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A parameter identification scheme of the visco-hyperelastic constitutive model of rubber-like materials based on general regression neural network

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Abstract

In this research, the hyperelastic strain energy density function based on the exponential–logarithmic invariant is extended to the visco-hyperelastic constitutive model to describe the mechanical characteristics of the rate dependence and large deformations of rubber-like materials. On the basis of the general regression neural network (GRNN) technique, a parameter identification approach for the visco-hyperelastic model is designed. In addition, the proposed research scheme is verified using various uniaxial experimental data of rubber-like materials. The comparison results reveal that the predicted stress responses agree well with the experimental data under different loading conditions. This paper concludes that the present model can describe the mechanical behavior of rubber-like materials and that the GRNN-based approach is practicable for parameter identification of complex visco-hyperelastic constitutive models.

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References

  1. Arlot, S., Celisse, A.: A survey of cross-validation procedures for model selection. Stat. Surv. 4, 40–79 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bazkiaei, A.K., Shirazi, K.H., Shishesaz, M.: A framework for model base hyper-elastic material simulation. J. Rubber Res. 23(4), 287–299 (2020)

    Article  Google Scholar 

  3. Beda, T.: An approach for hyperelastic model-building and parameters estimation a review of constitutive models. Eur. Polym. J. 50, 97–108 (2014)

    Article  Google Scholar 

  4. Brinson, H.F., Brinson, L.C.: Polymer Engineering Science and Viscoelasticity: An Introduction. Springer, Cham (2015)

    Book  Google Scholar 

  5. Carpi, F., De Rossi, D., Kornbluh, R., et al.: Dielectric Elastomers as Electromechanical Transducers: Fundamentals, Materials, Devices, Models and Applications of an Emerging Electroactive Polymer Technology. Elsevier, Amsterdam (2011)

    Google Scholar 

  6. Carpi, F., Anderson, I., Bauer, S., et al.: Standards for dielectric elastomer transducers. Smart Mater. Struct. 24(10), 105025 (2015)

    Article  Google Scholar 

  7. Darijani, H., Naghdabadi, R.: Hyperelastic materials behavior modeling using consistent strain energy density functions. Acta Mech. 213(3), 235–254 (2010)

    Article  MATH  Google Scholar 

  8. Elyasi, N., Taheri, K.K., Narooei, K., et al.: A study of hyperelastic models for predicting the mechanical behavior of extensor apparatus. Biomech. Model. Mechanobiol. 16(3), 1077–1093 (2017)

    Article  Google Scholar 

  9. Fatt, M.S.H., Ouyang, X.: Integral-based constitutive equation for rubber at high strain rates. Int. J. Solids Struct. 44(20), 6491–6506 (2007)

    Article  MATH  Google Scholar 

  10. Gent, A.N.: A new constitutive relation for rubber. Rubber Chem. Technol. 69(1), 59–61 (1996)

    Article  MathSciNet  Google Scholar 

  11. Goh, S., Charalambides, M., Williams, J.: Determination of the constitutive constants of non-linear viscoelastic materials. Mech. Time-Depend. Mater. 8(3), 255–268 (2004)

    Article  Google Scholar 

  12. Hou, J., Lu, X., Zhang, K., et al.: Parameters identification of rubber-like hyperelastic material based on general regression neural network. Materials 15(11), 3776 (2022)

    Article  Google Scholar 

  13. Im, S., Kim, W., Kim, H., et al.: Artificial neural network modeling of anisotropic hyperelastic materials based on computational crystal structure data. In: AIAA Scitech 2020 Forum, p. 0397 (2020)

  14. Khajehsaeid, H., Arghavani, J., Naghdabadi, R.: A hyperelastic constitutive model for rubber-like materials. Eur. J. Mech. A/Solids 38, 144–151 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Khajehsaeid, H., Arghavani, J., Naghdabadi, R., et al.: A visco-hyperelastic constitutive model for rubber-like materials: a rate-dependent relaxation time scheme. Int. J. Eng. Sci. 79, 44–58 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kim, D.H., Ghaffari, R., Lu, N., et al.: Flexible and stretchable electronics for biointegrated devices. Annu. Rev. Biomed. Eng. 14(1), 113–128 (2012)

    Article  Google Scholar 

  17. Li, C., Lua, J.: A hyper-viscoelastic constitutive model for polyurea. Mater. Lett. 63(11), 877–880 (2009)

    Article  Google Scholar 

  18. Li, T., Keplinger, C., Baumgartner, R., et al.: Giant voltage-induced deformation in dielectric elastomers near the verge of snap-through instability. J. Mech. Phys. Solids 61(2), 611–628 (2013)

    Article  Google Scholar 

  19. Li, T., Zou, Z., Mao, G., et al.: Agile and resilient insect-scale robot. Soft Rob. 6(1), 133–141 (2019)

    Article  Google Scholar 

  20. Li, Y., Sang, J., Wei, X., et al.: Inverse identification of hyperelastic constitutive parameters of skeletal muscles via optimization of AI techniques. Comput. Methods Biomech. Biomed. Eng. 24(15), 1647–1659 (2021)

    Article  Google Scholar 

  21. Lion, A.: A constitutive model for carbon black filled rubber: experimental investigations and mathematical representation. Contin. Mech. Thermodyn. 8(3), 153–169 (1996)

    Article  MathSciNet  Google Scholar 

  22. Mansouri, M., Darijani, H.: Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach. Int. J. Solids Struct. 51(25–26), 4316–4326 (2014)

    Article  Google Scholar 

  23. Mao, G., Huang, X., Liu, J., et al.: Dielectric elastomer peristaltic pump module with finite deformation. Smart Mater. Struct. 24(7), 075026 (2015)

    Article  Google Scholar 

  24. Martins, P., Natal Jorge, R., Ferreira, A.: A comparative study of several material models for prediction of hyperelastic properties: application to silicone-rubber and soft tissues. Strain 42(3), 135–147 (2006)

    Article  Google Scholar 

  25. Matin, Z., Moghimi Zand, M., Salmani Tehrani, M., et al.: A visco-hyperelastic constitutive model of short-and long-term viscous effects on isotropic soft tissues. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 234(1), 3–17 (2020)

    Article  Google Scholar 

  26. Mooney, M.: A theory of large elastic deformation. J. Appl. Phys. 11(9), 582–592 (1940)

    Article  MATH  Google Scholar 

  27. Narooei, K., Arman, M.: Generalization of exponential based hyperelastic to hyper-viscoelastic model for investigation of mechanical behavior of rate dependent materials. J. Mech. Behav. Biomed. Mater. 79, 104–113 (2018)

    Article  Google Scholar 

  28. Ogden, R.W.: Non-linear Elastic Deformations. Courier Corporation, Chelmsford (1997)

    Google Scholar 

  29. Ogden, R.W., Saccomandi, G., Sgura, I.: Fitting hyperelastic models to experimental data. Comput. Mech. 34(6), 484–502 (2004)

    Article  MATH  Google Scholar 

  30. Patra, K., Sahu, R.K.: A visco-hyperelastic approach to modelling rate-dependent large deformation of a dielectric acrylic elastomer. Int. J. Mech. Mater. Des. 11(1), 79–90 (2015)

    Article  Google Scholar 

  31. Rivlin, R.S., Thomas, A.: Large elastic deformations of isotropic materials viii. Strain distribution around a hole in a sheet. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci. 243(865), 289–298 (1951)

    MathSciNet  MATH  Google Scholar 

  32. Rooki, R.: Application of general regression neural network (GRNN) for indirect measuring pressure loss of Herschel–Bulkley drilling fluids in oil drilling. Measurement 85, 184–191 (2016)

    Article  Google Scholar 

  33. Specht, D.F., et al.: A general regression neural network. IEEE Trans. Neural Netw. 2(6), 568–576 (1991)

    Article  Google Scholar 

  34. Steinmann, P., Hossain, M., Possart, G.: Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data. Arch. Appl. Mech. 82(9), 1183–1217 (2012)

    Article  MATH  Google Scholar 

  35. Sunderland, P., Yu, W., Månson, J.A.: A thermoviscoelastic analysis of process-induced internal stresses in thermoplastic matrix composites. Polym. Compos. 22(5), 579–592 (2001)

    Article  Google Scholar 

  36. Talebi, S., Darijani, H.: A pseudo-strain energy density function for mechanical behavior modeling of visco-hyperelastic materials. Int. J. Mech. Sci. 208(106), 652 (2021)

    Google Scholar 

  37. Taylor, R.L., Pister, K.S., Goudreau, G.L.: Thermomechanical analysis of viscoelastic solids. Int. J. Numer. Methods Eng. 2(1), 45–59 (1970)

    Article  MATH  Google Scholar 

  38. Treloar, L.G.: The Physics of Rubber Elasticity. Oxford University Press, Oxford (1975)

    Google Scholar 

  39. Xiang, Y., Zhong, D., Wang, P., et al.: A physically based visco-hyperelastic constitutive model for soft materials. J. Mech. Phys. Solids 128, 208–218 (2019)

    Article  MathSciNet  Google Scholar 

  40. Yeoh, O.H.: Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66(5), 754–771 (1993)

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 12172270), the Qin Chuangyuan “Scientists+Engineers” Team Construction Project in Shaanxi Province (2022KXJ-085), and the Fundamental Research Funds for the Central Universities in China, the Application Innovation Program of China Aerospace Science and Technology Corporation (No. 6230112002) and the Basic Research Priorities Program from Equipment Development Department of China (No. 514010304-302-2).

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Authors and Affiliations

  1. State Key Laboratory for Strength and Vibration of Mechanical Structure, School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, China

    Shenghao Chen, Chunguang Wang, Xuan Lu & Qun Li

  2. Shaanxi Coal and Chemical Technology Research Institute Co. Ltd, Xi’an, 710075, China

    Maoqing Li & Mengjie Li

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  1. Shenghao Chen
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  2. Chunguang Wang
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Correspondence to Qun Li.

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Chen, S., Wang, C., Lu, X. et al. A parameter identification scheme of the visco-hyperelastic constitutive model of rubber-like materials based on general regression neural network. Arch Appl Mech 93, 3229–3241 (2023). https://doi.org/10.1007/s00419-023-02434-z

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