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We present a new approach and an algorithm for optimizing the materialconfiguration and behaviour of a fluid saturated porous medium in a two-scalesetting. The state problem is governed by the Biot model describing thefluid-structure interaction in homogenized poroelastic structures. However, theapproach is widely applicable to multiphysics problems involving severalmacroscopic fields where homogenization provides the relationship between themicroconfigurations and the macroscopic mathematical model. The optimizationvariables describe the local microstructure design by virtue of the pore shapewhich determines the effective medium properties - the material coefficients -computed by the homogenization method. The main idea of the numericaloptimization strategy consists in a) employing a precomputed database of thematerial coefficients associated to the geometric parameters and b) applyingthe sequential global programming (SGP) method for solving the problem ofmacroscopically optimized distribution of material coefficients. Although thereare similarities with the free material optimization (FMO) approach, onlyeffective material coefficients are considered admissible, for which awell-defined set of corresponding configurable microstructures exist. Due tothe flexibility of the SGP approach, different types of microstructures withfully independent parametrizations can easily be handled. The efficiency of theconcept is demonstrated by a series of numerical experiments. We show that theSGP method can handle simultaneously multiple types of microstructures withnontrivial parametrizations using a considerably low and stable number of stateproblems to be solved.

A Sequential Global Programming Approach for Two-scale Optimization of Homogenized Multiphysics Problems with Application to Biot Porous Media