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8 - Strength and Toughness of Network Materials

Published online by Cambridge University Press:  15 September 2022

Catalin R. Picu
Catalin R. Picu
Affiliation:
Rensselaer Polytechnic Institute, New York
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Summary

Damage accumulation and rupture of network materials are discussed in this chapter. The chapter is divided into two parts addressing the rupture of networks without and with pre-existing defects. The relation between the network structure and the strength and ductility of materials without pre-existing cracks is defined, and examples from gels, cellulose networks, and nonwovens are provided. The effect of the fiber tortuosity, fiber aspect ratio, fiber preferential alignment, and the variability of fiber and crosslink properties on network strength is discussed. As in other materials, the size effect on strength is important in Network materials and a section is dedicated to statistical aspects of the strength. Failure under multiaxial loading conditions is compared with failure in uniaxial tension. The second part of the chapter presents an analysis of the propagation of cracks in networks. Pronounced notch insensitivity is observed in many materials and numerous examples are presented. Special attention is given to toughness and guidelines are provided to assist the toughening of quasi-brittle Network materials. A subsection is dedicated to the strength, toughness, and fatigue resistance of elastomers and gels.

Keywords

strengthbrittle to ductile transitionsize effectmultiaxial failuredamagenotch insensitivitytougheningcrack propagationcavitationfatigue
Type
Chapter
Information
Network Materials
Structure and Properties
 , pp. 278 - 337
Publisher: Cambridge University Press
Print publication year: 2022

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References

Akagi, Y., Katashima, T., Sakurai, H., Chung, U. I. & Sakai, T. (2013a). Ultimate elongation of polymer gels with controlled network structure. RSC Adv. 3, 13251–13258.CrossRefGoogle Scholar
Akagi, Y., Matsunaga, T., Shibayama, M., Chung, U. I. & Sakai, T. (2010). Evaluation of topological defects in tera-PEG gels. Macromolecules 43, 488–493.CrossRefGoogle Scholar
Akagi, Y., Sakurai, H., Gong, J. P., Chungm, U. I. & Sakai, T. (2013b). Fracture energy of polymer gels with controlled network structure. J. Chem. Phys. 139, 144905.Google Scholar
Alava, M. J. & Niskanen, K. (2006). The physics of paper. Rep. Prog. Phys. 69, 669–723.CrossRefGoogle Scholar
Alava, M. J., Nukala, P. K. V. V. & Zapperi, S. (2009). Size effects in statistical fracture. J. Phys. D: Appl. Phys. 42, 214012.CrossRefGoogle Scholar
de Arcangelis, L., Redner, S. & Herrmann, H. J. (1985). A random fuse model for breaking processes. J. Physique (Paris) Lett. 46, L585–L590.Google Scholar
Balankin, A. S., Susarrey, O., Mora Santos, C. A., et al. (2011). Stress concentration and size effect in fracture of notched heterogeneous material. Phys. Rev. E 83, 015101(R).CrossRefGoogle ScholarPubMed
Ball, J. M. (1982). Discontinuous equilibrium solutions and cavitation in nonlinear elasticity. Phil. Trans. R. Soc. A 306, 557–611.Google Scholar
Bazant, Z. P. (2004). Scaling theories for quasi-brittle structural failure. Proc. Nat. Acad. Sci. 101, 13400–13407.Google Scholar
Bekar, I., Fatt, M. S. H. & Padovan, J. (2002). Deformation and fracture of rubber under tensile impact loading. Tire Sci. Technol. 30, 45–58.CrossRefGoogle Scholar
Benitez, J. A. & Walther, A. (2017). Cellulose nanofibril nanopapers and bioinspired nanocomposites: A review to understand the mechanical property space. J. Mater. Chem. A 5, 16003–16024.CrossRefGoogle Scholar
Bergstrom, P., Hossain, S. & Uesaka, T. (2019). Scaling behaviour of strength of 3D-, semi-flexible-, cross-linked fibre network. Int. J. Sol. Struct. 166, 68–74.Google Scholar
Berthier, E., Kollmer, J. E., Henke, S. E., et al. (2019). Rigidity percolation control of the brittle-ductile transition in disordered networks. Phys. Rev. Mat. 3, 075602.Google Scholar
Boonstra, B. S. T. (1950). Tensile properties of natural and synthetic rubbers at elevated and subnormal temperatures. Rubber Chem. Technol. 23, 338–346.Google Scholar
Borodulina, S., Kulachenko, A., Galland, S. & Nygards, M. (2012). Stress–strain curve of paper revisited. Nordic Pulp Paper Res. J. 27, 318–328.CrossRefGoogle Scholar
Borodulina, S., Motamedian, H. R. & Kulachanko, A. (2018). Effect of fiber and bond strength variations on the tensile stiffness and strength of fiber networks. Int. J. Sol. Struct. 154, 19–32.Google Scholar
Brandberg, A. & Kulachenko, A. (2020). Compression failure in dense non-woven fiber networks. Cellulose 27, 6065–6082.Google Scholar
Bueche, F. & Dudek, T. J. (1963). Tensile strength of amorphous gum. Rubber Chem. Technol. 36, 1–10.CrossRefGoogle Scholar
Burla, F., Dussi, S., Martinez-Torres, C., et al. (2020). Connectivity and plasticity determine collagen network fracture, Proc. Nat. Acad. Sci. 117, 8326–8334.Google Scholar
Chen, C., Wang, Z. & Suo, Z. (2017). Flaw sensitivity of highly stretchable materials. Exteme Mech. Lett. 10, 50–57.CrossRefGoogle Scholar
Chen, N., Koker, M. K. A., Uzun, S. & Silberstein, M. N. (2016a). In-situ X-ray study of the deformation mechanisms of non-woven polypropylene. Int. J. Sol. Struct. 97–98, 200–208.CrossRefGoogle Scholar
Chen, Y., Ridruejo, A., González, C., Llorca, J. & Siegmund, T. (2016b). Notch effect in failure of fiberglass non-woven materials. Int. J. Sol. Struct. 96, 254–264.CrossRefGoogle Scholar
Chocron, S., Pintor, A., Galvez, F., et al. (2008). Lightweight polyethylene nonwoven felts for ballistic impact analysis: material characterization. Composites B 39, 1240–1246.CrossRefGoogle Scholar
Choi, I. S., Roland, C. M. & Bissonnette, L. C. (1994). An elastomeric ejection system. Rubber Chem. Technol. 67, 892–903.CrossRefGoogle Scholar
Choi, K. J., Spruiell, J. E., Fellers, J. F. & Wadsworth, L. C. (1988). Strength properties of melt blown nonwoven webs. Polym. Eng. Sci. 28, 81–89.CrossRefGoogle Scholar
Chou-Wang, M. S. & Horgan, C. O. (1989). Void nucleation and growth for a class of incompressible nonlinearly elastic materials. Int. J. Solids Struct. 25, 1239–1254.Google Scholar
Combaz, E., Bacciarini, C., Charvet, R., Dufour, W. & Mortensen, A. (2011). Multiaxial yield behaviour of Al replicated foam. J. Mech. Phys. Sol. 59, 1777–1793.CrossRefGoogle Scholar
Coran, A. Y. (1978). Vulcanization. In Science and technology of rubber, Eirich, F. R., ed. Academic Press, New York, p. 291.Google Scholar
Curtin, W. L. (1998). Size scaling of strength in heterogeneous materials, Phys. Rev. Lett. 80, 1445–1449.Google Scholar
Deogekar, S., Islam, M. R. & Picu, R. C. (2019). Parameters controlling the strength of stochastic fibrous materials. Int. J. Sol. Struct. 168, 194–202.CrossRefGoogle ScholarPubMed
Deogekar, S. & Picu, R. C. (2018). On the strength of random fiber networks. J. Mech. Phys. Sol. 116, 1–16.Google Scholar
Deogekar, S. & Picu, R. C. (2021). Strength of stochastic fibrous materials under multiaxial loading. Soft Matt. 17, 704–714.Google Scholar
Deshpande, V. S. & Fleck, N. A. (2001). Multi-axial yield behaviour of polymer foams. Acta Materialia 49, 1859–1866.CrossRefGoogle Scholar
Dickie, R. A. & Smith, T. L. (1969). Ultimate tensile properties of elastomers. VI – strength and extensibility of a styrene-butadiene rubber vulcanizate in equal biaxial tension. J. Poly. Sci. A-2 Poly Phys 7, 687–707.Google Scholar
Driscoll, M. M., Chen, B. G., Beuman, T. H., et al. (2016). The role of rigidity in controlling material failure. Proc. Nat. Acad. Sci. 113, 10813–10817.CrossRefGoogle ScholarPubMed
Dussi, S., Tauber, J. & van der Gucht, J. (2020). Athermal fracture of elastic networks: How rigidity challenges the unavoidable size-induced brittleness. Phys. Rev. Lett. 124, 018002.Google Scholar
Duxbury, P. M., Kim, S. G. & Leath, P. L. (1994). Size effect and statistics of fracture in random materials. Mater. Sci. Eng. A 176, 25–31.CrossRefGoogle Scholar
Eriksson, M., Torgnysdotter, A. & Wagberg, L. (2006). Surface modification of wood fibers using polyelectrolyte multilayer technique: Effects on fiber joint and paper strength properties. Ind. Eng. Chem. Res. 45, 5279–5286.Google Scholar
Fang, J. & Li, H. (2012). A facile way to tune mechanical properties of artificial elastomeric proteins-based hydrogels. Langmuir 28, 8260–8265.Google Scholar
Forsstrom, J., Torgnysdotter, A. & Wagberg, L. (2005). Influence of fibre/fibre joint strength and fibre flexibility on the strength of papers from unbleached kraft fibres. Nordic Pulp Paper Res. J. 20, 186–191.Google Scholar
Fukasawa, M., Sakai, T., Chung, U. & Haraguchi, K. (2010). Synthesis and mechanical properties of a nanocomposite gel consisting of a tetra-PEG/Clay network. Macromolecules 43, 4370–4378.Google Scholar
Ganghoffer, J. F. & Schultz, J. (1995). A new theoretical approach to cavitation in rubber. Rubber Chem. Technol. 68, 757–772.Google Scholar
Gent, A. N. & Lindley, P. B. (1959). Internal rupture of bonded rubber cylinders in tension. Proc. R. Soc. London 249A, 195–205.Google Scholar
Gent, A. N., Razzaghi-Kashani, M. & Hamed, G. R. (2003). Why do cracks turn sideways? Rubber Chem. Technol. 76, 122–131.Google Scholar
Gent, A. N. & Tobias, R. H. (1982). Threshold tear strength of elastomers. J. Polym. Sci. Polym. Phys. Ed. 20, 2051–2058.CrossRefGoogle Scholar
Gent, A. N. & Tompkins, D. A. (1969). Surface energy effects for small holes or particles in elastomers. J. Polym. Sci. A-2 Poly Phys 7, 1483–1488.Google Scholar
Gong, J. P. (2010). Why are double network hydrogels so tough? Soft Matt. 6, 2583–2590.Google Scholar
Goutianos, S., Mao, R. & Peijs, T. (2018). Effect of inter-fibre bonding on the fracture of fibrous networks with strong interactions. Int. J. Sol. Struct. 136–137, 271–278.Google Scholar
Green, A. E. & Zerna, W. (1954). Theoretical elasticity. Clarendon Press, Oxford.Google Scholar
Gumbel, E. J. (1935). Les valeurs extrêmes des distributions statistiques. Annales de l’Institut Henri Poincaré, 5, 115–158.Google Scholar
Gustafsson, P. & Niskanen, K. (2011). Paper as an engineering material. In Mechanics of paper products, Niskanen, K., ed. de Gruyter, Berlin, pp. 5–28.CrossRefGoogle Scholar
Hajiali, F. & Shojaei, A. (2017). Network structure and mechanical properties of PDMS filled with nanodiamond. Comp. Sci. Technol. 142, 227–234.Google Scholar
Hamdi, A., Abdelaziz, M. N., Hocine, N. A., Heuillet, P. & Benseddiq, N. (2006). A fracture criterion of rubber-like materials under plane stress conditions. Polym. Testing 25, 994–1005.CrossRefGoogle Scholar
He, M. Y. & Hutchinson, J. W. (1989). Crack deflection at an interface between dissimilar elastic materials. Int. J. Sol. Struct. 25, 1053–1067.Google Scholar
Henriksson, M., Berglund, L. A., Isaksson, P., Lindstrom, T. & Nishino, T. (2008). Cellulose nanopaper structures of high toughness. Biomacromolecules 9, 1579–1585.CrossRefGoogle ScholarPubMed
Heyden, S. (2000). Network modelling for the evaluation of mechanical properties of cellulose fiber fluff. PhD Thesis, Lund University, Lund, Sweden.Google Scholar
Holmes, G. A. & Letton, A. (1994). The dynamic mechanical characterization of a 6300 (340/22,500) weight average molecular weight system. Poly. Eng. Sci. 34, 1635–1643.Google Scholar
Horii, M. & Nemat-Nasser, S. (1993). Micromechanics: overall properties of heterogeneous materials. North-Holland, Amsterdam.Google Scholar
Hou, H. S. & Abeyaratne, R. (1992). Cavitation in elastic and elastic-plastic solids. J. Mech. Phys. Solids 40, 571–592.Google Scholar
Isaksson, P. & Dumont, P. J. J. (2014). Approximation of mode I crack-tip displacement fields by a gradient enhanced elasticity theory. Eng. Fract. Mech. 117, 1–11.Google Scholar
Ito, K. (2007). Novel cross-linking concept of polymer network: Synthesis, structure, and properties of slide-ring gels with freely movable junctions. Polym. J. 39, 489–499.CrossRefGoogle Scholar
Iwamoto, S., Isogai, A. & Iwata, T. (2011). Structure and mechanical properties of wet-spun fibers made from natural cellulose nanofibers. Biomacromolecules 12, 831–836.CrossRefGoogle ScholarPubMed
James, R. D. & Spector, S. J. (1991). The formation of filamentary voids in solids. J. Mech. Phys. Solids 39, 783–813.CrossRefGoogle Scholar
Kluppel, M. (2008). Evaluation of viscoelastic master curves of filled elastomers and applications to fracture mechanics. J. Phys.: Cond. Matt. 21, 035104.Google Scholar
Knauss, W. G. (2015). A review of fracture in viscoelastic materials. Int. J. Fract. 196, 99–146.Google Scholar
Koh, C. T., Strange, D. G. T., Tonsomboon, K. & Oyen, M. L. (2013). Failure mechanisms in fibrous scaffolds. Acta Biomater. 9, 7326–7334.Google Scholar
Krasnoshlyk, V., Rolland du Roscoat, S., Dumont, P. J. J. & Isaksson, P. (2018). Influence of the local mass density variation on the fracture behavior of fiber network materials. Int. J. Sol. Struct. 138, 236–244.Google Scholar
Kulachenko, A. & Uesaka, T. (2012). Direct simulations of fiber network deformation and failure. Mech. Mater. 51, 1–14.Google Scholar
Lake, G. J. (1995). Fatigue and fracture of elastomers. Rubber Chem. Tech. 68, 435–460.Google Scholar
Lake, G. J. (2003). Fracture mechanics and its application to failure in rubber articles. Rubber Chem. Tech. 76, 567–591.Google Scholar
Lake, G. J. & Lindley, P. B. (1964). Ozone cracking, flex cracking and fatigue of rubber. Part 1. Cut growth mechanisms and how they result in fatigue failure. Rubber J. 146, 24–30.Google Scholar
Lake, G. J. & Lindley, P. B. (1965). The mechanical fatigue limit for rubber. J. Appl. Poly. Sci. 9, 1233–1251.Google Scholar
Lake, G. J. & Thomas, A. G. (1967). The strength of highly elastic materials. Proc. R. Soc. London 300, 108–119.Google Scholar
Li, J., Suo, Z. & Vlassak, J. J. (2014). Stiff, strong, and tough hydrogels with good chemical stability. J. Mater. Chem. B 2, 6708–6713.Google Scholar
Lindley, P. B. (1972). Energy for crack growth in model rubber components. J. Strain Anal. 7, 132–140.CrossRefGoogle Scholar
Lindley, P. B. (1973). The relation between hysteresis and the dynamic crack growth resistance of natural rubber. Int. J. Fract. 9, 449–462.Google Scholar
Lopez-Pamies, O. (2009). Onset of cavitation in compressible, isotropic, hyperelastic solids. J. Elast. 94, 115–145.Google Scholar
Mai, T. T., Matsuda, T., Nakajima, T., Gong, J. P. & Urayama, K. (2018). Distinctive characteristics of internal fracture in tough double network hydrogels revealed by various modes of stretching, Macromolecules 51, 5245–5257.CrossRefGoogle Scholar
Malakhovsky, I., & Michels, M. A. J. (2007). Effect of disorder strength on the fracture pattern in heterogeneous networks. Phys. Rev. B 76, 1–13.CrossRefGoogle Scholar
Malho, J. M., Ouellet-Plamondon, C., Ruggeberg, M., et al. (2015). Enhanced plastic deformation of nanofibrillated cellulose film by adsorbed moisture and protein-mediated interactions. Biomacromolecules 16, 311–318.Google Scholar
Mao, R., Goutianos, S., Tu, W., et al. (2017). Comparison of fracture properties of cellulose nanopaper, printing paper and buckypaper. J. Mater. Sci. 52, 9508–9519.Google Scholar
Mark, J. E. (1992). Molecular aspects of rubber-like elasticity. Angew. Makromol. Chem. 202, 1–30.CrossRefGoogle Scholar
Mark, J. E. (1999). Improved elastomers through control of network chain distributions. Rubber Chem. Technol. 72, 465.CrossRefGoogle Scholar
Mark, J. E. & Erman, B. (1988). Rubberlike elasticity: A molecular primer. Wiley & Sons, New York.Google Scholar
Mars, W. V. & Fatemi, A. (2002). A literature survey on fatigue analysis approaches for rubber. Int. J. Fatigue 24, 949–961.CrossRefGoogle Scholar
Mars, W. V. & Fatemi, A. (2004). Factors that affect the fatigue life of rubber: A literature survey. J. Rubber Chem. Tech. 77, 391–412.Google Scholar
McEvoy, H., Ross-Murphy, S. B. & Clark, A. H. (1985). Large deformation and ultimate properties of biopolymer gels: 1. Single biopolymer component systems. Polymer 26, 1483–1492.Google Scholar
Myung, D., Waters, D., Wiseman, M., et al. (2008). Progress in the development of interpenetrating polymer network hydrogels. Polym. Adv. Technol., 19, 647–657.Google Scholar
Nagaoka, S. (1989). Mechanical properties of composite hydrogels. Poly. J. 21, 847–850.Google Scholar
Nawab, Y., Casari, P., Boyard, N. & Jacquemin, F. (2013). Characterization of the cure shrinkage, reaction kinetics, bulk modulus and thermal conductivity of thermoset resin from a single experiment. J. Mater. Sci. 48, 2394–2403.Google Scholar
Normand, V., Lootens, D. L., Amici, E., Plucknett, K. P. & Aymard, P. (2000). New insight into agarose gel mechanical properties. Biomacromolecules 1, 730–738.Google Scholar
Ovaska, M., Betalan, Z., Misksic, A., et al. (2017). Deformation and fracture of echinoderm collagen networks. J. Mech. Beh. Biomed. Mater. 65, 42–52.Google Scholar
Oyen, M. L., Cook, R. F. & Calvin, S. E. (2004). Mechanical failure of human fetal membrane tissues. J. Mater. Sci. 15, 651–658.Google Scholar
Patel, P. C. & Kothari, V. K. (2001). Influence of fibre/fibre joint strength and fibre flexibility on the strength of papers from unbleached kraft fibres. Indian J. Fiber Text. Res. 26, 409–413.Google Scholar
Picu, R. C., Krawczyk, K. K., Wang, Z., et al. (2019). Toughening in nanosilica-reinforced epoxy with tunable filler-matrix interface properties. Comp. Sci. Technol. 183, 107799.Google Scholar
Poisson, J. L., Lacroix, F., Meo, S., Berton, G. & Ranganathan, N. (2011). Biaxial fatigue behavior of a polychloroprene rubber. Int. J. Fatigue 33, 1151–1157.Google Scholar
Popil, R. E. (2017). The physical testing of paper. Smithers Group Company, Shrewsbury, UK.Google Scholar
Purslow, P. P. (1985). The physical basis of meat texture: Observations on the fracture behaviour of cooked bovine M. Semitendinosus. Meat Science 12, 39–60.Google Scholar
Rawal, A., Patel, S. K., Kumar, V., Saraswat, H. & Sayeed, M. M. A. (2013). Damage analysis and notch sensitivity of hybrid needlepunched nonwoven materials. Textile Res. J. 83, 1103–1112.Google Scholar
Rawal, A. & Sayeed, M. M. A. (2013). Mechanical properties and damage analysis of jute-polypropylene hybrid nonwoven geotextiles. Geotextiles and Geomembranes 37, 54–60.CrossRefGoogle Scholar
Ridruejo, A., Gonzalez, C. & Llorca, J. (2012). Failure locus of polypropylene nonwoven fabrics under in-plane biaxial deformation. Comptes Rendus Mechanique 340, 307–319.Google Scholar
Ridruejo, A., Jubera, R., González, C. & LIorca, J. (2015). Inverse notch sensitivity: Cracks can make nonwoven fabrics stronger, J. Mech. Phys. Sol. 77, 61–69.Google Scholar
Roland, C. M. (2006). Mechanical behavior of rubber at high strain rates. Rubber Chem. Technol. 79, 429–459.Google Scholar
Sakai, T., Matsunaga, T., Yamamoto, Y., et al. (2008). Design and fabrication of a high-strength hydrogel with ideally homogeneous network structure from tetrahedron-like macromonomers. Macromolecules 41, 5379–5384.Google Scholar
Sehaqui, H., Ezekiel Mushi, N., Morimune, S., et al. (2012). Cellulose nanofiber orientation in nanopaper and nanocomposites by cold drawing. ACS Appl. Mater. Interfaces 4, 1043–1049.Google Scholar
Shi, L., Long, K., Zhong, Y., et al. (2020). Compressive and shear performance of three-dimensional rigid stochastic fibrous networks: Experiment, finite element simulation, and factor analysis, J. Eur. Ceram. Soc. 40, 115–126.Google Scholar
Sinha-Ray, S., Khansari, S., Yarin, A. L. & Pourdeyhimi, B. (2012). Effect of chemical and physical crosslinking on tensile characteristics of solution-blown soy protein nanofiber mats. Ind. Eng. Chem. Res. 51, 15109–15121.CrossRefGoogle Scholar
Smith, T. L. (1958). Dependence of the ultimate properties of a GR-S rubber on strain rate and temperature. J. Poly. Sci. 32, 99–113.Google Scholar
Smith, T. L. (1963). Ultimate tensile properties of elastomers. I. Characterization by a time and temperature independent failure envelope. J. Polym. Sci. 1, 3597–3615.Google Scholar
Smith, T. L. (1964). Ultimate tensile properties of elastomers. II: Comparison of failure envelopes for unfilled vulcanizates. J. Appl. Phys. 35, 27–36.Google Scholar
Smith, T. L. (1967). Ultimate tensile properties of Elastomers. III. Dependence of the Failure Envelope on Crosslink Density. Rubber Chem. Technol. 40, 544–555.Google Scholar
Stachewicz, U., Peker, I., Tu, W. & Barber, A. H. (2011). Stress delocalization in crack tolerant electrospun nanofiber networks, ACS Appl. Mater. Interfaces 3, 1991–1996.Google Scholar
Stauffer, S. R. & Peppas, N. A. (1992). Poly(vinyl alcohol) hydrogels prepared by freeze–thawing cyclic processing. Polymer 33, 3932–3936.CrossRefGoogle Scholar
Stok, K. & Oloyede, A. (2007). Conceptual fracture parameters for articular cartilage. Clinical Biomech. 22, 725–735.Google Scholar
Sun, C. C. & Mark, J. E. (1987). The effect of network chain length distribution, specifically bimodality, on strain-induced crystallization. J. Poly. Sci. 25, 2073–2083.Google Scholar
Sun, J. Y., Zhao, X., Illeperuma, W. R. K., et al. (2012). Highly stretchable and tough hydrogels. Nature, 489, 133–136.Google Scholar
Sun, T. L., Kurokawa, T., Kuroda, S., et al. (2013). Physical hydrogels composed of polyampholytes demonstrate high toughness and viscoelasticity. Nature Mater. 12, 932–937.Google Scholar
Tada, H., Paris, P. C. & Irwin, G. R. (1973). The stress analysis of cracks handbook. Del Research Corporation, St. Louis, MO.Google Scholar
Tanaka, Y., Fukao, K. & Miyamoto, Y. (2000). Fracture energy of gels. Eur. J. Phys. E 3, 395–401.Google Scholar
Tang, M. Y., Letton, A. & Mark, J. E. (1984). Impact resistance of unfilled and filled bimodal thermosets of PDMS. Colloid Poly. Sci. 262, 990–992.Google Scholar
Taylor, D., O’Mara, N., Ryan, E., Takaza, M. & Simms, C. (2012). The fracture toughness of soft tissues. J. Mech. Beh. Biomed. Mater. 6, 139–147.Google Scholar
Thomas, A. G. (1955). Rupture of rubber. II. The strain concentration at an inclusion. J. Poly. Sci. 18, 177–188.Google Scholar
Thomas, A. G. (1958). Rupture of rubber. V. Cut growth in natural rubber vulcanizates. J. Poly. Sci. 31, 467–480.Google Scholar
Thomas, A. G. (1960). Rupture of rubber. VI. Further experiments on the tear criterion. J. Appl. Polym. Sci. 3, 168–174.Google Scholar
Thomas, A. G. (1994). The development of fracture mechanics for elastomers. Rubber Chem. Tech. 67, G50–G60.Google Scholar
Tonsomboom, K. & Oyen, M. L. (2013). Composite electrospun gelatin fiber–alginate gel scaffolds for mechanically robust tissue engineered cornea. J. Mech. Beh. Biomed. Mater. 21, 185–194.Google Scholar
Torquato, S. (2002). Random heterogeneous materials. Springer, New York.Google Scholar
Torres-Rendon, J. G., Schacher, F. H., Ifuku, S. & Walther, A. (2014). Mechanical performance of macrofibers of cellulose and chitin nanofibrils aligned by wet-stretching: A critical comparison. Biomacromolecules 15, 2709–2717.Google Scholar
Tsunoda, K., Busfield, J. J. C., Davies, C. K. L. & Thomas, A. G. (2000). Effect of materials variables on the tear behavior of a non-crystalizing elastomer. J. Mater. Sci. 35, 5187–5198.Google Scholar
Tutwiler, V., Singh, J., Litvinov, R. I., et al. (2020). Rupture of blood clots: Mechanics and pathophysiology. Sci. Adv. 6, eabc0496.Google Scholar
Wang, Q., Mynar, J. L., Yoshida, M., et al. (2010). High-water-content mouldable hydrogels by mixing clay and a dendritic molecular binder. Nature, 463, 339–343.Google Scholar
Weibull, W. (1961). Fatigue testing and analysis of results. Pergamon Press, Oxford.Google Scholar
Yang, C., Yin, T. & Suo, Z. (2019). Polyacrylamide hydrogels. I. Network imperfection. J. Mech. Phys. Sol. 131, 43–55.Google Scholar
Zhang, L., Rocklin, D. Z., Sander, L. M. & Mao, X. (2017). Fiber networks below the isostatic point: Fracture without stress concentration, Phys. Rev. Mater. 1, 052602(R).Google Scholar
Zhao, X. (2014). Multi-scale multi-mechanism design of tough hydrogels: Building dissipation into stretchy networks, Soft Matt. 10, 672–687.CrossRefGoogle ScholarPubMed
Zhu, H., Zhu, S., Jia, Z., et al. (2015). Anomalous scaling law of strength and toughness of cellulose nanopaper. Proc. Nat. Acad. Sci. 112, 8971–8976.Google Scholar

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