Comparative Assessment of Hyperelastic Models for Simulating Mechanical Hysteresis in Synthetic Yarns for Offshore Mooring

Articles in Press

Document Type : Research Paper

Authors
Daniel Magalhães da Cruz
Felipe Tempel Stumpf
Jakson Manfredini Vassoler
Applied Mechanics Group (GMAp), Graduate Program in Mechanical Engineering (PROMEC), Federal University of Rio Grande do Sul (UFRGS), 425, Sarmento Leite Street, Porto Alegre, 90050-170, Brazil
10.22055/jacm.2026.49306.5879
Abstract
Synthetic fibers are widely employed in offshore mooring systems due to their high specific strength, low weight, corrosion resistance, and favorable fatigue performance. However, their mechanical response under cyclic loading is complex, involving nonlinear elasticity, viscoelasticity, energy dissipation, stiffness evolution, and load-history dependence. Reliable constitutive models are therefore essential for predictive analysis and design. This study presents a systematic comparative assessment of phenomenological hyperelastic strain energy models for simulating mechanical hysteresis in synthetic yarns. The constitutive framework combines finite deformations, incompressibility, and viscoelastic memory through an internal variable, with model parameters identified by constrained numerical optimization using stabilized experimental hysteresis curves as reference data. Seven fiber classes were investigated: aramid, high-modulus polyethylene (HMPE), low-creep HMPE, liquid crystal polymer (LCP), polyamide (PA), polyester (PET), and high-elongation polyester (HE PET). Twenty strain energy models were evaluated under the same computational framework, resulting in 140 material-model combinations. The simulations reproduced the experimental hysteresis responses with good overall consistency, yielding a global mean error of 3.325%. Stumpf-Marczak provided the best global performance, followed by Davies-De-Thomas, Yeoh Modified, and Bechir-Boufala-Chevalier. Aramid and LCP presented the lowest material mean errors, whereas PA exhibited the highest, associated with its more complex stress–strain curvature changes during cycling. The results demonstrate that model selection depends on the material response and that greater mathematical complexity does not necessarily ensure better fitting. The study provides an exploratory comparative baseline for constitutive model selection and highlights the need to balance fitting accuracy, numerical robustness, and computational effort in offshore mooring applications.
Keywords
Cyclic behavior
Hyperelastic models
Synthetic fibers
Continuum mechanics
Parameter optimization
Strain energy function
Subjects

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[1] Del Vecchio, C.J.M., Light weight materials for deep water moorings, Ph.D. Thesis, University of Reading, Reading, UK, 1992.
[2] Weller, S.D., Johanning, L., Davies, P., Banfield, S.J., Synthetic mooring ropes for marine renewable energy applications, Renewable Energy, 83, 2015, 1268-1278.
[3] Bastos, M.B., Silva, A.L.N., Evaluating Offshore Rope Fibers: Impact on Mooring Systems Integrity and Performance, Offshore Technology Conference, Houston, USA, OTC-30830-MS, 2020.
[4] Li, D., Lian, Y., Zheng, J., Chen, W., Liu, H., Yim, S.C., Review of Synthetic Fiber Ropes for Deepwater Moorings, 44th International Conference on Ocean, Offshore and Arctic Engineering, Vancouver, Canada, 2025.
[5] McKenna, H.A., Hearle, J.W.S., O'Hear, N., Handbook of fibre rope technology, Woodhead Publishing, 2004.
[6] da Cruz, D.M., Zangalli, L.B., Barreto, M.A., da Silva, A.L.N., Bastos, I.N., Offshore mooring challenges for FOWT systems and MRE devices: Synthetic fiber solutions for mooring ropes, Proceedings of the Rio Oil and Gas, Rio de Janeiro, Brazil, 2024.
[7] Weller, S.D., Davies, P., Vickers, A.W., Johanning, L., Synthetic rope responses in the context of load history: Operational performance, Ocean Engineering, 83, 2014, 111-124.
[8] Lian, Y., Zhang, Y., Xie, Y., Zheng, J., Chen, W.X., Chen, S.C., Zhang, J., Xue, M.A., Yim, S.C., Effects of bedding-in loading history on mechanical behaviors of aramid HMPE and polyester mooring ropes, Ocean Engineering, 321, 2025, 120413.
[9] Lechat, C., Bunsell, A.R., Davies, P., Piant, A., Mechanical behaviour of polyethylene terephthalate & polyethylene naphthalate fibres under cyclic loading, Journal of Materials Science, 41(6), 2006, 1745-1756.
[10] Liu, H., Huang, W., Lian, Y., Li, L., An experimental investigation on nonlinear behaviors of synthetic fiber ropes for deepwater moorings under cyclic loading, Applied Ocean Research, 45, 2014, 22-32.
[11] Li, G., Li, W., Lin, S., Li, H., Ge, Y., Sun, Y., Dynamic stiffness of braided HMPE ropes under long-term cyclic loads: A full-scale experimental investigation, Ocean Engineering, 230, 2021, 109076.
[12] da Cruz, D.M., Begnini, G.R., Cruz Junior, A.J., Stumpf, F.T., Vassoler, J.M., Clain, F.M., Guilherme, C.E.M., Normalized stiffness assessment in mechanical protocol: polyester sub-ropes for offshore mooring systems, Ships and Offshore Structures, 2025, 1-17.
[13] Brinson, H.F., Brinson, L.C., Polymer Engineering Science and Viscoelasticity: An Introduction, Springer-Verlag New York, 2008.
[14] Khan, A.S., Lopez-Pamies, O., Kazmi, R., Thermo-mechanical large deformation response and constitutive modeling of viscoelastic polymers over a wide range of strain rates and temperatures, International Journal of Plasticity, 22(4), 2006, 581-601.
[15] Al-Rub, R.K.A., Tehrani, A.H., Darabi, M.K., Application of a large deformation nonlinear-viscoelastic viscoplastic viscodamage constitutive model to polymers and their composites, International Journal of Damage Mechanics, 24(2), 2015, 198-244.
[16] Fallahi, H., Taheri-Behrooz, F., Phenomenological constitutive modeling of the non-linear loading-unloading response of UD fiber-reinforced polymers, Composite Structures, 292, 2022, 115671.
[17] Nguyen, N., Thiagarajan, K., Nonlinear viscoelastic modeling of synthetic mooring lines, Marine Structures, 85, 2022, 103257.
[18] Talebi, S., Darijani, H., A pseudo-strain energy density function for mechanical behavior modeling of visco-hyperelastic materials, International Journal of Mechanical Sciences, 208, 2021, 106652.
[19] Portillo, F.J.S., Sempere, O.C., Marques, E.A.S., Lozano, M.S., Da Silva, L.F.M., Mechanical Characterisation and Comparison of Hyperelastic ‎Adhesives: Modelling and Experimental Validation, Journal of Applied and Computational Mechanics, 8(1), 2022, 359-369.
[20] Shah, N.H., Ali, S.F., A hyperelastic strain energy function for isotropic rubberlike materials, International Journal of Mechanical Sciences, 279, 2024, 109472.
[21] Anssari-Benam, A., Hyperinelasticity: An energy-based constitutive modelling approach to isothermal large inelastic deformation of polymers. Part I, Journal of the Mechanics and Physics of Solids, 192, 2024, 105790.
[22] Eisenträger, S., Maurer, L., Juhre, D., Altenbach, H., Eisentraeger, J., Implementation of isotropic hyperelastic material models: a »template« approach, Acta Mechanica, 236(3), 2025, 1899-1934.
[23] Bahreman, M., Darijani, H., Fooladi, M., Constitutive modeling of isotropic hyperelastic materials using proposed phenomenological models in terms of strain invariants, Polymer Engineering & Science, 56(3), 2016, 299-308.
[24] Melly, S.K., Liu, L., Liu, Y., Leng, J., A review on material models for isotropic hyperelasticity, International Journal of Mechanical System Dynamics, 1(1), 2021, 71-88.
[25] Larbi, S., Tewfik, G., Mechri, A., Rezak, A., Optimization of a Specialized Forming Code for Rubber Products, Journal of Applied and Computational Mechanics, 2026, DOI: 10.22055/jacm.2026.48588.5345.
[26] da Cruz, D.M., Penaquioni, A., Zangalli, L.B., Bastos, M.B., Bastos, I.N., da Silva, A.L.N., Non-destructive testing of high-tenacity polyester sub-ropes for mooring systems, Applied Ocean Research, 134, 2023, 103513.
[27] Hoss, L., Modelos constitutivos hiperelásticos para elastômeros incompressíveis: ajuste, comparação de desempenho e proposta de um novo modelo, M.Sc. Thesis, Graduate Program in Mechanical Engineering, Federal University of Rio Grande do Sul, Porto Alegre, Brazil, 2009.
[28] da Cruz, D.M., Estudo teórico, experimental e numérico do comportamento viscoelástico e caracterização de fibras sintéticas poliméricas, B.Sc. Thesis, School of Engineering, Federal University of Rio Grande, Rio Grande, Brazil, 2022.
[29] Stumpf, F.T., Guilherme, C.E.M., da Cruz, D.M., da Silva, A.H.M.F.T., Bastos, M.B., A general constitutive model for the numerical simulation of different synthetic fibres used in offshore mooring, Ships and Offshore Structures, 18(9), 2023, 1338-1344.
[30] da Cruz, D.M., Guilherme, C.E.M., Stumpf, F.T., Bastos, M.B., Numerical Assessment of Mechanical Behavior of Mooring Lines Using Hybrid Synthetic Fiber-Rope Segments, Offshore Technology Conference, Houston, USA, OTC-31906-MS, 2022.
[31] Stumpf, F.T., Barreto, M.A., da Cruz, D.M., Guilherme, C.E.M., Numerical simulation of multi-material hybrid lines for offshore mooring, Ocean Engineering, 305, 2024, 117979.
[32] da Cruz, D.M., Popiolek Júnior, T.L., Barreto, M.A., Guilherme, C.E.M., Stumpf, F.T., Evaluation of energy models for numerical simulation of the mechanical behavior of polyester multifilaments, The Journal of Engineering and Exact Sciences, 9(1), 2023, 15321–01e.
[33] da Cruz, D.M., Barreto, M.A., Zangalli, L.B., Stumpf, F.T., Vassoler, J.M., Guilherme, C.E.M., Numerical simulation of the stress-strain behavior of polymeric fibers for mooring offshore structures, Proceedings XLIV Ibero-Latin American Congress on Computational Methods in Engineering, Porto, Portugal, 2023.
[34] da Cruz, D.M., Popiolek Júnior, T.L., Barreto, M.A., de Souza, S.P., Zangalli, L.B., Cruz Junior, A.J., Martins, T.C., da Silva, A.L.N., Bastos, I.N., Guilherme, C.E.M., Numerical simulation with hyperelastic constitutive model for high-performance multifilaments used in offshore mooring ropes, The Journal of Engineering and Exact Sciences, 10(2), 2024, 17255.
[35] da Cruz, D.M., Zangalli, L.B., Barreto, M.A., da Silva, A.L.N., Bastos, I.N., Numerical Simulation of Creep Behavior in Low Creep HMPE Fibers Used for Offshore Mooring Ropes, Offshore Technology Conference Brasil, Rio de Janeiro, Brazil, OTC-36033-MS, 2025.
[36] da Cruz, D.M., Bastos, I.N., da Silva, A.L.N., Vassoler, J.M., Stumpf, F.T., Cruz Junior, A.J., Martins, T.C., Clain, F.M., Guilherme, C.E.M., Dynamic Cycle Simulation in Offshore Mooring Fibers: Modified Mathematical Models and Dependence on Invariants of Continuum Mechanics, VETOR - Journal of Exact Sciences and Engineering, 35(1), 2025, e18256.
[37] da Cruz, D.M., Zangalli, L.B., Barreto, M.A., Bastos, I.N., da Silva, A.L.N., Numerical simulation of the stress-strain behavior of polyester subropes for offshore mooring and relationship with change stiffness during the test protocol, Proceedings of the Rio Oil and Gas, Rio de Janeiro, Brazil, 2024.
[38] da Cruz, D.M., Zangalli, L.B., Cruz Junior, A.J., da Silva, A.L.N., Bastos, I.N., Guilherme, C.E.M., Clain, F.M., Vassoler, J.M., Stumpf, F.T., Constitutive Simulation of Synthetic Fibers for Offshore Mooring Under Cyclic Loading: Hysteresis Stabilization and Stiffness Evolution, Proceedings XLVI Ibero-Latin American Congress on Computational Methods in Engineering, Vitória, Brazil, 2025.
[39] da Cruz, D.M., Popiolek Júnior, T.L., Bastos, I.N., da Silva, A.P., da Silva, A.L.N., Vassoler, J.M., Stumpf, F.T., Numerical Modeling of the Stress-Strain Response in Progressive Loading Cycles of Polyester Multifilaments, Anais do XXVIII Encontro Nacional de Modelagem Computacional e XVI Encontro de Ciência e Tecnologia de Materiais, Montes Claros, Brazil, 2025.
[40] American Society for Testing and Materials, Standard Test Methods for Linear Density of Textile Fibers, ASTM D1577-07, 2018.
[41] International Organization for Standardization, Textiles — Yarns from packages — Determination of single-end breaking force and elongation at break using constant rate of extension (CRE) tester, ISO 2062, 2009.
[42] International Organization for Standardization, Textiles — Standard atmospheres for conditioning and testing, ISO 139, 2005.
[43] Simo, J.C., Hughes, T.J.R., Computational Inelasticity, Springer Science & Business Media, 2006.
[44] Flory, P.J., Thermodynamic relations for high elastic materials, Transactions of the Faraday Society, 57, 1961, 829-838.
[45] The MathWorks, Inc., fmincon: Solve constrained nonlinear multivariable minimization problem, 2026, https://www.mathworks.com/help/optim/ug/fmincon.html.
[46] Holzapfel, G.A., Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science, John Wiley & Sons, 2000.
[47] Truesdell, C., Noll, W., The Non-Linear Field Theories of Mechanics, Springer-Verlag Berlin, 1965.
[48] Beatty, M.F., Topics in Finite Elasticity: Hyperelasticity of Rubber, Elastomers, and Biological Tissues—With Examples, Applied Mechanics Reviews, 40(12), 1987, 1699-1734.
[49] Amin, A.F.M.S., Alam, M.S., Okui, Y., An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification, Mechanics of Materials, 34(2), 2002, 75-95.
[50] Bechir, H., Boufala, K., Chevalier, Y., Strain energy density function for carbon black filled rubber vulcanized for industrial applications, Mécanique & Industries, 3(3), 2002, 245-252.
[51] Davies, C.K.L., De, D.K., Thomas, A.G., Characterization of the Behavior of Rubber for Engineering Design Purposes. 1. Stress-Strain Relations, Rubber Chemistry and Technology, 67(4), 1994, 716-728.
[52] Gent, A.N., Thomas, A.G., Forms for the stored (strain) energy function for vulcanized rubber, Journal of Polymer Science, 28(118), 1958, 625-628.
[53] Hartmann, S., Neff, P., Polyconvexity of generalized polynomial-type hyperelastic strain energy functions for near-incompressibility, International Journal of Solids and Structures, 40 (11), 2003, 2767-2791.
[54] Humphrey, J.D., Yin, F.C.P., On Constitutive Relations and Finite Deformations of Passive Cardiac Tissue: I. A Pseudostrain-Energy Function, Journal of Biomechanical Engineering, 109(4), 1987, 298-304.
[55] Knowles, J.K., The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids, International Journal of Fracture, 13(5), 1977, 611-639.
[56] Mooney, M., A Theory of Large Elastic Deformation, Journal of Applied Physics, 11(9), 1940, 582-592.
[57] Rivlin, R.S., Saunders, D.W., Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber, Philosophical Transactions of the Royal Society of London, Series A: Mathematical and Physical Sciences, 243(865), 1951, 251-288.
[58] Treloar, L.R.G., The elasticity and related properties of rubbers, Reports on Progress in Physics, 36(7), 1973, 755-826.
[59] Stumpf, F.T., Marczak, R.J., Constitutive framework of a new hyperelastic model for isotropic rubber-like materials for finite element implementation, Latin American Journal of Solids and Structures, 18(2), 2021, e346.
[60] Veronda, D.R., Westmann, R.A., Mechanical characterization of skin—Finite deformations, Journal of Biomechanics, 3(1), 1970, 111-124.
[61] Yamashita, Y., Kawabata, S., Approximated form of the strain energy-density function of carbon black filled rubbers for industrial applications, International Polymer Science and Technology, 20, 1993, T-52.
[62] Yeoh, O.H., Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates, Rubber Chemistry and Technology, 63(5), 1990, 792-805.
[63] Yeoh, O.H., Some Forms of the Strain Energy Function for Rubber, Rubber Chemistry and Technology, 66(5), 1993, 754-771.
[64] Seyfi, B., Rassoli, A., Imeni Markhali, M., Fatouraee, N., Characterization of the Nonlinear Biaxial Mechanical Behavior‎ of Human Ureter using Constitutive Modeling and Artificial‎ Neural Networks, Journal of Applied and Computational Mechanics, 8(4), 2022, 1186-1195.
[65] Topol, H., Al-Chlaihawi, M.J., Demirkoparan, H., Merodio, J., Bifurcation of Fiber-Reinforced Cylindrical Membranes under‎ Extension, Inflation, and Swelling, Journal of Applied and Computational Mechanics, 9(1), 2023, 113-128.
[66] Al-Chlaihawi, M.J., Font, A., Topol, H., Demirkoparan, H., Merodio, J., Bulging and Bending of a Thick-Walled Cylinder with Residual Stress under Combined Extension and Inflation, Journal of Applied and Computational Mechanics, 12(3), 2026, 1256-1275.
[67] Asth, L.S., de Lima, K.C., Moreira, C.S., Knupp, D.C., Stutz, L.T., Parameter Estimation and Strain Energy Model Class Selection for a Hyperelastic Composite Under Compression, VETOR - Journal of Exact Sciences and Engineering, 36(1), 2026, e20864.
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