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The development of technological methods for processing and manufacturing of functional (with a priori targeted properties) polycrystalline materials and products made of these materials still remains an acute problem. A multilevel modeling approach offers researchers the opportunity to describe inelastic deformation by applying internal variables that give an effective characterization of the material structure at different structural scale levels. High temperature plastic deformation is accompanied by these processes, which leads to a significant rearrangement of the meso- and microstructure of the material. The most substantial contribution to changing the properties of polycrystals is made by the evolution of grain and defect structures at the expense of dynamic recrystallization, which significantly depends on dynamic recovery. In this paper, we consider the problem of the coalescence of subgrains undergoing rotation during inelastic hot deformation. This process is called subgrain coalescence, and it is one of the dynamic recovery mechanisms responsible for changes in the fine subgrain structure. Under applied thermomechanical loads, the coalescence process promotes the formation of recrystallization nuclei and their subsequent growth, which can greatly change the grain structure of a polycrystal. The problem was solved in terms of the advanced statistical model of inelastic deformation, modified to describe the subgrain coalescence process. The model takes into account the local interactions between contacting structural elements (subgrains). These have to be considered so that the grain coalescence caused by a decrease in subboundary energies during their progressive merging can be adequately analyzed. For this purpose, a subgrain structure quite similar to the real structure was modeled using Laguerre polyhedra. Subgrain rotations were investigated using the developed model, which relies on the consideration of the excess density edge component of the same sign dislocations on incidental subgrain boundaries. The results of modeling of a copper polycrystal are presented, and the effects of temperature and strain rate on the subgrain coalescence process is demonstrated.

A group of authors has developed a multilevel mathematical model that focuses on functional disorders in a human body associated with various chemical, physical, social, and other factors. At this point, the researchers have come up with structure, basic definitions and concepts of a mathematical model at the “macrolevel” that allow describing processes in a human body as a whole. Currently we are working at the “mesolevel” of organs and systems. Due to complexity of the tasks, this paper deals with only one meso-fragment of a digestive system model. It describes some aspects related to modeling multiphase flow in the antroduodenal portion of the gastrointestinal tract. Biochemical reactions, dissolution of food particles, and motor, secretory, and absorbing functions of the tract are taken into consideration. The paper outlines some results concerning influence of secretory function disorders on food dissolution rate and tract contents acidity. The effect which food density has on inflow of food masses from a stomach to a bowel is analyzed. We assume that the future development of the model will include digestive enzymes and related reactions of lipolysis, proteolysis, and carbohydrates breakdown.

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Physical multilevel models of inelastic deformation that take into account the material structure evolution hold promise for the development of functional materials. In this paper, we propose an advanced (modified via analyzing the mutual arrangement of crystallites) statistical multilevel model for studying thermomechanical processing of polycrystals that includes a description of the dynamic recrystallization process. The model is based on the consideration of homogeneous elements (grains, subgrains) aggregated into a representative volume (macropoint) under the Voigt hypothesis. In the framework of this statistical approach, there is no mandatory requirement for continuous filling of the computational domain with crystallites; however, the material grain structure cannot be created arbitrarily. Using the Laguerre polyhedra, we develop a method of grain structure simulation coupled with subsequent processing and transferring of the necessary data on the grain structure to the modified statistical model. Our research is of much current interest due to the fact that the mutual arrangement of crystallites, as well as the interfaces between them, has a significant impact on the properties of polycrystals, which are particularly important for physical mechanisms that provide and accompany the processes of inelastic deformation (recrystallization, grain boundary hardening, grain boundary sliding, etc.). The results of the simulations of the high-temperature deformation of a copper polycrystal, including the description of the recrystallization process, are presented.