Research

Our research is driven by the desire to develop advanced simulation methods for engineering problems.....

 

Our research is driven by the desire to develop advanced simulation methods for engineering problems with complex solid material response. Our objective is to establish modern modeling concepts for the predictive analysis and optimization of material behavior under (non-)mechanical influences, including thermo-chemo-magneto-electro-mechanical coupling. Our approach covers mathematical formulations of theoretical and computational models with an emphasis on continuum mechanics and associated materials theory. In particular, we are interested in describing the evolution of microstructures and its link to larger length scales via homogenization and scale-briding techniques.


In this spirit, we develop nonlinear models in the field of thermo-chemo-magneto-electro-elasticity, plasticity and fracture mechanics at different length scales. A main interest is in the design of associated variational approaches that allow for the development of robust and efficient numerical solution algorithms. Furthermore, we develop homogenization methods for the analysis and optimization of the effective repsonse of smart and multifunctional composites. Our investigations also cover the analysis of the material and structural instability of microstructured solids. Examples of our research activities in theoretical and computational solid mechanics are:

 

Coupled and dissipative materials

  • Magneto-mechanics. Magnetostrictive materials, magnetorheological elastomers
  • Electro-mechanics. Ferroelectrics, electroactive polymers, liquid crystal elastomers
  • Magneto-electro-mechanics. Magneto-electric composites at small and finite strains
  • Thermo-mechanics. Variational formulations for standard dissipative solids
  • Chemo-mechanics. Modeling of porous media (soil, lithium-ion batteries, hydrogels)
  • Fracture mechanics. Phase field modeling (brittle, ductile, hydraulic, coupled fracture)
  • Elasto-plasticity. (Gradient) plastiticity of crystalline and frictional materials

Modeling techniques

  • Computational homogenization. Smart and multifunctional composite materials
  • Phase-field modeling. Microstructure evolution, fracture, homogenization
  • Variational approaches. Incremental variational formulations for solid materials
  • Data-integrated methods. Data-driven mechanics, machine learning, neural networks
  • Stability analysis. Material and structural stability analysis, Bloch-Floquet analysis

In der Mitte von Schwierigkeiten liegen die Möglichkeiten.

Albert Einstein, Google
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