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DFG-Projekt NE 1498/4-1

Two-scale convergence in spaces with random measures applied to plasticity
November 2015 -- October 2017
Dr. Sergiy Nesenenko
DFG Eigene Stelle
The design and manufacturing of new engineering materials relies heavily on the development of adequate models for the description of the macroscopic behavior of materials with microstructure. These models have to incorporate the information from a microscale on the presence of voids or particle/fiber-reinforced structures in materials and on the mechanisms that determine the behavior under consideration. Experimentally it is well demonstrated that the hindering of the dislocation motion by other dislocations, reinforced micro-particles/fibers or by grain boundaries in alloys cause the hardening effects, which are observed at the structural scale. The nucleation and the growth of grain boundary cavities lead to microcracks developing along a gain boundary and further to failure or rupture of the material. The primal goal of this project is to derive the mathematically rigorous description of the macroscopic evolution of elasto/visco-plastic materials, which are periodically/randomly voided or reinforced by micro-inclusions of different geometry, during the deformation in Sobolev spaces with measures. Dependence of the macroscopic properties of porous or micro-structured materials on the shape of voids or constituent micro-inclusions, on their concentration, on their geometric arrangement and on the material parameters of their constituents must be investigated as well.

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