PAMM · Proc. Appl. Math. Mech. 17, 577 – 578 (2017) / DOI 10.1002/pamm.201710258 Microstructural influence on macroscopic response regarding fluid flow through porous media applying TPM 2 -Method Florian Bartel 1, * , Tim Ricken 1 , Jörg Schröder 2 , and Joachim Bluhm 2 1 Chair of Mechanics, Structural Analysis, and Dynamics, TU Dortmund, August-Schmidt-Str. 6, 44227 Dortmund 2 Institute of Mechanics, University of Duisburg-Essen, Universitätsstr. 15, 45141 Essen Thanks to the advancements in the digital era we are able to capture naturally grown and artificially manufactured microstruc- tures with various scanning devices like CT and MRT and can transfer the digital image data to finite element models. In addition, there has been a permanent improvement in the quality of additive reproduction technology. Looking at the biomed- ical industry producing organic parts, porous materials saturated with fluids play an important role. For this reason, we also have to develop appropriate simulation technology providing a description for porous materials regarding the underlying mi- crostructure. This contribution presents a numerical experiment for the flow through a porous body with different underlying microstructures applying the TPM 2 -Method. The different macroscopic behavior for the displacements, pressure distribution, and volumetric fluid flow for an isotropic and two differently orientated anisotropic microstructures are shown in section 3. c  2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction to TPM 2 -Method The TPM 2 -Method is considered as the Theory of Porous Media (TPM), cf. [1] or [2], embedded in the two-scale homogenization environment of the FE 2 -Method, see [3], [4]. In this framework we are able to describe large poro-elastic deformation and fluid flow through porous media as well as taking into account the discrete geometry of microscopic structures. Hence, TPM 2 -Method allows us to solve two-scale, non-linear, coupled and time dependent problems for bodies with a porous microstructure. As is with the standard TPM formulation, the governing equations - balance of mass, momentum and moment of momentum as well as the entropy inequality - are considered for all phases. The degrees of freedom considered are displacement and hydrostatic pressure, which may be used to determine stresses and volumetric fluid flows. For the micro-macro transition we transfer the macroscopic quantities such as the deformation gradient, fluid stress and pressure gradient to the microstructure and receive an averaged material tangent as a response. Hereby, we satisfy Hill-Mandel homogeneity condition. 2 Numerical experiment: Flow through porous body with varying microstructure Fig. 1: BVP: Flow through porous cantilever. As a numerical experiment, we considered a clamped body consisting of a porous material and analyzed the macroscopic deformation behaviour by applying a flow from the left to the right hand side and varied the underlying microsturucture. The macroscopic Boundary Value Problem (BVP) is illustrated in Fig. 1. We regarded a rectangular body, where the displacement degrees of freedom were fixed on the left hand side. The flow through the body was achieved by applying a pressure load (λ = 10 N/mm 2 ), which was linearly increased over 50 time increments. On the right hand side the pressure was set to zero. The macroscopic body was meshed with 320 finite elements. The evaluation points were on element 10, 290 and 310. Fig. 2: i) Microstructural design, ii) Rep- resentative Volume Element (RVE), iii) Dis- cretized RVE with 10×10 finite elements and two different material parameter sets for low and high permeability. We designed three different microstructures, one is isotropic and two are aniso- tropic. As an example, in Fig. 2 i) one of the anisotropic microstructures is il- lustrated, from which we extracted the geometry of the RVE (Fig. 2 ii)), which was discretized with 10 × 10 finite elements (Fig. 2 iii)). The black and white domains consist of porous materials each with different material properties. The black material is more stiff and less permeable in relation to the white material. The numerical values for the Lam´ e constants and Darcy permeability are listed in Tab. 1. As lower level boundary condition, a mixed Dirichlet-Reuss type is chosen. Table 1: Material constants for the different domains of the microstructure Material constants 1 st Lam´ e μ S 2 nd Lam´ e λ S Darcy k d Black domain 26 287 0.1 White domain 16 187 1.0 ∗ Corresponding author: e-mail florian.bartel@tu-dortmund.de, phone +49 231 755 4682, fax +49 231 755 2532 c  2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim