where are the deformation coefficients of the system.

Assuming a uniform deformation, a point located at will be shifted to , which leads to the displacement defined as

(3.2) |

Further generalization leads to a description for non-uniform deformation, introducing a position dependent vector function ,

(3.3) |

Restricting to small displacements from , the displacement function can be developed into a Taylor series and truncated after the linear term at , leading to a relation between the local displacement tensor and the displacement function,

Therefore, the displacement can be expressed as . Frequently, the displacements are expressed via the strain tensor to describe the deformation of a body in three dimensions. In the limit of small deformations, the strain tensor is known as the Green tensor or Cauchy's infinitesimal strain tensor,

(3.4) |

The relative length change in the direction is described by the diagonal coefficients , while the off-diagonal elements denote the angular distortions by shear strains.

Also very common are the engineering strains , which are linked with the strain tensor as follows:

(3.5) |

The Voigt notation uses the six indipendent components of the strain tensor in a more compact vector form

(3.6) |

T. Windbacher: Engineering Gate Stacks for Field-Effect Transistors