Nonlinear Mechanical Properties of Random Networks Composed of Nonlinear Fibers

Subject Areas : composite materials

Reyhaneh Mirkhani ¹ , Ali Asghar Alamdar ² , Saeed Ebrahimi ³

1 - PhD student in Textile Engineering, Yazd University, Yazd, Iran.
2 - Associate Professor, Faculty of Textile Engineering, Yazd University, Yazd, Iran.
3 - Department of Mechanical Engineering,Yazd University, Iran

Received: 2021-08-10 Accepted : 2021-12-10 Published : 2024-08-28

Keywords: Athermal Fibers, Biopolymer Networks, Lattice Structure, Mechanical Properties, Nonlinear Fiber, Random Networks ,

Abstract :

The disordered fibrous networks provide load-bearing and main structural to different biological materials such as soft tissues. These networks display a highly nonlinear stress-strain relationship behavior when subjected to mechanical loads. This nonlinear strain-stiffening behavior is dependent on the network microstructure and properties of constituting fiber. We conduct a comprehensive computational study to characterize the importance of material properties of individual fibers as well as the local connectivity or coordination number and bending rigidity in the overall nonlinear mechanical response of a 3D random fiber network. The presented model shows the nonlinear stiffening with increasing applied shear strain more than critical shear strain. We determine the amount of strain-stiffening as a function of network microstructure parameters and the amount of nonlinearity of the fibers. The results show that the constitutive behavior of fibers displays much more strain-stiffening than networks made up of linear fibers. We find that the importance of the nonlinear reaction of individual fiber materials in the general mechanical behavior of networks becomes more important with increasing network connectivity. Furthermore, the amount of stress created in the network under shear increases with the enhanced connectivity of the network due to an increase in the network stiffness. Our model points to the important role of the mechanical response of individual fiber as well as the microstructure of the network in determining the overall mechanical properties of the 3D random network, which could be used to design and better understand the complex biomimetic network systems such as biological tissues and artificial engineering networks.

References:

[1] Humphries, D. L., Grogan, J. A., and Gaffney, E. A., The Mechanics of Phantom Mikado Networks, Journal of Physics Communications, Vol. 2, No. 5, 2018, pp. 055015.
[2] Bhadriraju, K., Hansen, L. K., Extracellular Matrix-and Cytoskeleton-Dependent Changes in Cell Shape and Stiffness, Experimental Cell Research, Vol. 278, No. 1, 2002, pp. 92-100.
[3] Lodish, H., Berk, A., Kaiser, C. A., Kaiser, C., Krieger, M., Scott, M. P., and Matsudaira, P., Molecular Cell Biology, Macmillan, 2008.
[4] Hatami-Marbini, H., Etebu, E., Hydration Dependent Biomechanical Properties of The Corneal Stroma, Experimental Eye Research, Vol. 116, 2013, pp. 47-54.
[5] Hatami-Marbini, H., Rohanifar, M., Mechanical Properties of Subisostatic Random Networks Composed of Nonlinear Fibers, Soft Matter, Vol. 16, No. 30, 2020, pp. 7156-7164.
[6] Hatami-Marbini, H, Mofrad, M. R., Cellular and Biomolecular Mechanics and Mechanobiology, 2011.
[7] Reinhart-King, C. A., Dembo, M., and Hammer, D. A., Cell-Cell Mechanical Communication Through Compliant Substrates, Biophysical Journal, Vol. 95, No. 12, 2008, pp. 6044-6051.
[8] Winer, J. P., Oake, S., and Janmey, P. A., Non-Linear Elasticity of Extracellular Matrices Enables Contractile Cells to Communicate Local Position and Orientation, PloS One, Vol. 4, No. 7, 2009, pp. e6382.
[9] Abhilash, A. S., Baker, B. M., Trappmann, B., Chen, C. S., and Shenoy, V. B., Remodeling of Fibrous Extracellular Matrices by Contractile Cells: Predictions From Discrete Fiber Network Simulations, Biophysical Journal, Vol. 107, No. 8, 2014, pp. 1829-1840.
[10] Chen, Y. C., Chen, M., Gaffney, E. A., and Brown, C. P., Effect of Crosslinking in Cartilage-Like Collagen Microstructures, Journal of the Mechanical Behavior of Biomedical Materials, Vol. 66, 2017, pp. 138-143.
[11] MacKintosh, F. C., Käs, J., and Janmey, P. A., Elasticity of Semiflexible Biopolymer Networks, Physical Review Letters, Vol. 75, No. 24, 1995, pp. 4425.
[12] Storm, C., Pastore, J. J., MacKintosh, F. C., Lubensky, T. C., and Janmey, P. A., Nonlinear Elasticity in Biological Gels, Nature, Vol. 435, No. 7039, 2005, pp. 191-194.
[13] Chaudhuri, O., Parekh, S. H., and Fletcher, D. A., Reversible Stress Softening of Actin Networks, Nature, Vol. 445, No. 7125, 2007, pp. 295-298.
[14] Broedersz, C. P., MacKintosh, F. C., Modeling Semiflexible Polymer Networks, Reviews of Modern Physics, Vol. 86, No. 3, 2014, pp. 995.
[15] Meng, F., Terentjev, E. M., Theory of Semiflexible Filaments and Networks, Polymers, Vol. 9, No. 2, 2017, pp. 52.
[16] Hatami-Marbini, H., Picu, C. R., Modeling the Mechanics of Semiflexible Biopolymer Networks: Non-Affine Deformation and Presence of Long-Range Correlations, In Advances in Soft Matter Mechanics, Springer, Berlin, Heidelberg, 2012, pp. 119-145.
[17] Head, D. A., Levine, A. J., and MacKintosh, F. C., Deformation of Cross-Linked Semiflexible Polymer Networks, Physical Review Letters, Vol. 91, No. 10, 2003, pp. 108102.
[18] Rohanifar, M., Hatami-Marbini, H., Numerical Modelling of Mechanical Properties of 2D Cellular Solids with Bi-Modulus Cell Walls, Mechanics of Advanced Materials and Structures, Vol. 28, No. 3, 2021, pp. 321-329.
[19] Sheinman, M., Broedersz, C. P., and MacKintosh, F. C., Nonlinear Effective-Medium Theory of Disordered Spring Networks, Physical Review E, Vol.85, No. 2, 2012, pp. 021801.
[20] Licup, A. J., Sharma, A., and MacKintosh, F. C., Elastic Regimes of Subisostatic Athermal Fiber Networks, Physical Review E, Vol. 93, No. 1, 2016, pp. 012407.
[21] Sharma, A., Licup, A. J., Rens, R., Vahabi, M., Jansen, K. A., Koenderink, G. H., and MacKintosh, F. C., Strain-Driven Criticality Underlies Nonlinear Mechanics of Fibrous Networks, Physical Review E, Vol. 94, No. 4, 2016, pp. 042407.
[22] Licup, A. J., Münster, S., Sharma, A., Sheinman, M., Jawerth, L. M., Fabry, B., and MacKintosh, F. C., Stress Controls the Mechanics of Collagen Networks, Proceedings of the National Academy of Sciences, Vol. 112, No. 31, 2015, pp. 9573-9578.
[23] Jin, T., Stanciulescu, I., Numerical Simulation of Fibrous Biomaterials with Randomly Distributed Fiber Network Structure, Biomechanics and Modeling in Mechanobiology, Vol. 15, No. 4, 2016, pp. 817-830.
[24] Storm, C., Pastore, J. J., Mackintosh, F. C., Lubensky, T. C., Janmey P. A, Nonlinear Elasticity in Biological Gels, Letters to Nature, No. 435, 2005, pp. 191–194.
[25] Gardel, M. L., Shin, J. H., and Weitz, D. A., Elastic Behavior of Cross-Linked and Bundled Actin Networks, Science, Vol. 304, 2004, pp. 1301–1305.
[26] Hatami-Marbini, H., Picu, C. R., Modeling the Mechanics of Semiflexible Biopolymer Networks: Non-Affine Deformation and Presence of Long-Range Correlations, In Advances in Soft Matter Mechanics, 1rd ed, Springer, Berlin, Heidelberg, 2012, pp. 119–145.
[27] Broedersz, C. P., MacKintosh, F. C., Modeling Semiflexible Polymer Networks, Rev. Mod. Phys, No. 86, 2014, pp. 995–1036.
[28] Wilhelm, J., Frey, E., Elasticity of Stiff Polymer Networks, Phys. Rev. Lett., No. 91, Vol. 10, 2003, pp. 108103.
[29] Head, D. A., Levine, A. J., and MacKintosh, F. C., Deformation of Cross-Linked Semiflexible Polymer Networks, Phys. Rev. Lett., No. 91, Vol. 10, 2003, pp. 108102-1:4.
[30] Reinhardt, J. W., Gooch, K. J., Agent-Based Modeling Traction Force Mediated Compaction of Cell-Populated Collagen Gels Using Physically Realistic Fibril Mechanics, J. Biomech. Eng., Vol. 136, 2014, pp. 021024:1-9.
[31] Hatami-Marbini, H., Simulation of the Mechanical Behavior of Random Fiber Networks with Different Microstructure, Eur Phys J. E. Soft Matter,Vol. 41, 2018, pp. 1-1: 7
[32] Hatami-Marbini, H., Scaling Properties of Three-Dimensional Random Fiber Networks, Philos. Mag. Lett.,Vol. 96, 2016, pp. 165-174.
[33] Hatami-Marbini, H., Shriyan, V., Topology Effects on Nonaffine Behavior of Semiflexible Fiber Networks, Phys. Rev. E., Vol. 96, 2017, pp. 062502-1:7.
[34] Heussinger, C., Frey, E., Floppy Modes and Nonaffine Deformations in Random Fiber Networks, Phys. Rev. Lett., Vol. 97, 2006, pp. 10550-1:4
[35] Lindström, S. B., Kulachenko, A., Jawerth, L. M., and Vader, D. A., Finite-Strain, Finite-Size Mechanics of Rigidly Cross-Linked Biopolymer Networks, Soft Matter, Vol. 9, No. 30, 2013, pp. 7302-7313.
[36] Broedersz, C. P., Mao, X., Lubensky, T. C., and MacKintosh, F. C., Criticality and Isostaticity in Fiber Networks, Nature Physics, Vol. 7, No. 12, 2011, pp. 983-988.
[37] Yang, L., Van der Werf, K. O., Fitié, C. F., Bennink, M. L., Dijkstra, P. J., and Feijen, J., Mechanical Properties of Native and Cross-Linked Type I Collagen Fibrils, Biophysical Journal, Vol. 94, No. 6, 2008, pp. 2204-2211.
[38] Hatami-Marbini, H., Scaling Properties of Three-Dimensional Random Fiber Networks, Philosophical Magazine Letters, Vol. 96, No. 5, 2016, pp. 165-174.
[39] Piechocka, I. K., Jansen, K. A., Broedersz, C. P., Kurniawan, N. A., MacKintosh, F. C., and Koenderink, G. H., Multi-Scale Strain-Stiffening of Semiflexible Bundle Networks, Soft Matter, Vol. 12, No. 7, 2016, pp. 2145-2156.