Modern engineering materials such as poylmers and even metals and alloys may undergo (very) large deformations. In such cases, the geometrically
linearised theory introduced in courses like "Mechanics III" and "Introduction to Theory of Materials" is not applicable anymore. In this course, the
essential kinematic and kinetic relations of three dimensional boundary value problems are introduced and thoroughly discussed using a geometrically
exact formulation. The focus is thereby placed on elastic material response, which will then be extended in the course "Finite Inelasticity". In
particular, the following topics will be comprehensively discussed:
- Nonlinear kinematics: deformation, strain measures, rotation and stretch, invariants
- Objective time derivatives, frame indifference
- Balance equations, stress power, 1st and 2nd laws of thermodynamics, stress measures
- Variational principles
- Fundamentals of constitutive modelling: general principles, growth conditions, convexity conditions
- Hyperelasticity, incompressible and compressible material models
