TPM²

In future applications it will be essential to consider the influences of discrete microstructures. Today it is possible, to receive the discrete topology of the microstructure of a material by CT-scanning. The information can be transferred to a finite element model. Therefore we are preparing the TPM for a two-scale homogenisation technique where the macroscopic body as well as the micostructure is analysed with the Finite Element Method.

The poro-elastic material description is based on the Theory of Porous Media (TPM), see [1], [2]. We derived a two-phase material model regarding a solid and a fluid phase.

For the two-scale approach the FE²-Method is applied, where both the global macroscopic structure and the underlying micro-structure are analysed with the Finite Element Method, see [3], [4].

Therefore, the weak forms for the macroscopic and the microscopic scale are formulated and an averaged macroscopic tangent moduli considering the micro-scale is derived. Additionally, the formulation of lower level boundary conditions, which refer to the quantities that are transmitted from the macro- to the micro-scale, under strict compliance of the Hill-Mandel homogeneity condition is taken into account.

[1] R. de Boer and W. Ehlers.
Theorie der Mehrkomponentenkontinua mit Anwendung auf bodenmechanische Probleme. Technical report, Teil I, Forschungsberichte aus dem Fachbereich 
Bauwesen, Heft 40, Universität-GH-Essen, 1986.

[2] W. Ehlers.
Poröse Medien -- ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie.
Technical Report 47, Universität-GH Essen, 1989.

[3] Christian Miehe.
Computational micro-to-macro transitions for discretised micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy.
Computer methods in applied mechanics and engineering, 2002.

[4] Jörg Schröder.
CISM Course "Plasticity and Beyond: Microstructures. Crystal-Plasticity and Phase Transitions", Chapter A numerical two-scale
homogenization scheme: the FE²-method.
Springer Verlag, 2013.

Bartel, F., Ricken, T., Schröder, J. and Bluhm, J.
Microstructural influence on macroscopic response regarding fluid flow through porous media applying TPM² Method.
Proc. Appl. Math. Mech., 17, 577-578 (2017) / DOI 10.1002/pamm.201710258

A two-scale homogenisation approach for fluid saturated porous media based
on TPM and FE2-Method
89rd GAMM Annual Meeting, Munich, Germany, 2018

A two-scale homogenisation approach for fluid saturated porous media based
on TPM and FE2-Method
9. Workshop junger Nachwuchswissenschaftler in der Mechanik, Zell am See,
Austria, 2018

A two-scale homogenisation approach for fluid saturated porous media based
on TPM and FE2-Method
7th GACM, Stuttgart, Germany, 2017

A two-scale homogenisation approach for fluid saturated porous media based
on TPM and FE2-Method
30th COMPLAS, Barcelona, Spain, 2017

A two-scale homogenisation approach for fluid saturated porous media based
on TPM and FE2-Method
88rd GAMM Annual Meeting, Weimar, Germany, 2017

A two-scale homogenisation approach for fluid saturated porous media based
on TPM and FE2-Method
8. Workshop junger Nachwuchswissenschaftler in der Mechanik, Zell am See,
Austria, 2017

A two-scale homogenisation approach for fluid saturated porous media based on TPM and FE2-Method
SEMC 2016, Cape Town, South Afrika, 2016

A two-scale homogenisation approach for fluid saturated porous media based on TPM and FE2-Method
87rd GAMM Annual Meeting, Braunschweig, Germany, 2016

A two-scale homogenisation approach for fluid saturated porous media based on TPM and FE2-Method
7. Workshop junger Nachwuchswissenschaftler in der Mechanik, Zell am See, Austria, 2016

A two-scale homogenisation approach for fluid saturated porous media based on TPM and FE2-Method
Evolutionary Solid Bodies, Bollendorf, Germany, 2015

A two-scale homogenisation approach for fluid saturated porous media based on TPM and FE2-Method
XXV International Workshop on Computational Micromechanics of Materials, Bochum, Germany,2015.

A two-scale homogenisation approach for fluid saturated porous media based on TPM and FE2-Method
Forschungskolloquium Baustatik - Baupraxis 2015, Döllnsee, Germany, 2015

A two-scale homogenisation approach for fluid saturated porous media based on TPM and FE2-Method
86rd GAMM Annual Meeting, Lecce, Italy, 2015

A two-scale homogenisation approach for fluid saturated porous media based on TPM and FE2-Method
6. Workshop junger Nachwuchswissenschaftler in der Mechanik, Zell am See, Austria, 2015