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The purpose of the present article is to make a model using analyticalequations, based on elasticity theory of continuous media for smalldeformations, with the aim of completely characterizing the material in theirmechanical properties as well as the principal stresses-strains of thin films.The approach differs from the standard literature which usually brings crystalsymmetries or is directly concerned with crystalline materials. It is entirelypossible to define and to analyze anisotropy in elastic media from firstprinciples in thin films. Therefore, the constitutive relation between strainand 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 onNewton's laws and energy conservation. As an application, it use the techniqueand data developed by Faurie et al (2005) in fiber-textured gold film depositedonto Kapton substrate by combining synchrotron X-Ray diffraction in situtensile testing. As the gold thin film and substrate are consideredtransversely isotropic, therefore, is firstly required a texture analysis withthe purpose of determining the possible Euler angles ($\phi$) and ($\psi$) foreach crystallographic direction that can be used in the model equations. Withthe data, it is possible to make graphics, $\varepsilon$ (strain) X F, forevery force applied to the sample. Comparing the experimental graphs with thetheoretical equations it was possible obtained their mechanical properties andthe principal stresses-strains of the anisotropic gold thin film. The resultsare compared with the results of Faurie et al (2005).

Elastic constants and stress-strain in thin films: application in fiber-textured gold film by X-Ray diffraction