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On the Formulation and the Micromechanical Origin of Non-Classical Models of Diffusion

关于非经典扩散模型的表述和微观力学起源

基本信息

批准号：
214100946
负责人：
Professor Dr.-Ing. Paul Steinmann
金额：
--
依托单位：
Lehrstuhl für Technische Mechanik (LTM)
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2012
资助国家：
德国
起止时间：
2011-12-31 至 2021-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/214100946?language=en
关键词：
Formulation Micromechanical Origin Non Classical

项目摘要

Diffusion processes are of utmost importance for a variety of applications in engineering and natural sciences. Drug transport in biological tissue, charge and discharge cycles in batteries, or the formation of microscructures in alloys are just a few examples. There, however, the classical diffusion model of Fickian-type often fails in explaining the complex nature of these phenomena and thus, more sophisticated non-classical diffusion models are employed. In view of the diversity of these models, the overarching goal of the project is thereby the clarification of the micromechanical origin of non-classical diffusion models. Therefore, a generic class of first and second gradient-type rigid diffusors and micromorphic-type diffusors has been formulated and implemented in the first project phase using different computational methods, e.g. finite elements, natural elements, and isogeometric analysis. Based on that, computational homogenization is and will further be carried out to determine the unknown macroscale constitutive response from the constitutive response at the microscale. Dictated by the characteristic length of the underlying microstructure, we consider the microscale problem to be either stationary or instationary, which induces size effects to the macroscale solution. To better account for small length scales at the micro-level, we propose for the second project phase the introduction and formulation of energetic interfaces at the microscale to describe phenomena like anomalous diffusion along or across an interface or surface tension when coupled to deformation. In numerous engineering applications, diffusion accompanies deformation, for which reason their coupling is particularly important and will be intensively studied within the framework of computational homogenization. Moreover, to further elucidate the micromechanics of diffusion processes we plan to employ a discrete model and identify its impact on the macroscale solution. We believe that the outcome of the of this project is of particular importance in engineering and material sciences, e.g. for the development of new materials or joining processes.

扩散过程对于工程和自然科学中的各种应用都是极其重要的。药物在生物组织中的传输，电池的充放电循环，或合金中微结构的形成，只是其中的几个例子。然而，Fickian类型的经典扩散模型往往不能解释这些现象的复杂性质，因此，采用了更复杂的非经典扩散模型。鉴于这些模型的多样性，该项目的首要目标是澄清非经典扩散模型的微观起源。因此，在项目第一阶段，采用了不同的计算方法，如有限元、自然单元和等几何分析，建立并实施了一类通用的第一和第二梯度型刚性扩散器和微形态扩散器。在此基础上，正在并将进一步进行计算均匀化，从微观尺度的本构响应确定未知的宏观尺度本构响应。由微观结构的特征长度决定，我们认为微观尺度问题要么是静止的，要么是暂定的，这就导致了宏观尺度解的尺寸效应。为了更好地解释微观层面上的小长度尺度，我们建议在第二个项目阶段引入和制定微观尺度上的高能界面，以描述沿界面或跨界面的异常扩散或与变形耦合时的表面张力等现象。在许多工程应用中，扩散伴随着变形，因此它们的耦合尤为重要，并将在计算均匀化的框架内进行深入的研究。此外，为了进一步阐明扩散过程的微观力学，我们计划使用离散模型并确定其对宏观解的影响。我们认为，该项目的成果在工程和材料科学方面具有特别重要的意义，例如在开发新材料或加入工艺方面。