Viscoelastic models revisited: characteristics and interconversion formulas for generalized Kelvin–Voigt and Maxwell models
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Tschoegl, N.W.: Time dependence in material properties: an overview. Mech. Time Depend. Mater. 1, 3–31 (1997)
Casula, G., Carcione, J.: Generalized mechanical model analogies of linear viscoelastic behaviour. Bolletino di Geofis. Teor. ed Appl. 34, 235–256 (1992)
Menard, K.P., Peter, K.: Dynamic Mechanical Analysis: a Practical Introduction. CRC Press, Washington DC (1999)
Chawla, A., Mukherjee, S., Karthikeyan, B.: Characterization of human passive muscles for impact loads using genetic algorithm and inverse finite element methods. Biomech. Model. Mechanobiol. 8, 67–76 (2009)
Fatemifar, F., Salehi, M., Adibipoor, R., et al.: Three-phase modeling of viscoelastic nanofiber-reinforced matrix. J. Mech. Sci. Technol. 28, 1039–1044 (2014)
Matter, Y.S., Darabseh, T.T., Mourad, A.H.I.: Flutter analysis of a viscoelastic tapered wing under bending–torsion loading. Meccanica 53, 3673–3691 (2018)
Forte, A.E., Gentleman, S.M., Dini, D.: On the characterization of the heterogeneous mechanical response of human brain tissue. Biomech. Model. Mechanobiol. 16, 907–920 (2017)
Ding, H.: Steady-state responses of a belt-drive dynamical system under dual excitations. Acta Mech. Sin. 32, 156–169 (2016)
Manda, K., Xie, S., Wallace, R.J., et al.: Linear viscoelasticity—bone volume fraction relationships of bovine trabecular bone. Biomech. Model. Mechanobiol. 15, 1631–1640 (2016)
Nantasetphong, W., Jia, Z., Amirkhizi, A., et al.: Dynamic properties of polyurea-milled glass composites. Part I: experimental characterization. Mech. Mater. 98, 142–153 (2016)
Liu, H., Yang, J., Liu, H.: Effect of a viscoelastic target on the impact response of a flat-nosed projectile. Acta Mech. Sin. 34, 162–174 (2018)
Li, Y., Hong, Y., Xu, G.K., et al.: Non-contact tensile viscoelastic characterization of microscale biological materials. Acta Mech. Sin. 34, 589–599 (2018)
Bai, T., Tsvankin, I.: Time-domain finite-difference modeling for attenuative anisotropic media. Geophysics 81, C69–C77 (2016)
Zhang, Y., Lian, Z., Zhou, M., et al.: Viscoelastic behavior of a casing material and its utilization in premium connections in high-temperature gas wells. Adv. Mech. Eng. 10, 168781401881745 (2018)
Baumgaertel, M., Winter, H.H.: Determination of discrete relaxation and retardation time spectra from dynamic mechanical data. Rheol. Acta 28, 511–519 (1989)
Nikonov, A., Davies, A.R., Emri, I.: The determination of creep and relaxation functions from a single experiment. J. Rheol. 49, 1193–1211 (2005)
Sorvari, J., Malinen, M.: On the direct estimation of creep and relaxation functions. Mech. Time Depend. Mater. 11, 143–157 (2007)
Renaud, F., Dion, J.: A new identification method of viscoelastic behavior: application to the generalized Maxwell model. Mech. Syst. Signal Process. 25, 991–1010 (2011)
Bang, K., Jeong, H.Y.: Combining stress relaxation and rheometer test results in modeling a polyurethane stopper. J. Mech. Sci. Technol. 26, 1849–1855 (2012)
Soo Cho, K.: Power series approximations of dynamic moduli and relaxation spectrum. J. Rheol. 57, 679–697 (2013)
Chen, D.L., Chiu, T.C., Chen, T.C., et al.: Using DMA to simultaneously acquire Young’s relaxation modulus and time-dependent Poisson’s ratio of a viscoelastic material. Procedia Eng. 79, 153–159 (2014)
Pacheco, J.E.L., Bavastri, C.A., Pereira, J.T.: Viscoelastic relaxation modulus characterization using Prony series. Lat. Am. J. Solids Struct. 12, 420–445 (2015)
Kim, M., Bae, J.E., Kang, N., et al.: Extraction of viscoelastic functions from creep data with ringing. J. Rheol. 59, 237–252 (2015)
Jung, J.W., Hong, J.W., Lee, H.K., et al.: Estimation of viscoelastic parameters in Prony series from shear wave propagation. J. Appl. Phys. 119, 234701 (2016)
Bonfitto, A., Tonoli, A., Amati, N.: Viscoelastic dampers for rotors: modeling and validation at component and system level. Appl. Sci. 7, 1181 (2017)
Poul, M.K., Zerva, A.: Time-domain PML formulation for modeling viscoelastic waves with Rayleigh-type damping in an unbounded domain: theory and application in ABAQUS. Finite Elem. Anal. Des. 152, 1–16 (2018)
Gross, B.: Mathematical Structure of the Theories of Viscoelasticity. Hermann & Co., Paris (1953)
Loy, R.J., Anderssen, R.S.: Interconversion relationships for completely monotone functions. SIAM J. Math. Anal. 46, 2008–2032 (2014)
Park, S.W., Schapery, R.A.: Methods of interconversion between linear viscoelastic material functions. Part I: a numerical method based on Prony series. Int. J. Solids Struct. 36, 1653–1675 (1999)
Schapery, R.A., Park, S.W.: Methods of interconversion between linear viscoelastic material functions. Part II: an approximate analytical method. Int. J. Solids Struct. 36, 1677–1699 (1999)
Sorvari, J., Malinen, M.: Numerical interconversion between linear viscoelastic material functions with regularization. Int. J. Solids Struct. 44, 1291–1303 (2007)
Luk-Cyr, J., Crochon, T., Li, C., et al.: Interconversion of linearly viscoelastic material functions expressed as Prony series: a closure. Mech. Time Depend. Mater. 17, 53–82 (2013)