Abstract
An understanding of the structure–property relationship is essential for the estimation of mechanical properties of nano-materials like polymeric nanofibers and biological materials like cells and tissues. The properties of these structures are closely related to the internal molecular structure and therefore a multiscale based mathematical modeling is required for the determination of its macroscopic properties. In this investigation, we present multiscale mathematical models to estimate the mechanical properties of polymeric nanofibers from the basic building blocks to the macroscale nanofibrous structures and also study the homogenization of biological cells considering the microcellular constituents.Theoretical analysis of polymeric nanofibers based scaffolds are necessary towards designing novel bio-medical applications, while through homogenization of biological cells new diagnostic tools based on mechanical properties could be developed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Aboudi J (1991) Mechanics of composite materials – A unified micromechanical approach. Elsevier, Amsterdam
Balac I, Milovancevic M, Tang C-Y, Uskokovic PS, Uskokovic DP (2004) Estimation of elastic properties of a particulate polymer composite using a face-centered cubic FE model. Mater Lett 58:2437–2441
Baltussen JJM, Northolt MG, van der Hout R (1997) The continuous chain model for the elastic extension of polymer fibers in the glassy state. J Rheol 41:549–573
Costa KD, Yin FCP (1999) Analysis of indentation: Implications for measuring mechanical properties with atomic force microscopy. J Biomech Eng-T ASME 121:462–471
Costa KD, Sim AJ, Yin FC-P (2006) Non-Hertzian approach to analyzing mechanical properties of endothelial cells probed by atomic force microscopy. J Biomech Eng-T ASME 128:176–184
Fambri L, Pergoretti A, Fenner R, Incardona D, Migliaresi C (1997) Biodegradable fibres of poly(L-lactic acid) produced by melt spinning. Polymer 38:79–85
Freed LE, Vunjak-Novakovic G, Biron RJ, Eagles DB, Lesnoy DC, Barlow SK, Langer R (1994) Biodegradable polymer scaffolds for tissue engineering. Bio/Technol 12:689–693
Griebel M, Hamaekers J (2004) Molecular dynamics simulations of the elastic moduli of polymer-carbon nanotube composites. Comput Method Appl M 193:1773–1788
Hibbitt K, and Sorensen Inc, HKS (2002) ABAQUS standard, Version 6.3-2. HKS, Providence, RI
Hoogsteen W, Postema AR, Pennings AJ, ten Brinke G (1990) Crystal structure, conformation, and morphology of solution-spun poly(L-lactide) fibers. Macromolecules 23:634–642
Hu S, Eberhard L, Chen J, Love JC (2004) Mechanical anisotropy of adherent cells probed by a three-dimensional magnetic twisting device. Am J Physiol-Cell Ph 287:C1184–C1191
Humphrey JD (2002) On mechanical modeling of dynamic changes in the structure and properties in adherent cells. Math Mech Solids 7:521–539
Inai R, Kotaki M, Ramakrishna S (2005) Structure and properties of electrospun PLLA single nanofibres. Nanotechnology 16:208–213
Karcher H, Lammerding J, Huang H, Lee RT, Kamm RD, Kaazempur-Mofrad MR (2003) A three-dimensional viscoelastic model for cell deformation with experimental verification. Biophys J 85:3336–3349
Lee JH, Park TG, Park HS, Lee DS, Lee YK, Yoon SC, Nam J-D (2003) Thermal and mechanical characteristics of poly(-lactic acid) nanocomposite scaffold. Biomaterials 24:2773–2778
Leenslag JW, Pennings AJ (1987) High-strength poly(L-lactide) fibres by a dry-spinning/hot-drawing process. Polymer 28:1695–1702
Lim JY, Kim SH, Lim S, Kim YH (2002) Improvement of flexural strengths of poly(L-lactic acid) by solid-state extrusion. Macromol Chem Phys 202:2447–2453
Mezghani K, Spruiell JE (1998) High speed melt spinning of poly(L-lactic acid) filaments. J Polym Sci Part B: Polym Phys 36:1005–1012
Mura T (1997) Micromechanics of defects in solids. Martinus Nijhoff, Hague, The Netherlands
Mylvaganam K, Zhang LC (2004) Important issues in a molecular dynamics simulation for characterising the mechanical properties of carbon nanotubes. Carbon 42:2025–2032
Na S, Sun Z, Meininger GA, Humphrey JD (2004) On atomic force microscopy and the constitutive behavior of cells. Biomech Model Mechanobiol 3:75–84
Ohayon J, Tracqui P (2005) Computation of adherent cell elasticity for critical cell-bead geometry in magnetic twisting experiments. Ann Biomed Eng 33:131–141
Pabst W, Gregorova E (2004) Effective elastic properties of alumina–zirconia composite ceramics – Part 2. Micromechanical modeling. Ceram Silik 48:14–23
Rappe AK, Casewit CJ, Colwell KS, Goddard WA, Skiff WM (1992) UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations. J Am Chem Soc 114:10024-10035
Reddy JN (2006) An introduction to the finite element method, 3rd edn. McGraw-Hill, New York
Reddy JN (2004) An introduction to nonlinear finite element analysis. Oxford University Press, Oxford
Reddy JN (2008) An introduction to continuum mechanics with applications. Cambridge University Press, New York
Rotsch C, Radmacher M (2000) Drug-induced changes of cytoskeletal structure and mechanics in fibroblasts: An atomic force microscopy study. Biophys J 78:520–535
Tan EPS, Lim CT (2004) Physical properties of a single polymeric nanofiber. Appl Phys Lett 84:1603–1605
Tan EPS, Lim CT (2006) Nanomechanical characterization of nanofibers – A review. Compos Sci Technol 66:1099–1108
Thelen S, Barthelat F, Brinson LC (2004) Mechanics considerations for microporous titanium as an orthopaedic implant material. J Biomed Mater Res 69A:601–610
Unnikrishnan VU, Reddy JN (2005) Characteristics of silicon doped carbon nanotube reinforced nanocomposites. Int J Multiscale Comput Eng 3:437–450
Unnikrishnan VU, Unnikrishnan GU, Reddy JN, Lim CT (2007) Atomistic-mesoscale coupled mechanical analysis of polymeric nanofibers. J Mater Sci 42:8844–8852
Unnikrishnan GU, Unnikrishnan VU, Reddy JN (2007) Constitutive material modeling of cell: A micromechanics approach. J Biomed Eng 129:315–323
Zussman E, Rittel D, Yarin AL (2003) Failure modes of electrospun nanofibers. Appl Phys Lett 82:3958–3960
Acknowledgements
The authors gratefully acknowledge the support of this research through Oscar S. Wyatt Endowed Chair funds at the Texas A&M University.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Reddy, J.N., Unnikrishnan, V.U., Unnikrishnan, G.U. (2009). Computational Homogenization of Polymeric Nanofiber Scaffolds and Biological Cells. In: Gilat, R., Banks-Sills, L. (eds) Advances in Mathematical Modeling and Experimental Methods for Materials and Structures. Solid Mechanics and Its Applications, vol 168. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3467-0_7
Download citation
DOI: https://doi.org/10.1007/978-90-481-3467-0_7
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-3466-3
Online ISBN: 978-90-481-3467-0
eBook Packages: EngineeringEngineering (R0)