Optimization of the porous material described by the Biot model

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:156

Article

Huebner, D.³  Rohan, E.^1,2  Lukes, V.^1,2  Stingl, M.³ 

[1] Univ West Bohemia, Fac Appl Sci, Dept Mech, Univ 22, Plzen 30614, Czech Republic

[2] Univ West Bohemia, Fac Appl Sci, NTIS New Technol Informat Soc, Univ 22, Plzen 30614, Czech Republic

[3] Friedrich Alexander Univ Erlangen Nurnberg, Dept Math, Cauerstr 11, D-91058 Erlangen, Germany

关键词: Porous media;    Shape optimization;    Material optimization;    Homogenization;    Biot model;    Sensitivity analysis;    Two-scale modelling;   

DOI  :  10.1016/j.ijsolstr.2018.08.016

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Ltd. All rights reserved.

【 授权许可】

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