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On Thermodynamic Consistency of Homogenization-Based Multiscale Theories

机译：基于均质化的多尺度理论的热力学一致性

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摘要

In this paper, the necessary and sufficient conditions for fulfilling the thermodynamic consistency of computational homogenization schemes in the framework of hierarchical multiscale theories are defined. The proposal is valid for arbitrary homogenization based multiscale procedures, including continuum and discontinuum methods in either scale. It is demonstrated that the well-known Hill-Mandel variational criterion for homogenization scheme is a necessary, but not a sufficient condition for the micro-macro thermodynamic consistency when dissipative material responses are involved at any scale. In this sense, the additional condition to be fulfilled considering that the multiscale thermodynamic consistency is established. The general case of temperature-dependent, higher order elastoplasticity is considered as theoretical framework to account for the material dissipation at micro and macro scales of observation. It is shown that the thermodynamic consistency enforces the homogenization of the nonlocal terms of the finer scale's free energy density; however, this does not lead to nonlocal gradient effects on the coarse scale. Then, the particular cases of local isothermal elastoplasticity and continuum damage are considered for the purpose of the proposed thermodynamically consistent approach for multiscale homogenizations.
机译：本文定义了在分层多尺度理论框架内满足计算均化方案热力学一致性的充要条件。该建议适用于基于任意均质化的多尺度程序，包括任一尺度的连续和不连续方法。结果表明，当涉及耗散材料响应的任何规模时，均质方案的众所周知的Hill-Mandel变分准则是必要的，但不是充分的条件。从这个意义上讲，考虑到建立了多尺度热力学一致性，需要满足的附加条件。温度相关的高阶弹塑性的一般情况被认为是在微观和宏观尺度上解释材料耗散的理论框架。结果表明，热力学一致性迫使较细尺度的自由能密度的非局部项均匀化。但是，这不会在粗尺度上导致非局部渐变效果。然后，考虑局部等温弹塑性和连续介质破坏的特殊情况，以提出用于多尺度均质化的热力学一致方法。

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  • 来源
    《Journal of engineering materials and technology》 |2017年第3期|031011.1-031011.9|共9页
  • 作者

    Felipe Lopez Rivarola; Guillermo Etse; Paula Folino;

  • 作者单位

    LMNI-INTECIN (UBA-CONICET), Facultad de Ingenieria, Universidad de Buenos Aires, Av. Las Heras 2214, Buenos Aires C1127AAR, Argentina;

    Department of "Construcciones y Estructuras," Facultad de Ingenieria, Universidad de Buenos Aires, Buenos Aires C1127AAR, Argentina;

    LMNI-INTECIN (UBA-CONICET), Facultad de Ingenierfa, Universidad de Buenos Aires, Av. Las Heras 2214, Buenos Aires C1127AAR, Argentina;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
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