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<p>The present study provides an effective step in the advancement of relevant studies on the mechanical behavior of materials. Although bi-films have a great effect on the mechanical behavior as well as fracture of materials, most of our knowledge about this phenomenon is related to experimental predictions to the extent of knowing their structure and how they are formed. Regarding the formation and structure of bi-films as well as their laboratory limitations and scales, it is necessary to look for the general mathematical modeling of their mechanical behavior and development it to the most known behavior of them as viscoelasticity behavior. The size effects are considered using Eringen’s nonlocal elastic theory. In this paper, for the first time, mechanical analysis of bi-films is studied. Oxide films as double-layer cavities in the material structure create a combined system with connections between components that have a specific structure. In order to study their mechanical modeling efforts lead to sufficiently valuable results, it is necessary to investigate them with a special attitude. In this paper, considering all required thermal and mechanical variables with their changed classes, the second law of thermodynamics is considered using a novel version of the Borchers’ (Rep Math Phys 22:29–48, 1985) perspective. According to the mathematical structure and physical foundations of Borchers’ approach, it provides the possibility of generalization to composed systems and can be considered a special solution for the purpose of mechanical modeling of bi-films. In this paper, unified general energy-based model for all loading classes is established, and in the following, the extracted equations are developed considering nonlocal viscoelasticity theory. Due to the fact that strain has the main essential role in the investigation of the mechanical behavior of bi-films, established model is developed to the complete kinematic form as a reasonable form for the desired problem. Finally, the mathematical structure of the established model as well as its physical bases are studied and discussed generally using one of the well-known unified continuum mechanics approaches. An applied example is studied, and the matching of the results with the expected results is shown generally. It is concluded that due to that the established model simultaneously has the first and second laws of thermodynamics as its basis, and therefore, can be presented as a unified model to study mechanical behavior of bi-films.</p>

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General mechanical analysis of bi-films using a novel Borchers’ approach to the second law of thermodynamics and development to nonlocal viscoelasticity strain field

  • 期刊论文

  • 发表日期：

    2026年1月3日

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  • Saeed Shahsavari,
  • S. M. A. Boutorabi,
  • Mehran Moradi,
  • Pooya Torkaman

摘要

The present study provides an effective step in the advancement of relevant studies on the mechanical behavior of materials. Although bi-films have a great effect on the mechanical behavior as well as fracture of materials, most of our knowledge about this phenomenon is related to experimental predictions to the extent of knowing their structure and how they are formed. Regarding the formation and structure of bi-films as well as their laboratory limitations and scales, it is necessary to look for the general mathematical modeling of their mechanical behavior and development it to the most known behavior of them as viscoelasticity behavior. The size effects are considered using Eringen’s nonlocal elastic theory. In this paper, for the first time, mechanical analysis of bi-films is studied. Oxide films as double-layer cavities in the material structure create a combined system with connections between components that have a specific structure. In order to study their mechanical modeling efforts lead to sufficiently valuable results, it is necessary to investigate them with a special attitude. In this paper, considering all required thermal and mechanical variables with their changed classes, the second law of thermodynamics is considered using a novel version of the Borchers’ (Rep Math Phys 22:29–48, 1985) perspective. According to the mathematical structure and physical foundations of Borchers’ approach, it provides the possibility of generalization to composed systems and can be considered a special solution for the purpose of mechanical modeling of bi-films. In this paper, unified general energy-based model for all loading classes is established, and in the following, the extracted equations are developed considering nonlocal viscoelasticity theory. Due to the fact that strain has the main essential role in the investigation of the mechanical behavior of bi-films, established model is developed to the complete kinematic form as a reasonable form for the desired problem. Finally, the mathematical structure of the established model as well as its physical bases are studied and discussed generally using one of the well-known unified continuum mechanics approaches. An applied example is studied, and the matching of the results with the expected results is shown generally. It is concluded that due to that the established model simultaneously has the first and second laws of thermodynamics as its basis, and therefore, can be presented as a unified model to study mechanical behavior of bi-films.