Finite Element Method - Multiphase Materials
Finite Element Method - Multiphase Materials

• Antwortverhalten der Materialien im Rahmen einer kontinuumsmechanischen Beschreibung
• Motivation und Überblick
• Einführung in die Theorie poröser Medien (TPM)
• Entwicklung thermodynamisch konsistenter Materialgleichungen
• Kontinuumsmechanische Behandlung
• Beispiel: Flüssigkeitsgesättigter poröser Festkörper, Diskussion der Randbedingungen , Aufbereitung des gekoppelten Gleichungssystems für die numerische Behandlung, Verifikation des Berechnungskonzepts anhand numerischer Beispielrechnungen

Die Studierenden können

• Mehrphasensysteme kontinuumsmechanisch behandeln
• thermodynamisch konsistente Materialgleichungen bei Mehrphasensystemen formulieren
• Randbedingungen bei Mehrphasensystemen formulieren
• das gekoppelte Gleichungssystem für die numerische Behandlung aufbereiten
• das Berechnungskonzept anhand numerischer Beispielrechnungen verifizieren

• de Boer, R.: Theory of porous media - highlights in the historical development and current state, Springer-Verlag, 2000.
• Ricken, T.: Kapillarität in porösen Medien - Theoretische Untersuchung und numerische Simulation, Dissertation, Shaker Verlag, Aachen, 2002.
• Ricken, T., Schwarz, A., Bluhm, J.: A Triphasic Model of Transversely Isotropic Biological Tissue with Application to Stress and Biological Induced Growth, Computational Materials Science 39, 124 –- 136, 2007.

The Theory of Porous Media will be introduced as a conceptual access point for the discussion of discrete multi-phase materials. The conceptual procedure for the development of thermo-dynamically consistent material equations will be also be discussed. The solution of the resulting equation system occurs numerically under the use of the Finite Element Method (FEM). On account of the mostly strong, coupled and non-linear character of the equation system which is to be solved, special element models will be introduced.

- Motivation and Overview

- Introduction to the Theory of Porous Media (TPM)

- Development of thermo-dynamically consistent material equations

- Treatment of Continuum Mechanics

- Example: liquid saturated porous solids

- Discussion of boundary conditions

- Preparation of the coupled equation system for numerical treatment

- Verification of the calculation concept with the help of numerical example calculations

For many industrial applications a description of materials which are made up of many components is needed. Examples of this are liquid-saturated porous grounds, filters where gas is passed through or biomaterials. Furthermore, in process simulations such as steel production descriptions using multi-phase material models are reasonable. In the lecture the behavioral response of the materials within the framework of a continuum mechanical description will be discussed.

Students will be able to

- discuss the continuum mechanics of multi-phase systems

- formulate thermo-dynamically consistent material equations within multi-phase systems

- formulate boundary conditions within multi-phase systems

- prepare the coupled equation system for numerical treatment

- verify the calculation concept with the help of numerical example calculations

• de Boer, R.: Theory of porous media - highlights in the historical development and current state, Springer-Verlag, 2000.
• Ricken, T.: Kapillarität in porösen Medien - Theoretische Untersuchung und numerische Simulation, Dissertation, Shaker Verlag, Aachen, 2002.
• Ricken, T., Schwarz, A., Bluhm, J.: A Triphasic Model of Transversely Isotropic Biological Tissue with Application to Stress and Biological Induced Growth, Computational Materials Science 39, 124 –- 136, 2007.