  The purpose of the present article is to make a model using analytical
equations, based on elasticity theory of continuous media for small
deformations, with the aim of completely characterizing the material in their
mechanical properties as well as the principal stresses-strains of thin films.
The approach differs from the standard literature which usually brings crystal
symmetries or is directly concerned with crystalline materials. It is entirely
possible to define and to analyze anisotropy in elastic media from first
principles in thin films. Therefore, the constitutive relation between strain
and stress will be considered orthotropic, obeying the generalized Hooke's law.
A new equation for the stress of the film-substrate system is proposed based on
Newton's laws and energy conservation. As an application, it use the technique
and data developed by Faurie et al (2005) in fiber-textured gold film deposited
onto Kapton substrate by combining synchrotron X-Ray diffraction in situ
tensile testing. As the gold thin film and substrate are considered
transversely isotropic, therefore, is firstly required a texture analysis with
the purpose of determining the possible Euler angles ($\phi$) and ($\psi$) for
each crystallographic direction that can be used in the model equations. With
the data, it is possible to make graphics, $\varepsilon$ (strain) X F, for
every force applied to the sample. Comparing the experimental graphs with the
theoretical equations it was possible obtained their mechanical properties and
the principal stresses-strains of the anisotropic gold thin film. The results
are compared with the results of Faurie et al (2005).
