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The contribution of mechanical interactions to the constitutive modeling of fiber-reinforced elastomers. (English) Zbl 07305826
Summary: Hyperelastic fiber-reinforced materials are conventionally modeled based on the contributions of their constituent materials. A unified invariant-base constitutive model, named Matrix-Fiber-Interaction (MFI) model, is proposed to take into account particularly the mechanical interaction contribution of the constituent materials in fiber-reinforced elastomers with two fiber families. Its high predictive capability for the modeling of the behavior of composites with different material anisotropy is verified by several experiments. This model along with its structurally based framework of material characterization allows measuring distinct contributions of the matrix, fiber, and mechanical interactions in the sense that the latter can be determined regardless of the functional form of the fiber potential. Therefore, in this paper, the MFI model implemented in a user-defined subroutine is used to highlight the importance of mechanical interaction potential. Using three representative examples: uniaxial extension of single-layer plates with different material anisotropy, inflation-extension of a thin cylindrical tube, and load-coupling behaviors in composite laminates, its effect is analyzed. The comparisons of experiments with simulation results underline the prediction quality improvement using the interaction potential in the modeling of single-layer composites. For the two latter deformations, the simulation results comparatively indicate the effect of mechanical interaction potential for the modeling of more complicated structures.
74 Mechanics of deformable solids
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[1] Alhayani, A. A.; Rodríguez, J.; Merodio, J., Competition between radial expansion and axial propagation in bulging of inflated cylinders with application to aneurysms propagation in arterial wall tissue, Int. J. Eng. Sci., 85, 74-89 (2014)
[2] Bishop-Moser, J. L., Design of Generalized Fiber-Reinforced Elasto-Fluidic Systems (2014)
[3] Chaimoon, K.; Chindaprasirt, P., An anisotropic hyperelastic model with an application to soft tissues, Eur. J. Mech. Solid., 78, 103845 (2019) · Zbl 07126022
[4] Chebbi, E.; Wali, M.; Dammak, F., An anisotropic hyperelastic constitutive model for short glass fiber-reinforced polyamide, Int. J. Eng. Sci., 106, 262-272 (2016)
[5] Connolly, F.; Wagner, D. A.; Walsh, C. J.; Bertoldi, K., Sew-free anisotropic textile composites for rapid design and manufacturing of soft wearable robots, Extreme Mechan. Lett., 27, 52-58 (2019)
[6] Criscione, J. C.; Hunter, W. C., Kinematics and elasticity framework for materials with two fiber families, Continuum Mech. Therm., 15, 6, 613-628 (2003) · Zbl 1063.74006
[7] Felt, W.; Remy, C. D., A closed-form kinematic model for fiber-reinforced elastomeric enclosures, J. Mech. Robot., 10, 1, 14501 (2018)
[8] Felt, W.; Telleria, M. J.; Allen, T. F.; Hein, G.; Pompa, J. B.; Albert, K.; Remy, C. D., An inductance-based sensing system for bellows-driven continuum joints in soft robots, Aut. Robots, 1-14 (2017)
[9] Fereidoonnezhad, B.; Naghdabadi, R.; Arghavani, J., A hyperelastic constitutive model for fiber-reinforced rubber-like materials, Int. J. Eng. Sci., 71, 36-44 (2013)
[10] Gong, Y.; Peng, X.; Yao, Y.; Guo, Z., An anisotropic hyperelastic constitutive model for thermoplastic woven composite prepregs, Compos. Sci. Technol., 128, 17-24 (2016)
[11] Gong, Y.; Yan, D.; Yao, Y.; Wei, R.; Hu, H.; Xu, P.; Peng, X., An anisotropic hyperelastic constitutive model with tension-shear coupling for woven composite reinforcements, Int. J. Appl. Mech., 9, 6, 1750083 (2017)
[12] Guo, Z. Y.; Peng, X. Q.; Moran, B., A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus, J. Mech. Phys. Solid., 54, 9, 1952-1971 (2006) · Zbl 1120.74634
[13] Holzapfel, G. A.; Gasser, T. C., A viscoelastic model for fiber-reinforced composites at finite strains: continuum basis, computational aspects and applications, Comput. Methods Appl. Mech. Eng., 190, 34, 4379-4403 (2001)
[14] Holzapfel, G. A.; Gasser, T. C.; Ogden, R. W., A new constitutive framework for arterial wall mechanics and a comparative study of material models, J. Elasticity Phys. Sci. solids, 61, 1, 1-48 (2000) · Zbl 1023.74033
[15] Holzapfel, G. A.; Ogden, R. W., Constitutive modelling of passive myocardium: a structurally based framework for material characterization, Phil. Trans. Roy. Soc. Lond.: Math. Phys. Eng. Sci., 367, 1902, 3445-3475 (2009) · Zbl 1185.74060
[16] Holzapfel, G. A.; Ogden, R. W., An arterial constitutive model accounting for collagen content and cross-linking, J. Mech. Phys. Solid., 103682 (2019)
[17] Horný, L.; Netušil, M.; Horák, Z., Limit point instability in pressurization of anisotropic finitely extensible hyperelastic thin-walled tube, Int. J. Non Lin. Mech., 77, 107-114 (2015)
[18] Liu, H.; Holzapfel, G. A.; Skallerud, B. H.; Prot, V., Anisotropic finite strain viscoelasticity: constitutive modeling and finite element implementation, J. Mech. Phys. Solid., 124, 172-188 (2019)
[19] Mansouri, M. R.; Darijani, H., Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach, Int. J. Solid Struct., 51, 25, 4316-4326 (2014)
[20] Mansouri, M. R.; Darijani, H.; Baghani, M., On the correlation of FEM and experiments for hyperelastic elastomers, Exp. Mech., 57, 2, 195-206 (2017)
[21] Masson, I.; Fassot, C.; Zidi, M., Finite dynamic deformations of a hyperelastic, anisotropic, incompressible and prestressed tube. Applications to in vivo arteries, Eur. J. Mech. Solid., 29, 4, 523-529 (2010)
[22] Melnik, A. V.; Luo, X.; Ogden, R. W., A generalised structure tensor model for the mixed invariant I8, Int. J. Non Lin. Mech. (2018)
[23] Merodio, J.; Saccomandi, G., Remarks on cavity formation in fiber-reinforced incompressible non-linearly elastic solids, Comput. Mater. Sci., 25, 5, 778-792 (2006) · Zbl 1099.74015
[24] Milani, A. S.; Nemes, J. A., An intelligent inverse method for characterization of textile reinforced thermoplastic composites using a hyperelastic constitutive model, Compos. Sci. Technol., 64, 10-11, 1565-1576 (2004)
[25] Murphy, J. G., Transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants, Eur. J. Mech. Solid., 42, 90-96 (2013) · Zbl 1406.74501
[26] Peng, X.; Guo, G.; Zhao, N., An anisotropic hyperelastic constitutive model with shear interaction for cord-rubber composites, Compos. Sci. Technol., 78, 69-74 (2013)
[27] Peng, X. Q.; Guo, Z. Y.; Moran, B., An anisotropic hyperelastic constitutive model with fiber-matrix shear interaction for the human annulus fibrosus, J. Appl. Mech., 73, 5, 815-824 (2006) · Zbl 1111.74590
[28] Ren, J.-s.; Zhou, J.-w.; Yuan, X., Instability analysis in pressurized three-layered fiber-reinforced anisotropic rubber tubes in torsion, Int. J. Eng. Sci., 49, 4, 342-353 (2011) · Zbl 1231.74085
[29] Spencer, A. J.M., Constitutive theory for strongly anisotropic solids, (Continuum Theory of the Mechanics of Fibre-Reinforced Composites (1984), Springer), 1-32 · Zbl 0588.73117
[30] Topol, H.; Demirkoparan, H.; Pence, T. J., Morphoelastic fiber remodeling in pressurized thick-walled cylinders with application to soft tissue collagenous tubes, Eur. J. Mech. Solid., 77, 103800 (2019) · Zbl 07111002
[31] Treloar, L. R.G., The elasticity of a network of long-chain molecules, I. Trans. Faraday Soc., 39, 36-41 (1943)
[32] Tricerri, P.; Dedè, L.; Gambaruto, A.; Quarteroni, A.; Sequeira, A., A numerical study of isotropic and anisotropic constitutive models with relevance to healthy and unhealthy cerebral arterial tissues, Int. J. Eng. Sci., 101, 126-155 (2016)
[33] Wagner, D. R.; Lotz, J. C., Theoretical model and experimental results for the nonlinear elastic behavior of human annulus fibrosus, J. Orthop. Res., 22, 4, 901-909 (2004)
[34] Zidi, M.; Cheref, M., Finite deformations of a hyperelastic, compressible and fibre reinforced tube, Eur. J. Mech. Solid., 21, 6, 971-980 (2002) · Zbl 1027.74004
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