E2-02

Micromechanics of Materials and Homogenization Methods

Content

The course Micromechanics of Materials and Homogenization Method advances the topics of the core course Computational Mechanics of Materials. It is structured into the parts computational mechanics of three-dimensional material models at small strains, micro-mechanically-based material models, homogenization methods and computational mechanics of solid materials at large strains. Basic contents are thermodynamics of a general internal variable formulation of inelasticity at small strains, linear and nonlinear elasticity, finite element implementation of nonlinear elasticity, viscoelasticity, rate-independent and rate-dependent plasticity, micromechanically-based models of plasticity for crystalline solids, introduction to homogenization methods and micro-to-macro transitions, a general internal variable formulation of inelasticity at large strains, approaches to the modeling and numerics of finite elasticity and finite viscoelasticity. The following topics will be covered:

  • Thermodynamics of a general internal variable formulation of inelasticity at small strains
  • Linear and nonlinear elasticity (isotopic spectral forms, anisotropic models based on structural tensors)
  • Finite Element implementation of nonlinear elasticity
  • Viscoelasticity (linear and nonlinear models, stress update algorithms and consistent linearization)
  • Rate-independent and rate-dependent plasticity (theoretical formulations, stress update algorithms and local variational formulations, consistent linearization)
  • Micromechanically-based models of plasticity for crystalline solids
  • Introduction to homogenization methods and micro-to-macro transitions
  • General internal variable formulation of inelasticity at large strains
  • Approaches to the modelling and numerics finite elasticity and finite viscoelasticity
Materials
  • Complete notes on blackboard
  • Exercise material will be handed out in the exercises
Audience

Students of COMMAS, Civil Engineering, Simulation Technology and other interested listeners

Assistant

E.Polukhov

Prerequistites

3 of 3 assignments

Contact

Marc-André Keip
Prof. Dr.-Ing.

Marc-André Keip

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