SGER: Fractals, Anomalous Heat Conduction and Thermoelasticity

SGER：分形、反常热传导和热弹性

• 批准号: 0833070
• 负责人: Martin Starzewski
• 金额: --
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-05-01 至 2009-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0833070&HistoricalAwards=false
• 关键词: SGER; Fractals; Anomalous; Heat; Conduction

ABSTRACTResearch Objectives and ApproachesThe principal objective of this project is to develop a continuum thermoelasticity of materials with anomalous (non-Fourier type) heat conduction from the standpoint of fractal material structures. This will substantially broaden the scope of materials whose mechanics can be handled by partial differential equations. While the conventional mate¬rials in most continuum theories are assumed to be smooth and to satisfy the postulate of separation of scales, the planned research, being focused on fractal materials, will drop that requirement. New forms of differential equations will be derived and employed in solution of the initial-boundary value problems, and new fundamental understanding of constitutive responses (thermo-elasticity and thermo-viscoelasticity) of various materials having fractal geometries will be developed. Societal BenefitsThis project will have impact on the applicability of continuum mechanics (and physics) to studies of material response. The highly complex media which have so far been the domain of condensed matter physics, geophysics and biophysics etc. (polymer clusters, gels, rock systems, percolating networks, nervous systems, pulmonary systems...) will become open to studies conventionally reserved for smooth materials. This will allow the set-up and solution of initial-boundary value problems of very complex/multiscale materials of both elastic and inelastic type. Two graduate students will be involved in this research. The proposed research goes hand-in-hand with the writing of a monograph Thermoelasticity with Finite Wave Speeds (for Oxford Mathematical Monographs) on thermoelastodynamics of materials with anoma¬lous heat conduction.

摘要：研究目的和方法本项目的主要目的是从分形材料结构的角度研究具有异常（非傅立叶型）热传导的材料的连续热弹性。这将大大拓宽材料的范围，其力学可以用偏微分方程来处理。虽然在大多数连续介质理论中，传统材料被假设为光滑的，并且满足尺度分离的假设，但计划研究的重点是分形材料，将放弃这一要求。新形式的微分方程将被导出并用于解决初始边值问题，并将发展对具有分形几何形状的各种材料的本构响应（热弹性和热粘弹性）的新的基本理解。社会效益本项目将对连续介质力学（和物理学）在材料响应研究中的适用性产生影响。迄今为止属于凝聚态物理、地球物理学和生物物理学等领域的高度复杂的介质（聚合物团簇、凝胶、岩石系统、渗透网络、神经系统、肺系统……）将向传统上为光滑材料保留的研究开放。这将允许建立和解决弹性和非弹性类型的非常复杂/多尺度材料的初始边界值问题。两名研究生将参与这项研究。拟议的研究与关于异常热传导材料的热弹性动力学的专著《有限波速热弹性》（牛津数学专著）的撰写密切相关。