<![CDATA[This research presents a profound methodological and scientific-critical appraisal of the fundamental logical and mathematical foundations of a scientific work published in the journal “EUREKA: Physics and Engineering”. As a result of a comprehensive analysis, seven (7) fundamental methodological errors that contradict the classical principles of continuum mechanics and the theory of thermoelasticity were identified and proven within the considered model: (A1) incorrect choice of primary state variables (unknowns) in continuum dynamics; (A2) misinterpretation of Saint-Venant’s kinematic compatibility equations as governing dynamic equations for the internal state of a body; (A3) unjustified reformulation of classical equilibrium equations without prior assurance of the integrability of the displacement field; (A4) strictly erroneous inclusion of the temperature effect into compatibility conditions that are purely geometric in nature; (A5) the physical and mathematical impossibility of specifying strain components as arbitrary functions on boundary surfaces (rendering the problem ill-posed); (A6) a linear contradiction in the ratio of unknowns to differential relations, leading to an overdetermined system; (A7) the artificial introduction of unjustified Poisson-type equations that do not stem from classical model principles. In this paper, each methodological deficiency is fully exposed through rigorous component-wise differentiation, precise analytical counterexamples, and reliance on classical fundamental literature. According to the findings of this appraisal, the mathematical structure of the analyzed model violates the most sacred principles of continuum mechanics; hence, the numerical results and scientific conclusions presented therein must be considered physically unreliable.]]>
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