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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至关重要。生物组织中的药物运输、电池中的充电和放电循环或合金中微结构的形成只是几个例子。然而，在那里，经典的菲克型扩散模型往往无法解释这些现象的复杂性，因此，更复杂的非经典扩散模型。鉴于这些模型的多样性，该项目的总体目标是澄清非经典扩散模型的微观力学起源。因此，第一和第二梯度型刚性扩散器和微形态型扩散器的通用类已经在第一项目阶段中使用不同的计算方法（例如，有限元、自然单元和等几何分析）来制定和实施。在此基础上，计算均匀化正在并将进一步进行，以确定未知的宏观尺度的本构响应在微观尺度上的本构响应。根据微结构的特征长度，我们认为微尺度问题是平稳的或非平稳的，这导致了宏观尺度解的尺寸效应。为了更好地解释在微观层面上的小长度尺度，我们建议在第二个项目阶段的引入和制定充满活力的界面在微观尺度上描述的现象，如异常扩散沿着或跨界面或表面张力时，耦合到变形。在许多工程应用中，扩散伴随着变形，因此它们的耦合特别重要，并将在计算均匀化的框架内进行深入研究。此外，为了进一步阐明扩散过程的微观力学，我们计划采用离散模型，并确定其对宏观尺度的解决方案的影响。我们相信该项目的成果在工程和材料科学中特别重要，例如对于新材料或连接工艺的开发。