located at the displacement to is defined as
(3.2) |
(3.3) |
(3.4) |
Thus, the displacements can be written as .
Usually, instead of the displacements , the strain tensor is used to quantify the the deformation of an body in three dimensions. In the case of small deformations, the strain tensor is known as the Green tensor or Cauchy's infinitesimal strain tensor, which is defined as
Frequently, in literature the engineering strains are used which are related to the components of the strain tensor via
(3.6) |
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