Optimization of the porous material described by the Biot model

The paper is devoted to the shape optimization of microstructures generating porous locally periodic materials saturated by viscous fluids. At the macroscopic level, the porous material is described by the Biot model defined in terms of the effective medium coefficients, involving the drained skelet...

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Bibliographic Details
Published in:International journal of solids and structures 2019-01, Vol.156-157, p.216-233
Main Authors: Hübner, D., Rohan, E., Lukeš, V., Stingl, M.
Format: Article
Language:English
Subjects:
Anisotropy
Biot model
Coefficients
Compressibility
Computational fluid dynamics
Design optimization
Elasticity
Homogenization
Material optimization
Mathematical models
Microstructure
Optimization
Parameterization
Permeability
Porous materials
Porous media
Regularization
Sensitivity analysis
Shape optimization
Stiffness
Two-scale modelling
Unit cell
Viscous fluids
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Summary:The paper is devoted to the shape optimization of microstructures generating porous locally periodic materials saturated by viscous fluids. At the macroscopic level, the porous material is described by the Biot model defined in terms of the effective medium coefficients, involving the drained skeleton elasticity, the Biot stress coupling, the Biot compressibility coefficients, and by the hydraulic permeability of the Darcy flow model. By virtue of the homogenization, these coefficients are computed using characteristic responses of the representative unit cell consisting of an elastic solid skeleton and a viscous pore fluid. For the purpose of optimization, the sensitivity analysis on the continuous level of the problem is derived. We provide sensitivities of objective functions constituted by the Biot model coefficients with respect to the underlying pore shape described by a B-spline box which embeds the whole representative cell. We consider material design problems in the framework of which the layout of a single representative cell is optimized. Then we propose a sequential linearization approach to the two-scale problem in which local microstructures are optimized with respect to macroscopic design criteria. Numerical experiments are reported which include stiffness maximization with constraints guaranteeing minimum required permeability, and vice versa. Issues of the design and anisotropy and the spline box parametrization are discussed. In order to avoid remeshing, a geometric regularization technique based on injectivity constraints is applied.
ISSN:0020-7683
1879-2146
DOI:10.1016/j.ijsolstr.2018.08.016