Macroscopic Behavior and Field Fluctuations in Random Heterogeneous Materials: Theory and Applications

随机异质材料的宏观行为和场涨落：理论与应用

• 批准号: 0201454
• 负责人: Pedro Ponte Castaneda
• 金额: --
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-01 至 2006-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0201454&HistoricalAwards=false
• 关键词: Macroscopic; Behavior; Field; Fluctuations; Random

Macroscopic Behavior and Field Fluctuations in Heterogeneous Materials: Theory and Applications This project is concerned with heterogeneous material systems with nonlinear constitutive behavior and complex, random microstructures that evolve in time. Because of their scientific and technological importance, the focus will be on viscoplastic systems including porous and other composite materials, as well as polycrystals. There are three principal themes that will be investigated in the context of multi-scale modeling of these material systems: (i) macroscopic, or effective behavior, (ii) field fluctuations, and (iii) microstructure evolution. Close interactions with experimentalists and numerical analysts will ensure the practical relevance of the work, as well as the development of numerical tools for eventual industrial use. The effective behavior serves to characterize the average response of heterogeneous materials at a sufficiently large length scales, and can be estimated by means of suitable homogenization techniques. Although homogenization estimates are already available for composites and polycrystals, it is proposed here to make use of the "second-order'" method that has been developed recently by the PI. This method has been found to deliver accurate estimates for some model, two-dimensional problems and it is proposed to apply it to model the effective behavior of three-dimensional viscoplastic composites and polycrystals using experimentally measured microstructural information. This "second-order'" method has the further advantage that it automatically delivers estimates for the "second moments" of the field fluctuations. The field fluctuations can be used to measure the strain and stress heterogeneities in the constituent phases of a composite, or grains in a polycrystal. Such information can be useful to model the development of twinning and other instabilities in polycrystals, as well as incipient failure in composites. The field fluctuations can also be used to generate more accurate (and smoother) predictions for texture evolution. Analogous investigations can also be carried out in the context of porous materials, where the microstructure (pore size, shape, orientation and distribution) is also known to evolve during a typical deformation process, such as extrusion or hot forging. Parts of this work will be carried out in close collaboration with three C.N.R.S. laboratories in France. Complementary numerical and experimental investigations will be carried out in these laboratories, which will be supported by the CNRS in France. A separate proposal will be submitted to the Division of International Programs for additional travel expenses under the NSF/CNRS cooperative scheme.

异质材料中的宏观行为和场波动：理论与应用该项目涉及具有非线性本构行为和随时间演化的复杂、随机微观结构的异质材料系统。由于其科学和技术重要性，重点将放在粘塑性系统上，包括多孔材料和其他复合材料以及多晶体。在这些材料系统的多尺度建模背景下将研究三个主要主题：（i）宏观或有效行为，（ii）场波动，以及（iii）微观结构演化。与实验学家和数值分析师的密切互动将确保工作的实际相关性，以及开发用于最终工业用途的数值工具。有效行为用于表征异质材料在足够大的长度尺度上的平均响应，并且可以通过合适的均质化技术来估计。尽管均质化估计已经可用于复合材料和多晶，但这里建议使用 PI 最近开发的“二阶”方法。已发现该方法可以为某些模型、二维问题提供准确的估计，并建议将其应用于使用实验测量的微观结构信息来模拟三维粘塑性复合材料和多晶的有效行为。这种“二阶”方法还有一个优点，即它可以自动提供场波动“二阶矩”的估计。场波动可用于测量复合材料的组成相或多晶中的晶粒的应变和应力异质性。这些信息可用于模拟多晶中孪生和其他不稳定性的发展以及复合材料中的初期失效。场波动还可用于生成更准确（且更平滑）的纹理演化预测。类似的研究也可以在多孔材料的背景下进行，其中微观结构（孔径、形状、方向和分布）也已知在典型的变形过程（例如挤压或热锻造）中演变。这项工作的部分内容将与三个 C.N.R.S. 密切合作进行。法国的实验室。这些实验室将进行补充性的数值和实验研究，并得到法国国家科学研究中心的支持。将向国际项目司提交一份单独的提案，以了解 NSF/CNRS 合作计划下的额外差旅费用。