Одељење за математику, 26. фебруар 2021.

Наредни састанак Семинара биће одржан онлајн у петак, 26. фебруара 2021 са почетком у 14:15.

Предавач: Синиша Ђ. Месаровић, Универзитет у Вашингтону


Апстракт: Assume that the physics on the microscale (interactions between atoms, molecules, defects in crystals …) is understood. What is the appropriate mesoscale continuum theory for the problem? What are the assumptions involved and how do they define the limitations of the continuum model? To answer these questions, we begin with the definition of mesoscale continuum kinematics from the microscale kinematics. The geometry of micro-structure (e.g., order vs. disorder) has a decisive role in defining the continuum kinematics. We thus arrive at three kinematic formulations: mass continuum, lattice continuum and granular continuum. Then, upon formulating the power balance, we use the principle of virtual power to arrive at a variety of mathematical formulations: simple continuum with moving boundaries, phase field formulation, and, a higher order, size-dependent continuum. The problems considered include: mixing of fluids and capillary flows, granular flow/deformation, and, polycrystalline diffusional/dislocation creep accompanied by dislocation plasticity.

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