Construction of Porous Multiscale Heterogeneous Microstructures using Statistical Correlation Functions and Minimal Surfaces
Subject Areas :
Structural Mechanics
A Hasanabadi
1
(Mechanical Engineering Department, University of Birjand, Birjand, Iran)
Received: 2022-08-03
Accepted : 2022-10-05
Published : 2022-12-01
Keywords:
Statistical Correlation Function,
Heterogeneous Microstructure,
Multiscale modeling,
Minimal Surface,
Abstract :
Design multiphase heterogeneous structures in order to provide multifunctional properties has many applications in the field of material design. In this research, a new method for construction multiscale heterogeneous microstructure is presented. Using statistical correlation function, specifically, two-point correlation functions, bicontinuous two-phase structure is constructed that has solid and void phases. In order to construction the heterogeneous media, an exponentially decreasing sine function is used as autocovariance function. Then based on Schwartz P minimal surface the porous media structure, is divided into two parts; porous solid phase and void phase. From the point of view of continuity, the phases are investigated and it is observed both phases of the constructed microstructure are connected throughout the media. Using this method it is possible to construct bicontinuous multiscale microstructures that are solid and void phase in coarse scale and the solid phase can be constructed as void and solid phase in fine scale.
References:
Adams B.L., Kalidindi S.R., Fullwood David T., 2013, Microstructure-Sensitive Design for Performance Optimization, Butterworth-Heinemann, Waltham, MA 02451.
Wu J., Sigmund O., Groen J.P., 2021, Topology optimization of multi-scale structures: A review, Structural and Multidisciplinary Optimization 63(3): 1455-1480.
Liu X., Shapiro V., 2017, Sample-based synthesis of two-scale structures with anisotropy, Computer-Aided Design 90: 199-209.
Torquato S., 2002, Random Heterogeneous Materials: Microstructure and Macroscopic Properties, Springer-Verlag, New York.
Bendsøe M.P., Sigmund O., 2004, Topology Optimization Theory, Methods, and Applications, Springer-Verlag Berlin Heidelberg.
Torquato S., 1997, Effective stiffness tensor of composite media – i. Exact series expansion, Journal of the Mechanics and Physics of Solids 45(9): 1421-1448.
Torquato S., 2010, Optimal design of heterogeneous materials, Annual Review of Materials Research 40(1): 101-129.
Torquato S., Hyun S., Donev A., 2003, Optimal design of manufacturable three-dimensional composites with multifunctional characteristics, Journal of Applied Physics 94(9): 5748-5755.
Torquato S., Hyun S., Donev A., 2002, Multifunctional composites: Optimizing microstructures for simultaneous transport of heat and electricity, Physical Review Letters 89(26): 266601.
Fullwood D.T., Niezgoda S.R., Adams B.L., Kalidindi S.R., 2010, Microstructure sensitive design for performance optimization, Progress in Materials Science 55(6): 477-562.
Fatahi-Vajari A., Imam A., 2016, Lateral vibrations of single-layered graphene sheets using doublet mechanics, Journal of Solid Mechanics 8(4): 875-894.
Sadd M.H., 2014, Elasticity Theory, Applications, and Numerics, Academic Press, Oxford.
Ferrari M., Granik V.T., Imam A., Nadeau J.C., 1997, Advances in Doublet Mechanics, Springer-Verlag Berlin Heidelberg.
Azimzadeh Z., Fatahi-Vajari A., 2019, Coupled axial-radial vibration of single-walled carbon nanotubes via doublet mechanics, Journal of Solid Mechanics 11(2): 323-340.
Cule D., Torquato S., 1999, Generating random media from limited microstructural information via stochastic optimization, Journal of Applied Physics 86(6): 3428-3428.
Ballani F., Stoyan D., 2015, Reconstruction of random heterogeneous media, Journal of Microscopy 258(3): 173-178.
Bendsøe M.P., Kikuchi N., 1988, Generating optimal topologies in structural design using a homogenization method, Computer Methods in Applied Mechanics and Engineering 71(2): 197-224.
Guest J.K., Prévost J.H., 2006, Optimizing multifunctional materials: Design of microstructures for maximized stiffness and fluid permeability, International Journal of Solids and Structures 43(22-23): 7028-7047.
Bochenek B., Pyrz R., 2004, Reconstruction of random microstructures––a stochastic optimization problem, Computational Materials Science 31(1-2): 93-112.
Beran M.J., 1968, Statistical Continuum Theories, Monographs in Statistical Physics and Thermodynamics, Interscience, New York.
Kröner E., 1977, Bounds for effective elastic moduli of disordered materials, Journal of the Mechanics and Physics of Solids 25(2): 137-155.
Rémond Y., Ahzi S., Baniassadi M., Garmestani H., 2016, Applied Rve Reconstruction and Homogenization of Heterogeneous Materials, Wile-ISTE, Great Britain.
Hasanabadi A., Baniassadi M., Abrinia K., Safdari M., Garmestani H., 2016, 3D microstructural reconstruction of heterogeneous materials from 2D cross sections: A modified phase-recovery algorithm, Computational Materials Science 111: 107-115.
Kapfer S.C., Hyde S.T., Mecke K., Arns C.H., Schröder-Turk G.E., 2011, Minimal surface scaffold designs for tissue engineering, Biomaterials 32(29): 6875-6882.
Karcher H., Polthier K., 1996, Construction of triply periodic minimal surfaces, Philosophical Transactions: Mathematical, Physical and Engineering Sciences 354(1715): 2077-2104.
Schwarz H.A., 1890, Gesammelte Mathematische Abhandlungen, Springer.
Barkaoui A., Chamekh A., Merzouki T., Hambli R., Mkaddem A., 2014, Multiscale approach including microfibril scale to assess elastic constants of cortical bone based on neural network computation and homogenization method, International Journal for Numerical Methods in Biomedical Engineering 30(3): 318-338.
Pecci R., Baiguera S., Ioppolo P., Bedini R., Del Gaudio C., 2020, 3D printed scaffolds with random microarchitecture for bone tissue engineering applications: Manufacturing and characterization, Journal of the Mechanical Behavior of Biomedical Materials 103: 103583.
Sun C., Hui R., Roller J., 2010, Cathode materials for solid oxide fuel cells: A review, Journal of Solid State Electrochemistry 14(7): 1125-1144.
Gandy P.J.F., Bardhan S., Mackay A.L., Klinowski J., 2001, Nodal surface approximations to the p,g,d and i-wp triply periodic minimal surfaces, Chemical Physics Letters 336(3): 187-195.
Hasanabadi A., 2021, Microstructure design of heterogeneous material using multisided patch, Iranian Journal of Manufacturing Engineering 8(2): 32-40.
Coons S.A., 1967, Surfaces for Computer-Dided Design of Space Forms, Massachusetts Institute of Technilogy, United States.
Fullwood D.T., Niezgoda S.R., Kalidindi S.R., 2008, Microstructure reconstructions from 2-point statistics using phase recovery algorithms, Acta Materialia 52: 942-948.
Baniassadi M., Garmestani H., Li D.S., Ahzi S., Khaleel M., Sun X., 2011, Three-phase solid oxide fuel cell anode microstructure realization using two-point correlation functions, Acta Materialia 59: 30-43.
Torquato S., 2006, Necessary conditions on realizable two-point correlation functions of random media, Industrial and Engineering Chemistry Research 45: 6923-6928.
Hoshen J., Kopelman R., 1976, Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm, Physical Review B 14(8): 3438-3445.
Hasanabadi A., Baniassadi M., Abrinia K., Baghani M., Mazrouei Sebdani M., 2016, Evaluation of solid oxide fuel cell anode based on active triple phase boundary length and tortuosity, Energy Equipment and Systems 4(1): 11-19.
Wu D., Spanou A., Diez-Escuder A., Persson C., 2020, 3D-printed pla/ha composite structures as synthetic trabecular bone: A feasibility study using fused deposition modeling, Journal of the Mechanical Behavior of Biomedical Materials 103: 103608.
Riazat M., Baniasadi M., Mazrouie M., Tafazoli M., Moghimi Zand M., 2015, The effect of cathode porosity on solid oxide fuel cell performance, Energy Equipment and Systems 3(1): 25-32.
He W., Lv W., Dickerson J.H., 2014, Gas Transport in Solid Oxide Fuel Cells, Springer, New York.
