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

非均质材料中的宏观行为和场涨落：理论和应用本项目涉及具有非线性本构行为和复杂的、随机的微观结构的非均质材料系统。由于它们在科学和技术上的重要性，重点将放在粘塑性系统上，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，和(Iii)微结构演化。与实验者和数值分析员的密切互动将确保这项工作的实际意义，以及最终用于工业的数值工具的开发。有效行为用于在足够大的长度尺度上表征非均质材料的平均响应，并且可以通过适当的均化技术来估计。虽然对复合材料和多晶体的均匀化估计已经可用，但这里建议使用PI最近开发的“二阶”方法。这种方法已经被发现能够对一些模型、二维问题提供准确的估计，并建议将其应用于利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体的有效行为。这种“二阶”方法还有一个进一步的优点，那就是它能自动提供对场起伏的“第二时刻”的估计。场涨落可以用来测量复合材料组成相或多晶体中的颗粒中的应变和应力不均匀。这些信息可以用来模拟多晶体中孪晶和其他不稳定性的发展，以及复合材料中的早期失效。场波动还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情况下进行，其中微结构(孔的大小、形状、取向和分布)也已知在典型的变形过程中演变，如挤压或热锻造。这项工作的部分工作将与法国的三个CNRS实验室密切合作进行。在法国国家科学研究中心的支持下，这些实验室将进行补充的数值和实验研究。根据NSF/CNRS合作计划，将向国际方案司提交一份单独的提案，以支付额外的旅费。

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.