Material Theory

Theoretical and Computer-Oriented Material Theory

Content

The lecture provides an in-depth perspective on the formulation and algorithmic implementation of material models for the description of physically and geometrically nonlinear deformation and failure mechanisms of solids. Material models of elasticity, visco-elasticity, plasticity as well as damage and fracture at finite deformations are covered in the course. This also includes non-mechanical effects such as thermomechanical or electromechanical coupling. In addition to continuum mechanical models, discrete modeling approaches on different space and time scales are presented, and fundamental concepts of multi-scale models and mathematical homogenization techniques are addressed. The lecture covers theoretical and numerical aspects in a integrated sense. For example, model-specific algorithms for time integration, global solvers for coupled nonlinear field equations as well as different finite element formulations for the spatial discretization of nonlinear material models and discontinuities are considered. Many of the presented developments and methods are current topics in research. A specification and orientation of this broad subject based on the interests of the audience is possible. Contents:

  • Direct variational methods of finite elasticity and uniqueness
  • Anisotropic finite elasticity and isotropic tensor functions
  • Damage models and elements of fracture mechanics
  • Finite elasto-visco-plasticity of metals and polymers
  • Discrete models: particle methods and dislocation dynamics
  • Multi-scale models and numerical homogenization techniques
  • Material instabilities, phase transitions and microstructures
Materials
  • Complete notes on blackboard
  • Exercise material will be handed out in the exercises

Contact

Marc-André Keip
Prof. Dr.-Ing.

Marc-André Keip

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