Motivation
Modern materials in engineering, such as polymers, can be subjected to (very) large deformations under certain circumstances. In such cases, the geometrically linearized theory used in courses such as "Mechanics 2" and "Introduction to Materials Theory" is no longer sufficient. In this course, the essential kinematic and kinetic relations of three-dimensional boundary value problems are introduced via a geometrically exact formulation. The focus is on elastic material behavior, which is later expanded in the course "Finite Inelasticity". Continuum mechanics also forms the elementary basis for finite element applications and modern methods such as the use of neural networks in mechanics.
Topics covered
- Nonlinear kinematics: deformations, strain measures, rotation and stretches, invariants
- Objective time derivatives, observer independence
- Balance equations, stress power, first and second law of thermodynamics, stress measures
- Variational principles
- Fundamentals of material modeling: general principles, growth conditions, convexity
- Hyperelasticity, (in-)compressible material models
Learning objectives
The learning objectives of this course are explicitly listed for each unit and can be used as a learning progress check. The learning objectives cover all taxonomy levels from pure "knowledge" and "application" to "evaluation" and "creation".
