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

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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.