A general approach to the mechanical analysis of continuous local inhomogeneity using continuum mechanics theory and a new general energy-based-model

While usually we don't know complete geometrical and physical information on the occurred inhomogeneity, but in order to study the related phenomena, continuum mechanics theory as well as exiting energy-based models need direct information from the desired system in order to A General Approach to the Mechanical Analysis of Continuous Local Inhomogeneity Using Continuum Mechanics Theory and A New General Energy-Based- Modelapply the field equations. Of course, theories and ideas based on the unification of mechanics and thermodynamics can offer other solutions. This paper establishes a general energy based model to study effects of local inhomogeneity on the mechanical behavior of materials using thermodynamic laws with a new deviation as well as new approach to the total energy. In fact, the main goal is that the established model can be used with a wide range of applications and appropriate accuracy, both theoretically and experimentally, while not getting involved with excessive computational complexity. It can be noted that the extracted formulations develop possibility to study inhomogeneity effects on the mechanical behavior without any more limiting conditions. In addition, due to that study of the stored and dissipated energy, usually, has the main role in the investigating of the inhomogeneity effects on the mechanical behavior, also the point of view in the presented model is in complete agreement to provide the conditions for this study directly. Therefore, the prediction possibility of the inhomogeneity effects on the mechanical behavior will be provided with the smallest volume of needed calculations. Also, due to that the structure and properties of the inhomogeneity are unknown usually, the formulations aren't dependent to these knowledge directly, and can be analyzed theoretically and experimentally to study the homogeneity part, as a known material. In the following, feasible processes are studied using extracted formulations. To validate the equations, a rectangular material shape with local inhomogeneity is considered, and extracted equations are developed for that. To consider our mean on the stored and dissipated energies, it is assumed that the homogeneity part of material has viscoelastic behavior, and the equations are developed to Maxwell and Kelvin viscoelastic models in different homogeneity parts of the body. In the following, classical continuum mechanic theory due to elasticity theory is used, and the field equations are developed to the considered body. Finally, results are discussed, compared as well as their differences, and corresponding capabilities for functional completion are discussed. Finally, the fundamental equivalence of the results is studied, and matching of the results between continuum mechanics theory and extracted formulations is shown.