Continuum Mechanics

The knowledge of continuum mechanics and continuum thermodynamics is the fundamental requirement for the theoretical and algorithmic understanding of geometrically and physically nonlinear deformation, failure and transport processes in solids consisting of metallic, polymer or geological materials. This course offers a presentation of fundamental concepts of continuum mechanics and constitutive theory at finite elastic and inelastic strains. The chosen formulation accentuates geometrical aspects based on the modern terminology of differential geometry, which also includes the description of multi-field theories with thermo- and electromechanical coupling. Algorithmic aspects of the computer implementation of nonlinear continuum mechanics models are covered in parallel to the theoretical description. Contents:

• Tensor algebra and -analysis on manifolds
• Differential geometry of finite deformations
• Balance principles of nonlinear continuum thermodynamics
• Phenomenological material theory at finite strains
• Uniqueness of boundary value problems and stability theory

• Complete notes on blackboard
• Exercise material will be handed out in the exercises

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

A. Nateghi

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