In the framework of this module the continuum mechanical foundations are treated to describe the thermodynamical material behavior of several materials. Based on the kinematic, deformation measurements are introduced. The focus of this lecture are the balance laws of continuum mechanics to describe the behavior of solids, fluids and gases. The contents of the module are:
• Kinematics: Motion, Transport theorems, Deformations and strain measurements Deformations and strain velocities, Lie Derivation, Polar Decomposition, Spectral Decomposition
• Forces and stresses, Cauchy‘s lemma and theorem, Cauchy, Kirchhoff and Piola-Kirchhoff stress tensors
• Balance equations and entropy inequality Thermodynamic Modeling, Balance equation of mass, Balance equation of momentum, Balance equation of moment of momentum, Balance equation of energy (first law of thermodynamics), Entropy inequality (second law of thermodynamics)
The opportunities of application of the single field equations are presented in form of relevant problems and concerning simple material laws.
In the lecture students will acquire the skills necessary to describe the mechanical behavior of materials with the help of continuum mechanics. First, representations using familiar mechanical quantities from the bachelor study (i.e. stress and strain) will be formulated within the framework of continuum mechanics. Through this, students will acquire the skills for the abstraction of mechanical variables. Hereafter, the classical static and dynamic equilibrium relations will be derived from the balance equations. This will enable students to formulate concrete boundary-and-initial value problems out of the abstract formulations of continuum mechanics. Lastly, simple elastic material equations and the application possibilities of these field equations will be.
Holzapfel, G.A.: Nonlinear solid mechanics. Wiley, 2000.
Hutter, K. & Jöhnk, K.: Continuum Methods of Physical Modeling-Continuum Mechanics, Dimensional Analysis, Turbulence. Springer, 2004.
Müller, I.: Grundzüge der Thermodynamik. Springer, 1994.
Wilmanski, K.: Thermomechanics of continua. Springer, 1998.