Mesoscopic description of physical processes in structural materials is one of the most challenging aspects of understanding their behavior as it is the regime where atomic length scales merge with those of the continuum. It is the least understood regime compared to the atomic and continuum scales because the simplifications and advantages of theory in handling small/large length scales and fast/slow time scales no longer apply. One of the most challenging problems that has not been solved to date is how correlated defect domains affect the microstructure on the mesoscale and thus also the physical properties of materials. This problem will be solved by combining the classical Landau theory of phase transitions with the seminal 1958 work of Kröner in which dislocations are viewed as sources of incompatibility of elastic strains. The coupling of the microstructure with the incompatibility of strains will give rise to a new framework for the study of such mesoscale phenomena. In this formalism point defects will reduce to a simpler case as their fields are irrotational and thus do not contribute to the incompatibility of strains. The mesoscopic framework that will be developed in this project will contribute significantly to bridging of the so-called micron gap in the description of physical processes in crystalline materials. The role of defects, interfaces and microstructure is at the heart of understanding materials from nanometers to microns and the unique approach proposed here will address this issue. Implementing this theory will yield a mesoscopic computational tool for solving the inverse problem - designing novel materials with prescribed properties, such as resistance to fatigue and radiation damage.
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