АНАЛІЗ ВПЛИВУ МІКРОБУДОВИ НЕТКАНИХ МАТЕРІАЛІВ НА ЇХНІ МЕХАНІЧНІ ВЛАСТИВОСТІ
DOI:
https://doi.org/10.20998/2079-0775.2020.1.12Ключові слова:
механіка деформівного твердого тіла, матеріал із мережевою структурою, гомогенізація, шлях максимального просування, нетканий матеріалАнотація
У роботі розроблені методи розрахунку напружено-деформованого стану шляхом створення і застосування у практиці розрахунків нелінійних моделей деформування мережевих матеріалів на основі мікромеханіки суцільного середовища. Описані нелінійні математичні моделі деформування матеріалів у вигляді хаотичної мережевої структури одновимірних фрагментів, які побудовані із залученням принципово нових підходів до опису фізико-механічних властивостей на мікрорівні статистичних наборів волоконних ланцюжків і просторової гомогенізації їх макровластивостей. Порівняно із традиційними моделями вони більш адекватно моделюють особливості деформування матеріалів у вигляді просторових хаотичних та упорядкованих мережевих структур, оскільки не залучають низки додаткових нефізичних гіпотез. Це створює принципово нові можливості не тільки для аналізу властивостей таких матеріалів, але й при створенні нових із заданими властивостями.
Посилання
Treloar L.R.G. The Physics of Rubber Elasticity. 3rd edition. Oxford: Clarendon Press, 1975. 322 р.
Lodish H. Molecular Cell Biology. Cambridge: W.H. Freeman & Company, 2000. 973 р.
Boal D.H. Mechanics of the cell. Cambridge: Cambridge University Press, 2002. 406 p.
Holzapfel G.A., Ogden R.W. Mechanics of biological tissue New York: Springer Science & Business Media, 2006. 135 p.
Schmoller K.M., Lieleg O., Bausch A.R. Internal stress in kinetically trapped actin bundle networks. Soft Matter, 2008. Vol. 4(12). Р. 2365 –2367.
Schmoller K. M., Fernandez P., Arevalo R. C., Blair D. L., Bausch A. R. Cyclic hardening in bundled actin networks. Nature communications, 2010. Vol. 1. Р. 134.
Lang N. R., Münster S., Metzner C., Krauss P., Schürmann S., Lange J., ... Fabry, B. Estimating the 3D pore size distribution of biopolymer networks from directionally biased data. Biophysical journal, 2013. Vol. 105(9). P. 1967–1975.
Wen Q., Basu A., Winer J. P., Yodh A., Janmey P. A. Local and global deformations in a strain-stiffening fibrin gel. New Journal of Physics, 2007. Vol. 9(11). Р. 428.
Basu A., Wen Q., Mao X., Lubensky T. C., Janmey P. A., Yodh A. G. Nonaffine displacements in flexible polymer networks. Macromolecules, 2011. Vol. 44(6). Р. 1671–1679.
Stein A. M., Vader D. A., Jawerth L. M., Weitz D. A., Sander L. M.An algorithm for extracting the network geometry of three-dimensional collagen gels. Journal of microscopy, 2008. Vol. 232(3). Р. 463–475.
Ponti A., Machacek M., Gupton S.L., Waterman-Storer C.M., Danuser G. Two distinct actin networks drive the protrusion of migrating cells. Science, 2004. Vol. 305(5691). Р. 1782–1786.
Hearle J.W.S., J.J. Thwaites, J. Amirbayat Mechanics of flexible fibre assemblies. NATO advanced study institutes series. Applied sciences. Sijthoff & Noordhoff, 1980. Р. 293–310.
Picu R.C. Mechanics of random fiber networks-a review. Soft Matter. 2011. Vol. 7. P. 6768–6785.
Gibson L.J., M.F. Ashby, Harley B.A. Cellular Materials in Nature and Medicine. Cambridge: Cambridge University Press, 2010. 309 p.
Pai C. L., Boyce M. C., Rutledge G. C. On the importance of fiber curvature to the elastic moduli of electrospun nonwoven fiber meshes. Polymer, 2011. Vol. 52(26). Р. 6126–6133.
Yu B., Zhao X., Zeng Y., Qi D. The influence of process parameters on needle punched nonwovens investigated using image analysis. RSC Advances, 2017. Vol. 7(9). Р. 5183–5188.
Martínez-Hergueta F., Ridruejo A., González C., LLorca, J. Deformation and energy dissipation mechanisms of needle-punched nonwoven fabrics: A multiscale experimental analysis. International Journal of Solids and Structures, 2015. Vol. 64. Р. 120–131.
Hou X., Acar M., Silberschmidt V.V. 2D finite element analysis of thermally bonded nonwoven materials: Continuous and discontinuous models. Computational Materials Science, 2009. Vol. 46(3). Р. 700–707.
Ridruejo A., González C., LLorca J. Micromechanisms of deformation and fracture of polypropylene nonwoven fabrics. International Journal of Solids and Structures, 2011. Vol. 48(1). Р.153–162.
Tyan Y.C., Liao J.D., Klauser R., Wu I.D., Weng C.C. Assessment and characterization of degradation effect for the varied degrees of ultra-violet radiation onto the collagen-bonded polypropylene non-woven fabric surfaces. Biomaterials, 2002. Vol. 23(1). Р. 65–76.
Haverhals L.M., Reichert W.M., De Long H.C., Trulove P.C.Natural fiber welding. Macromolecular Materials and Engineering, 2010. Vol. 295(5). Р. 425–430.
Li H., Zhu C., Xue J., Ke Q., Xia Y. Enhancing the Mechanical Properties of Electrospun Nanofiber Mats through Controllable Welding at the Cross Points. Macromolecular Rapid Communications, 2017. Vol. 38(9).
Gandhi A., Asija N., Gaur K.K., Rizvi S.J.A., Tiwari V., Bhatnagar N. Ultrasound assisted cyclic solid-state foaming for fabricating ultra-low density porous acrylonitrile–butadiene–styrene foams. Materials Letters, 2013. Vol. 94. Р. 76–78.
Murr L.E., Gaytan S.M., Medina F., ..., Bracke J. Next-generation biomedical implants using additive manufacturing of complex, cellular and functional mesh arrays. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 2010. Vol. 368(1917). Р. 1999–2032.
Martínez-Hergueta F., Ridruej, A., Gonzále, C., Llorca J. Numerical simulation of the ballistic response of needle-punched nonwoven fabrics. International Journal of Solids and Structures, 2017. Vol. 106. Р. 56–67.
Martínez-Hergueta F., Ridruejo A., González C., LLorca J. Ballistic performance of hybrid nonwoven/woven polyethylene fabric shields. International Journal of Impact Engineering, 2018. Vol. 111. Р. 55–65.
Sun J.Y., Zhao X., Illeperuma W.R., ..., Suo Z. Highly stretchable and tough hydrogels. Nature, 2012. Vol. 489(7414). Р. 133–136.
Ethiraj G., Miehe C. Multiplicative magneto-elasticity of magnetosensitive polymers incorporating micromechanically-based network kernels. International Journal of Engineering Science, 2016. Vol. 102. Р. 93–119.
Winkler R. Deformation of semiflexible chains. J. Chem. Phys. 2003. Vol. 118. P. 2919–2928.
Huisman E., C. Storm, G. Barkema Monte Carlo study of multiply crosslinked semiflexible polymer networks. Phys. Rev. E , 2008. Vol. 78. Р. 051801(11).
van Dillen T., Onck P.R., van der Giessen E. Models for stiffening in cross-linked biopolymer networks: A comparative study. J. Mech. Phys. Solids. 2008. Vol. 56(6). P. 2240–2264.
Onck P., T. Koeman, T. van Dillen, E. van der Giessen Alternative explanation of stiffening in cross-linked semiflexible networks. Phys. Rev. Lett. 2005. Vol. 95. Р. 178102(4).
Huisman, E., Lubensky T. Internal stresses, normal modes, and nonaffinity in threedimensional biopolymer networks. Phys. Rev. Lett. 2011. Vol. 106(8). Р. 088301(4).
Blundell J., Terentjev E. The influence of disorder on deformations in semiflexible networks. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2011. Vol. 467. Р. 2330–2349.
Kuhn W. Beziehungen zwischen elastischen Konstanten und Dehnungsdoppelbrechung hochelastischer Stoffe / W. Kuhn, F. Grün // Colloid. Polym. Sci. 1942. Vol. 101(3). Р. 248–271.
Cox HL The elasticity and strength of paper and other fibrous materials. British journal of applied physics. 1952. Vol. 3(3). 72 р.
Storm C., Pastore J.J., MacKintosh F.C., …, Janmey P.A. Nonlinear elasticity in biological gels. Nature. 2005. Vol. 435(7039). Р. 191–194.
Blundell J., Terentjev E.Affine model of stress stiffening in semiflexible filament networks. ArXiv. 2008. 0808.4088: 1–11.
Arruda E.M., Boyce M.C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids. 1993. Vol. 41. Р. 389–412.
Kuhl E., K. Garikipati E.M. Arruda K. Grosh Remodeling of biological tissue: Mechanically induced reorientation of a transversely isotropic chain network. J. Mech. Phys. Solids. 2005. Vol. 53(7). Р. 1552–1573.
Kuhl E., Menzel A., Garikipati K. On the convexity of transversely isotropic chain network models. Philos. Mag. 2006. Vol. 86(21–22). Р. 3241–3258.
Palmer J.S., Boyce M.C. Constitutive modeling of the stressstrain behavior of F-actin filament networks. Acta Biomater. 2008. Vol. 4(3). Р. 597–612.
Head D., Levine A., MacKintosh F. Deformation of cross-linked semiflexible polymer networks. Phys. Rev. Lett. 2003. Vol. 91. P. 108102(4).
Kroon M. A constitutive model for strain-crystallising Rubber-like materials. Mech. Mater. 2010. Vol. 42(9). Р. 873–885.
Miehe C., Göktepe S., Lulei F. A micro-macro approach to rubber-like materials – Part I: the non-affine micro-sphere model of rubber elasticity. J. Mech. Phys. Solids. 2004. Vol. 52. Р. 2617–2660.
Băzant Z. P., Oh B.H. Efficient numerical integration on the surface of a sphere. Z. Angew. Math. Mech. 1986. Vol. 66. Р. 37–49.
Marckmann G., Verron E.Comparison of hyperelastic models for rubber-like materials. Rubber Chem. Technol. 2006. Vol. 79. Р. 835–858.
Treloar LRG Stress-strain data for vulcanised rubber under various types of deformation. Trans. Faraday Soc. 1944. Vol. 40. Р. 59–70.
Heussinger C., Schaefer B., Frey E. Nonaffine rubber elasticity for stiff polymer networks. Phys. Rev. E. 2007. Vol. 76. P. 031906(12).
James Hubert M., Eugene Guth Theory of the elastic properties of rubber. The Journal of Chemical Physics. 1943. Vol. 11(10). Р. 455–481.
Wang Ming Chen, Eugene Guth Statistical theory of networks of non-Gaussian flexible chains. The Journal of Chemical Physics. 1952. Vol. 20(7). Р. 1144–1157.
Ehret A.E., Itskov M., Schmid H. Numerical integration on the sphere and its effect on the material symmetry of constitutive equations: а comparative study. International journal for numerical methods in engineering. 2010. Vol. 81(2). Р. 189–206.
Verron Erwan Questioning numerical integration methods for microsphere (and microplane) constitutive equations. Mechanics of Materials. 2015. Vol. 89. Р. 216–228.
Deam R.T., Sam F. Edwards The theory of rubber elasticity. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 1976. Vol. 280(1296). Р. 317–353.
Heinrich G., Kaliske M.Theoretical and numerical formulation of a molecular based constitutive tube-model of rubber elasticity. Computational and Theoretical Polymer Science. 1997. Vol. 7(3). Р. 227–241.
Miehe C., Göktepe S. A micro–macro approach to rubber-like materials. Part II: the micro-sphere model of finite rubber viscoelasticity. Journal of the Mechanics and Physics of Solids. 2005. Vol. 53(10). Р. 2231–2258.
Göktepe S., Miehe C. A micro–macro approach to rubber-like materials. Part III: The micro-sphere model of anisotropic Mullins-type damage. Journal of the Mechanics and Physics of Solids. 2005. Vol. 53(10). Р. 2259–2283.
Linder C., M. Tkachuk, Miehe C. A micromechanically motivated diffusion-based transient network model and its incorporation into finite rubber viscoelasticity. Journal of the Mechanics and Physics of Solids. 2011. Vol. 59(10). Р. 2134–2156.
Miehe C., Joel Méndez Diez, S. Göktepe, Lisa-Marie Schänzel /Coupled thermoviscoplasticity of glassy polymers in the logarithmic strain space based on the free volume theory. International Journal of Solids and Structures. 2011. Vol. 48(13). Р. 1799–1817
Miehe C., S. Göktepe, Méndez Diez J. Finite viscoplasticity of amorphous glassy polymers in the logarithmic strain space. International Journal of Solids and Structures. 2009. Vol. 46(1). Р. 181–202.
Kuhl E., Menzel A., Garikipati K. On the convexity of transversely isotropic chain network models. Philosophical Magazine. 2006. Vol. 86(21–22). Р. 3241–3258.
Kuhl E., K. Garikipati, E.M. Arruda, Grosh K. Remodeling of biological tissue: mechanically induced reorientation of a transversely isotropic chain network. Journal of the Mechanics and Physics of Solids. 2005. Vol. 53(7). Р. 1552–1573.
Alastrué V., M.A. Martinez, M. Doblaré, Menzel A. Anisotropic microsphere-based finite elasticity applied to blood vessel modelling. Journal of the Mechanics and Physics of Solids. 2009. Vol. 57(1). Р. 178–203.
Menzel A., Waffenschmidt T. A microsphere-based remodelling formulation for anisotropic biological tissues. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. 2009. Vol. 367(1902). Р. 3499–3523.
Waffenschmidt T. Modelling and simulation of adaptation and degradation in anisotropic biological tissues. Ph.D. Thesis. 2013.
Holzapfel G.A., Unterberger M. J., Ogden R. W. An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins. Journal of the mechanical behavior of biomedical materials. 2014. Vol. 38. Р. 78–90.
Van Oosterwyck H., José F. Rodríguez, M. Doblaré, Aznar José M. García An affine micro-sphere-based constitutive model, accounting for junctional sliding, can capture F-actin network mechanics. Computer methods in biomechanics and biomedical engineering. 2013. Vol. 16(9). Р. 1002–1012.
Guilie Joachim, Thien-Nga Lê, Patrick Le Tallec Microsphere model for strain induced crystallization in rubber. In Proceedings of the 8th conference on constitutive models in rubbers, Taylor & Francis. 2013. p. 467–472.
Guilie Joachim, Thien-Nga Le, Patrick Le Tallec Micro-sphere model for straininduced crystallisation and three-dimensional applications. Journal of the Mechanics and Physics of Solids. 2015. Vol. 81. Р. 58–74.
Le Tallec P. polymer modelling: from macroscopic hyperelasticity to strain induced crystallisation //11th. World Congress on Computational Mechanics (WC CM XI) 5th. European Conference on Computational Mechanics (ECCM V) 6th. European Conference on Computational Fluid Dyn amics (ECFD VI) July 20–25, 2014, Barcelona, Spain
Mistry Sunny J., Sanjay Govindjee A micro-mechanically based continuum model for strain-induced crystallization in natural rubber. International Journal of Solids and Structures. 2014. Vol. 51(2). Р. 530–539.
Rastak R., Linder C. A non-affine micro-macro approach to strain-crystallizing rubber-like materials. Journal of the Mechanics and Physics of Solids, 2018. Vol. 111. Р. 67–99.
Thylander S., A. Menzel, Ristinmaa M. A non-affine electroviscoelastic microsphere model for dielectric elastomers: Application to VHB 4910 based actuators. Journal of Intelligent Material Systems and Structures. 2016. p. 1045389X16651157.
Rey T., G. Chagnon, D. Favier, Cam J.-B. Le Hyperelasticity with rate-independent microsphere hysteresis model for rubberlike materials. Computational Materials Science. 2014. Vol. 90. Р. 89–98.
Bergström J.S., Boyce M.C. Constitutive modeling of the large strain time-dependent behavior of elastomers. Journal of the Mechanics and Physics of Solids. 1998. Vol. 46(5). Р. 931–954.
Dal Hüsnü, Michael Kaliske Bergström–Boyce model for nonlinear finite rubber viscoelasticity: theoretical aspects and algorithmic treatment for the FE method. Computational Mechanics. 2009. Vol. 44(6). Р. 809–823.
Sáez P., Alastrué V., Peña E., Doblaré M., Martínez M.A. Anisotropic microsphere-based approach to damage in soft fibered tissue. Biomechanics and modeling in mechanobiology, 2012. Vol. 11(5). Р. 595–608.
Tkachuk M., Linder C. The maximal advance path constraint for the homogenization of materials with random network microstructure. Philosophical Magazine. 2012. Vol. 92. Р. 2779–2808.
Linder C., Miehe C., Tkachuk M. A micromechanically motivated diffusion-based transient network model and its incorporation into finite rubber viscoelasticity. Journal of the Mechanics and Physics of Solids. 2011. Vol. 59. Iss. 10. P.2134–2156.
Tkachuk M.M. Bazovi pidhodi pri doslidzhenni reaktsiyi volokonnih materialiv na zovnishne navantazhennya. Visnik natsionalnogo tehnichnogo universitetu «Kharkivskiy politehnichniy Institut». Kharkiv, NTU «KhPI». 2018, no. 7 (1283), pp. 132–141.
Tkachuk N.N. Analiz reaktsii volokonnyih materialov na deystvie nagruzok na osnove mikromehanicheskih modeley. Visnik natsionalnogo tehnichnogo universitetu «Kharkivskiy politehnichniy Institut». Kharkiv, NTU «KhPI», 2018, no. 25 (1301), pp. 149–155.
Tkachuk M.M. Metod pruzhnoyi gomogenizatsiyi bimodalnih merezh. Visnik natsionalnogo tehnichnogo universitetu «Kharkivskiy politehnichniy Institut». Kharkiv, NTU «KhPI». 2019, no. 7 (1332), pp. 107–113
Tkachuk M., Linder C. A micromechanically based model for viscoelasticity of rubbery polymers. 10th GAMM Seminar on Microstructures. TU Darmstadt, Germany. 2011. Р. 46.
Tkachuk M., Linder C. Microstructural driven Computational Modeling of Polymers. SimTech 2011. International Conference on Simulation Technology. Book of abstarcts: Advanced Mechanics of Multi-Scale and Multi-Field Problems. 2011. University of Stuttgart . P. 26.
Tkachuk M., Linder C. Microstructural driven computational modeling of polymers. Proceedings in Applied Mathematics and Mechanics. 2011. Vol. 11. Р. 557–558.
Tkachuk M., Linder C. The maximal advance path constraint for the homogenization of materials with random network microstructures. 11th GAMM seminar on microstructures. 2012. University of Duisburg-Essen, Germany. P. 46.
Tkachuk M., Linder C. The maximal advance path constraint for the homogenization of materials with random network microstructures. GAMM 2012. 83nd annual meeting of the international association of applied mathematics and mechanics. 2012. TU Darmstadt, Germany. Р. 198–199.
Tkachuk M., Linder C. Homogenization of random elastic networks with non-affine kinematics. Proceedings in applied mathematics and mechanics. 2012. Vol. 12. Р. 417–418.
Tkachuk M., Linder C. Dynamic relaxation with local artificial modes for the analysis of floppy fiber networks. PACAM XIII-6172. The pan american congress of applied mechanics. 2013. Houston, USA. Section 8-4. Biomembranes and tissues.
Tkachuk M. Numerical model for contact with adhesion based on Kalker’s variational principle. 7th GACM Colloquium on Computational Mechanics for Young Scientists from Academia and Industry, Stuttgart, 2017. Р. 190–193.
Chen N., M. N. Silberstein Determination of Bond Strengths in Non-woven Fabrics: a Combined Experimental and Computational Approach. Experimental Mechanics. 2018. Vol. 58(2). Р. 343–355.
Ridruejo A., C. González, J. LLorca A constitutive model for the in-plane mechanical behavior of nonwoven fabrics. International. Journal of Solids and Structures. 2012. No. 49(17). Р. 2215–2229.
Ridruejo A., R. Jubera, C. González, J. LLorca Inverse notch sensitivity: Cracks can make nonwoven fabrics stronger. Journal of the Mechanics and Physics of Solids. 2015. No. 77. Р. 61–69.
Martínez-Hergueta F., Ridruejo A., González C., LLorca J. Deformation and energy dissipation mechanisms of needle-punched nonwoven fabrics: A multiscale experimental analysis. International Journal of Solids and Structures. 2015. No. 64. Р. 120–131.
Martínez-Hergueta F., A. Ridruejo, C. González, J. LLorca A multiscale micromechanical model of needlepunched nonwoven fabrics. International Journal of Solids and Structures. 2016. No. 96. Р. 81–91.
Miehe, C., Schotte, J., & Lambrecht, M. Homogenization of inelastic solid materials at finite strains based on incremental minimization principles. Application to the texture analysis of polycrystals. Journal of the Mechanics and Physics of Solids, 2002. Vol. 50(10), pp. 2123–2167.
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