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

非均质材料的宏观行为和场波动：理论与应用本项目关注具有非线性本构行为和随时间演变的复杂随机微观结构的非均质材料系统。由于其科学和技术的重要性，重点将放在粘塑性系统，包括多孔和其他复合材料，以及多晶体。在这些材料系统的多尺度建模的背景下，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。与实验人员和数值分析人员的密切互动将确保工作的实际相关性，以及为最终工业用途开发数值工具。有效行为用于表征在足够大的长度尺度上的非均匀材料的平均响应，并且可以通过适当的均匀化技术来估计。虽然均匀化估计已经可用于复合材料和多晶体，它建议在这里使用的“二阶”的方法，最近已经开发的PI。这种方法已被发现提供准确的估计，一些模型，二维问题，它建议将其应用到三维粘塑性复合材料和多晶体使用实验测量的微观结构信息的有效行为建模。这种"二阶"方法的另一个优点是，它自动提供场波动的"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体中的晶粒中的应变和应力不均匀性。这些信息可用于模拟多晶体中的孪晶和其他不稳定性的发展，以及复合材料的初期失效。场波动也可以用于生成更准确（和更平滑）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，取向和分布）也已知在典型的变形过程中演变，例如挤压或热锻造。这项工作的一部分将与三个C.N.R.S.密切合作进行。法国的实验室在法国国家科学研究中心的支持下，将在这些实验室进行补充性的数值和实验研究。根据NSF/CNRS合作计划，将向国际方案司提交一份单独的建议书，以增加差旅费。

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.