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Research

Our research interests are driven by the desire to develop advanced simulation methods for engineering problems with complex solid material response. The overall objective is to establish concepts for predictive analyses and optimization of material behavior under mechanical and non-mechanical influences, including thermo-electro-magneto-mechanical coupling effects.

This covers the mathematically precise formulations of theoretical and computational models with an emphasis on continuum physics and the associated material theory. Thereby, we consider it imperative to describe the evolution of the material's micro-structure and its link to engineering macroscales via advanced homogenization and multiscale techniques.

In this spirit, we develop models of finite elasticity, visco-elasticity, plasticity, damage and fracture mechanics on different scales, including multiscale methods for micromechanically informed models. For many of these models we have designed novel variational principles, which allow the application of innovative mathematical tools and make the development of robust and efficient numerical solution algorithms feasible. Applications cover crystalline and polycrystalline materials, general composites, ceramics, rubbery and glassy polymers as well as granular media. Here are examples of our research activities in theoretical and computational solid mechanics:

Theory and numerics of materials

  • Variational concepts. Minimization and saddle point principles for dissipative evolution problems
  • Plasticity at finite strains. Different modeling approaches and geometric settings, state updates
  • Crystal plasticity. Robust active slip searches, state updates for rigid- and elasto-plasticity
  • Visco-elasticity. Alternative models, state updates, tangents, micromechanism-based formulations
  • Finite elasticity. Computational spectral representations, micromechanical settings for polymers
  • Damage mechanics. Continuous and discontinuous damage evolutions, micromechanical-based models
  • Fracture mechanics. Configurational-force-driven crack propagation, phase field models of fracture

Homogenization and multiscale modeling

  • Computational homogenization. Scale bridging in composites, polycrystals, polymers, granular media
  • Multiscale models. Hybrid micromechanism-informed models for metals, rubbery and glassy polymers
  • Texture evolution of polycrystals. Computational texture updates, orientation microstructures
  • Phase transitions. Relaxation of non-convex problems, deformation microstructures, phase fields

Coupled problems and multi-physics modeling

  • Thermo-mechanics. Thermo-elasticity and -plasticity, monolithic coupling and operator splits
  • Electro-magneto-mechanics. Electric and magnetic domain evolutions, macro-modeling of hystereses
  • Gradient plasticity. Multi-field variational principles and FE design for crystals and polycrystals
  • Configurational mechanics. Robust algorithms for crack propagation and adaptive mesh refinement

Finite element design and computational methods

  • Finite element design. Mixed finite elements for solid structures, shells and coupled problems
  • Adaptive FE methods. Configurational-force-driven r-adaptivity and h-adaptive mesh refinement
  • Numerical tools. Algorithms for spectral decomposition and computation of consistent tangents