The aim of my research is the development of efficient methods for mechanical homogenization in the context of large deformations. This is important for applications in which component parts or structures consist of mixtures of materials. These include, among others, fiber-reinforced composites, foams, porous materials, and mixtures of polymeres.
The homogenization consists in approximating the effective behavior of a heterogeneous micro-structure. This means to find the function describing the macroscopic response (stress, stiffness) of the microstructure to a prescribed macroscopic deformation. The main practical benefit of efficient computational homogenization is the avoidance of experimental studies.
In this work, as well as throughout the EMMA-Group, integral approaches are chosen. Potentials for gains of efficiency are identified and realized at each step from modeling to implementation. The utilized/developed methods include but are not limited to
- dimensional reduction via
- exploitation of invariances
- substitution of data-based methods for physical models
- artificial neural networks
- kernel interpolation and approximation
- efficient sampling of high-dimensional data by means of physically motivated methods
- efficient and stable FE formulations that are compatible with subsequent reduction methods