Course Objectives
This course aims to
- equip students with essential knowledge about nonlinear theory of continuous media.
- make students assimilate kinematics of deformable bodies at large strains.
- teach students the concept of stress and fundamental stress measures.
- provide students with the essential balance principles of continuum thermodynamics.
- give the fundamentals of constitutive theory and particularly hyperelasticity along with its algorithmic implementation.
Course Content
Tensor algebra and calculus. Kinematics of geometrically nonlinear
deformations. Tangent, volume, and area maps. Rates of deformation and
strain tensors. Pull back and push forward operations. Fundamental
stress measures. Conservation laws of continuum thermodynamics.
Principles of material frame invariance. Objective rates. Concepts of
material symmetry. Fundamental potentials of thermodynamics. Colemans
exploitation method. Compressible and incompressible hyperelasticity and
its algorithmic aspects. Representative constitutive models of
hyperelasticity.
Course Learning Outcomes
Taking this course, the students will
- have an essential background on the nonlinear theory of continuous media.
- be able to carry out geometric pull-back and push-forward
operations between Lagrangean, Eulerian, and mixed quantities through
the tools of kinematics at large strains.
- understand the concept of stress and differentiate different fundamental stress measures
- have the fundamental understanding of thermodynamic consistency of a constitutive model of continuum thermodynamics.
- be qualified to derive the fundamental balance principles of
continuum thermomechanics within the Lagrangean and Eulerian setting.
- be in a position to implement a hyperelastic material model algorithmically.