Title: Homogenization Methods for Problems with Multiphysics, Temporal and Spatial Coupling
Description: There are many natural and man-made materials with heterogeneous micro- or nanostructure (fine-scale structure) which represent a great interest for industry. Therefore there is a great demand for computational methods capable to model mechanical behavior of such materials. Direct numerical simulation resolving all fine-scale details using very fine mesh often becomes very expensive. One of alternative effective group of methods is the homogenization methods allowing to model behavior of materials with heterogeneous fine-scale structure. The essence of homogenization is to replace heterogeneous material with some equivalent effectively homogeneous material. The homogenization methods are proven to be effective in certain classes of problems while there is need to improve their performance, which includes extension of the range of applicability, simplification, usage with conventional FE software and reducing computational cost. In this dissertation methods extending the range of applicability of homogenization are developed.

Firstly, homogenization was extended of the case of full nonlinear electromechanical coupling with large deformations, which allows simulating effectively behavior of electroactive materials such as composites made of electroactive polymers. Secondly, homogenization was extended on wave problems where dispersion is significant and should be accounted for. Finally, the homogenization was extended on the case where the size of microstructure. The distinctive feature of the methods introduced in this dissertation is that they don't require higher order derivatives and can be implemented with conventional FE codes. The performance of methods is tested on various examples using Abaqus.