Two-scale convergence in spaces with random measures applied to plasticity

• Applicant: Dr. Sergiy Nesenenko
• Subject Area: Mathematics ; Mechanical Properties of Metallic Materials and their Microstructural Origins
• Term: from 2015 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 273738974

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 micro scale 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 nanoparticles/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. Direct numerical simulation of models containing several scales is usually prohibitive, even on advanced computing hardware, due to the necessity to use a very fine mesh to capture the scale effects. Therefore, for the construction of the efficient numerical algorithms for engineering materials possessing a periodic/stochastic microstructure, different homogenization methods are usually employed. These methods enable the passage from a microscopic description to a macroscopic description of the material behavior in a rigorous manner. In this work the mathematically rigorous description of the macroscopic evolution of elasto/visco-plastic materials, which are periodically/randomly voided or reinforced by rigid micro-/nanoinclusions of different geometry, during the deformation in Sobolev spaces with measures must be derived. Dependence of the macroscopic properties of porous or micro/nanostructured materials on the shape of voids or constituent micro-/nanoinclusions, on their concentration, on their geometric arrangement and on the material parameters of their constituents must be investigated.

• DFG Programme: Research Grants
• Co-Investigator: Privatdozent Dr. Kersten Schmidt