Poromechanics Beyond the Second Law of Thermodynamics

超越热力学第二定律的孔隙力学

• 批准号: 1462749
• 负责人: Martin Starzewski
• 金额: $ 30万
• 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: 2015
• 资助国家: 美国
• 起止时间: 2015-06-01 至 2018-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1462749&HistoricalAwards=false
• 关键词: Poromechanics; Beyond; Second; Law; Thermodynamics

The entire field of continuum mechanics has been developed subject to the axiom of the second law of thermodynamics. This axiom implies a non-negative rate of irreversible entropy production. Yet, the results of contemporary physics have shown that this law does not hold at very small spatial and/or temporal scales. The fluctuation theorem instead describes entropy as a stochastic quantity that is exponentially more likely to be positive than negative and, upon ensemble averaging, leads to the conventional second law inequality. This theorem has already replaced the second law in considerations of the rheological and thermal responses of liquids. Consequently, the continuum models for fluid filled porous media must be reformulated. The research outcomes would be significant both for the fundamental understanding of geological, biological and man-made materials. In particular, mechanistic description of the material responses will be modified according to the microstructure and its characteristic length scales. As a result, this research will provide new insight into the mechanics of highly complex media such as gels, fluid-saturated rock systems, cardiovascular and pulmonary tissues. The PI plans to offer short courses related to the mechanics of random and fractal materials and structures, and will expand the delivery of a high-school-level short course on fractals. Selected images and animations obtained through the research will be integrated into outreach programs to enrich the K-12 educational system. Research supported under this award seeks to define a paradigm shift in continuum mechanics and, especially, poromechanics. The research aims to answer the question how the consideration of the fluctuation theorem may alter our understanding of the continuum mechanics of porous media. A stochastic thermomechanics framework with internal variables considering the fluctuation theorem in place of the second law axiom will be formulated. The admission of random scatter in nanoscale systems, with possible violations of the Clausius-Duhem inequality, will lead to a modification of Darcy's law, of the poromechanical constitutive relations and of the heat conduction relations. The new formulation would explicitly account for scale dependence. The effective permeability and heat conduction moduli are expected to turn out to be higher than as dictated by classical continuum theories. Next, homogenized constitutive descriptions will be established based on a micropolar theory for the use in random, and possibly fractal, fluid-saturated media. New forms of field and differential equations will be derived and employed to derive solutions of relevant initial-boundary value problems, thereby modifying the conventional solutions of problems of continuum poromechanics.

连续介质力学的整个领域都是在热力学第二定律的公理下发展起来的。这个公理意味着不可逆熵产生的非负速率。然而，当代物理学的结果表明，这一定律在非常小的空间和/或时间尺度上并不成立。涨落定理将熵描述为一个随机量，它以指数方式更可能是正的而不是负的，并且在系综平均时，导致了传统的第二定律不等式。在考虑液体的流变和热响应时，这个定理已经取代了第二定律。因此，必须重新表述流体填充多孔介质的连续介质模型。研究成果将对地质、生物和人造材料的基本认识具有重要意义。特别是，材料响应的机械描述将根据微观结构及其特征长度尺度进行修改。因此，这项研究将为高度复杂介质的力学提供新的见解，如凝胶，流体饱和岩石系统，心血管和肺组织。PI计划提供与随机和分形材料和结构力学相关的短期课程，并将扩大高中水平的分形短期课程的交付。通过研究获得的选定图像和动画将被整合到外展计划中，以丰富K-12教育系统。该奖项支持的研究旨在定义连续介质力学，特别是孔隙力学的范式转变。研究的目的是回答问题如何考虑的波动定理可能会改变我们的多孔介质的连续介质力学的理解。考虑涨落定理代替第二定律公理的随机热力学框架将制定与内部变量。在纳米尺度系统中的随机散射，可能违反克劳修斯-迪昂不等式的承认，将导致修改达西定律，的poromechanical本构关系和热传导关系。新的提法将明确说明比额表的依赖性。的有效渗透率和热传导模量预计会变成高于所规定的经典连续介质理论。接下来，均匀化的本构描述将建立在微极理论的基础上，用于随机的，可能是分形的，流体饱和介质。新形式的场和微分方程将被导出并用于导出相关的初边值问题的解，从而修改连续介质孔隙力学问题的传统解。