References
- J. D. Ferry, Viscoelastic Properties of Polymers. New York: Wiley, 1980.
- R. M. Christensen, Theory of Viscoelasticity: An Introduction. New York: Elsevier, 1982.
- Y. M. Haddad, Viscoelasticity of Engineering Materials. Netherlands: Springer, 1995.
- H. F. Brinson and L. C. Brinson, Polymer Engineering Science and Viscoelasticity: An Introduction. New York: Springer, 2008.
- R. S. Lakes, Viscoelastic Materials. Cambridge: Cambridge University Press, 2009.
- H. Leaderman, Elastic and creep properties of filamentous materials and other high polymers. Washington D.C.: The Textile Foundation, 1943.
- J. D. Ferry, “Mechanical properties of substances of high molecular weight VI. Dispersion in concentrated polymer solutions and its dependence on temperature and concentration,” J. Am. Chem. Soc., vol. 72, no. 8, pp. 3746–3752, 1950. DOI: https://doi.org/10.1021/ja01164a117.
- A. M. Freudenthal, “Effect of rheological behavior on thermal stresses,” J. Appl. Phys., vol. 25, no. 9, pp. 1110–1117, 1954. DOI: https://doi.org/10.1063/1.1721824.
- H. H. Hilton, “Thermal stresses in thick walled cylinders exhibiting temperature dependent viscoelastic properties of the Kelvin type,” Proceedings of the Second U.S. National Congress on Applied Mechanics, 1954, pp. 547–553.
- M. A. Biot, “Linear thermodynamics and the mechanics of solids,” Proceedings of the Third U.S. National Congress on Applied Mechanics. American Society of Mechanical Engineers, 1958.
- S. C. Hunter, “Tentative Equations for the propagation of stress, strain and temperature fields in viscoelastic solids,” J. Mech. Phys. Solids, vol. 9, no. 1, pp. 39–51, 1961. DOI: https://doi.org/10.1016/0022-5096(61)90037-0.
- M. L. Williams, “Structural analysis of viscoelastic materials,” AIAA J., vol. 2, no. 5, pp. 785–808, 1964. DOI: https://doi.org/10.2514/3.2447.
- R. A. Schapry, “Application of thermodynamics to thermomechanical fracture and birefringent phenomena in viscoelastic media,” J. Appl. Phys., vol. 35, pp. 1451–1465, 1964. DOI: https://doi.org/10.1063/1.1713649.
- R. M. Christensen and P. M. Naghdi, “Linear non-isothermal viscoelastic solids,” Acta Mech., vol. 3, no. 1, pp. 1–12, 1967. DOI: https://doi.org/10.1007/BF01193596.
- R. A. Schapery, “Stress analysis of viscoelastic composite materials,” J. Compos. Mater., vol. 1, no. 3, pp. 228–267, 1967. DOI: https://doi.org/10.1177/002199836700100302.
- H. Poon and M. F. Ahmad, “A material point time integration procedure for anisotropic, thermo rheologically simple, viscoelastic solids,” Comput. Mech., vol. 21, no. 3, pp. 236–242, 1998. DOI: https://doi.org/10.1007/s004660050298.
- Z. A. Taylor, et al., “On modelling of anisotropic viscoelasticity for soft tissue simulation: Numerical solution and GPU execution,” Med. Image Anal., vol. 13, no. 2, pp. 234–244, 2009. DOI: https://doi.org/10.1016/j.media.2008.10.001.
- H. E. Pettermann and A. DeSimone, “An anisotropic linear thermo-viscoelastic constitutive law: Elastic relaxation and thermal expansion creep in the time domain,” Mech. Time Depend. Mater., vol. 22, no. 4, pp. 421–433, 2018. DOI: https://doi.org/10.1007/s11043-017-9364-x.
- A. V. Tobolsky and R. D. Andrews, “Systems manifesting superposed elastic and viscous behavior,” J. Chem. Phys., vol. 13, no. 1, pp. 3–27, 1945. DOI: https://doi.org/10.1063/1.1723966.
- F. Schwarzl and A. J. Staverman, “Time‐temperature dependence of linear viscoelastic behavior,” J. Appl. Phys., vol. 23, no. 8, pp. 838–843, 1952. DOI: https://doi.org/10.1063/1.1702316.
- L. W. Morland and E. H. Lee, “Stress analysis for linear viscoelastic materials with temperature variation,” Trans. Soc. Rheol., vol. 4, no. 1, pp. 233–263, 1960. DOI: https://doi.org/10.1122/1.548856.
- M. L. Williams, R. F. Landel and J. D. Ferry, “The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” J. Am. Chem. Soc, vol. 77, no. 14, pp. 3701–3707, 1955. DOI: https://doi.org/10.1021/ja01619a008.
- R. Muki and E. Sternberg, “On transient thermal stresses in viscoelastic materials with temperature-dependent properties,” J. Appl. Mech., vol. 28, no. 2, pp. 193–207, 1961. DOI: https://doi.org/10.1115/1.3641651.
- R. A. Schapery, “Approximation methods of transform inversion for viscoelastic stress analysis,” Proceedings of the Fourth U.S. National Congress of Applied Mechanics, 1962, vol. 2, pp. 1075–1084.
- E. H. Lee and T. G. Rogers, “Solution of viscoelastic stress analysis problems using measured creep or relaxation functions,” J. Appl. Mech., vol. 30, no. 1, pp. 127–133, 1963. DOI: https://doi.org/10.1115/1.3630057.
- J. S. Humphreys and C. J. Martin, “Determination of transient thermal stresses in a slab with temperature‐dependent viscoelastic properties,” Trans. Soc. Rheol., vol. 7, no. 1, pp. 155–170, 1963. DOI: https://doi.org/10.1122/1.548951.
- E. Sternberg, On the Analysis of Thermal Stresses in Visco-Elastic Solids," Fort Belvoir: Defense Technical Information Center, 1963.
- K. C. Valanis and G. Lianis, “A method of analysis of transient thermal stresses in thermorheologically simple viscoelastic solids,” J. Appl. Mech., vol. 31, no. 1, pp. 47–53, 1964. DOI: https://doi.org/10.1115/1.3629569.
- E. H. Lee and T. G. Rogers, “On the generation of residual stresses in thermoviscoelastic bodies,” J. Appl. Mech., vol. 32, no. 4, pp. 874–880, 1965. DOI: https://doi.org/10.1115/1.3627329.
- F. J. Lockett and L. W. Morland, “Thermal stresses in a viscoelastic thin-walled tube with temperature dependent properties,” Int. J. Eng. Sci., vol. 5, no. 12, pp. 879–898, 1967. DOI: https://doi.org/10.1016/0020-7225(67)90011-0.
- H. Ghoneim and C. A. Hieber, “Volume-relaxation effects on the thermal residual stresses in an injection-molded strip,” J. Therm. Stresses, vol. 19, no. 9, pp. 795–808, 1996. DOI: https://doi.org/10.1080/01495739608946209.
- X. Shi, A. K. Datta and S. Mukherjee, “Thermal fracture in a biomaterial during rapid freezing,” J. Therm. Stresses, vol. 22, no. 3, pp. 275–292, 1999.
- W. Araki, T. Adachi and A. Yamaji, “Prediction of fracture initiation in thermo-viscoelastic material,” J. Therm. Stresses, vol. 30, no. 5, pp. 459–474, 2007. DOI: https://doi.org/10.1080/01495730601146402.
- N. L. Troyani, C. J. Gomes and P. M. Báiz, “Capability for capturing temperability as a criterion for the validity of thermoviscoelastic constitutive equations,” J. Therm. Stresses, vol. 33, no. 1, pp. 37–54, 2009. DOI: https://doi.org/10.1080/01495730903409193.
- A. P. S. Selvadurai, “Transient thermo-viscoelastic response of a crack in a layered structure,” J. Therm. Stresses, vol. 15, no. 1, pp. 143–167, 1992. DOI: https://doi.org/10.1080/01495739208946126.
- M. A. Zocher, S. E. Groves and D. H. Allen, “A three-dimensional finite element formulation for thermoviscoelastic orthotropic media,” Int. J. Numer. Methods Eng., vol. 40, no. 12, pp. 2267–2288, 1997. DOI: https://doi.org/10.1002/(SICI)1097-0207(19970630)40:12<2267::AID-NME156>3.0.CO;2-P.
- S. R. White and Y. K. Kim, “Process-induced residual stress analysis of AS4/3501-6 composite material,” Mech. Adv. Mater. Struct., vol. 5, no. 2, pp. 153–186, 1998. DOI: https://doi.org/10.1080/10759419808945897.
- P. Sunderland, W. Yu and J. A. Manson, “Thermoviscoelastic analysis of process-induced internal stresses in thermoplastic matrix composites,” Polym. Compos., vol. 22, no. 5, pp. 579–592, 2001. DOI: https://doi.org/10.1002/pc.10561.
- L. G. Zhao, N. A. Warrior and A. C. Long, “A thermo-viscoelastic analysis of process-induced residual stress in fibre-reinforced polymer–matrix composites,” Mater. Sci. Eng. A, vol. 452–453, pp. 483–498, 2007. DOI: https://doi.org/10.1016/j.msea.2006.10.060.
- H. M. Anastasia and H. A. Rami, “A multi-scale framework for layered composites with thermo-rheologically complex behaviors,” Int. J. Solids Struct., vol. 45, pp. 2937–2963, 2008.
- A. Muliana and K. A. Khan, “A time-integration algorithm for thermo-rheologically complex polymers,” Comput. Mater. Sci., vol. 41, no. 4, pp. 576–588, 2008. DOI: https://doi.org/10.1016/j.commatsci.2007.05.021.
- S. Sawant and A. Muliana, “A thermo-mechanical viscoelastic analysis of orthotropic materials,” Compos. Struct., vol. 83, no. 1, pp. 61–72, 2008. DOI: https://doi.org/10.1016/j.compstruct.2007.03.008.
- H. Ashrafi, H. Keshmiri, M. R. Bahadori and M. Shariyat, “An FEM approach for three – Dimensional thermoviscoelastic stress analysis of orthotropic cylinders made of polymers,” AMR, vol. 685, pp. 295–299, 2013. DOI: https://doi.org/10.4028/www.scientific.net/AMR.685.295.
- J. Sorvari and J. Hämäläinen, “Time integration in linear viscoelasticity-a comparative study,” Mech. Time-Depend. Mater., vol. 14, no. 3, pp. 307–328, 2010. DOI: https://doi.org/10.1007/s11043-010-9108-7.
- T. Crochon, T. Schönherr, C. Li and M. Lévesque, “On finite-element implementation strategies of Schapery-type constitutive theories,” Mech. Time-Depend. Mater., vol. 14, no. 4, pp. 359–387, 2010. DOI: https://doi.org/10.1007/s11043-010-9115-8.
- M. Sadeghinia, K. M. B. Jansen and L. J. Ernst, “Characterization of the viscoelastic properties of an epoxy molding compound during cure,” Microelectron. Reliab., vol. 52, no. 8, pp. 1711–1718, 2012. DOI: https://doi.org/10.1016/j.microrel.2012.03.025.
- M. Abouhamzeh, J. Sinke, K. M. B. Jansen and R. Benedictus, “A new procedure for thermo-viscoelastic modelling of composites with general orthotropy and geometry,” Compos. Struct., vol. 133, pp. 871–877, 2015. DOI: https://doi.org/10.1016/j.compstruct.2015.08.050.
- M. Abouhamzeh, J. Sinke, K. M. B. Jansen and R. Benedictus, “Thermo-viscoelastic analysis of GLARE,” Compos. Part B Eng., vol. 99, pp. 1–8, 2016. DOI: https://doi.org/10.1016/j.compositesb.2016.05.060.
- S. S. Lee, “Boundary element analysis of viscoelastic solids under transient thermal state,” Eng. Anal. Bound. Elem., vol. 16, no. 1, pp. 35–39, 1995. DOI: https://doi.org/10.1016/0955-7997(95)00058-5.
- S. S. Lee, “Boundary element analysis of a viscoelastic thin-walled cylinder subjected to thermal transient,” Int. J. Press. Vessel. Pip., vol. 63, no. 2, pp. 195–198, 1995. DOI: https://doi.org/10.1016/0308-0161(94)00052-K.
- S. S. Lee and R. A. Westmann, “Application of high-order quadrature rules to time-domain boundary element analysis of viscoelasticity,” Int. J. Numer. Methods Eng., vol. 38, no. 4, pp. 607–629, 1995. DOI: https://doi.org/10.1002/nme.1620380407.
- C. Hwu, C. L. Hsu, C. W. Hsu and Y. C. Shiah, “Fundamental solutions for two-dimensional anisotropic thermo-magneto-electro-elasticity,” Math. Mech. Solids, vol. 24, no. 11, pp. 3575–3596, 2019. DOI: https://doi.org/10.1177/1081286519851151.
- V. T. Nguyen and C. Hwu, “Boundary element method for contact between multiple rigid punches and anisotropic viscoelastic foundation,” Eng. Anal. Bound. Elem., vol. 118, pp. 295–305, 2020. DOI: https://doi.org/10.1016/j.enganabound.2020.07.001.
- V. T. Nguyen and C. Hwu, “Time-stepping method for frictional contact of anisotropic viscoelastic solids,” Int. J. Mech. Sci., vol. 184, pp. 105836, 2020. DOI: https://doi.org/10.1016/j.ijmecsci.2020.105836.
- V. T. Nguyen and C. Hwu, “Analytical solutions and boundary element analysis for holes and cracks in anisotropic viscoelastic solids via time-stepping method,” Mech. Mater., vol. 160, pp. 103964, 2021. DOI: https://doi.org/10.1016/j.mechmat.2021.103964.
- V. Sladek and J. Sladek, “Boundary integral equation method in two-dimensional thermoelasticity,” Eng. Anal., vol. 1, pp. 135–148, 1984. DOI: https://doi.org/10.1016/0264-682X(84)90070-4.
- V. Sladek and J. Sladek, “Boundary integral equation method in thermoelasticity part III: Uncoupled thermoelasticity,” Appl. Math. Model., vol. 8, pp. 413–418, 1984. DOI: https://doi.org/10.1016/0307-904X(84)90047-7.
- Y. C. Chen and C. Hwu, “Boundary element analysis for viscoelastic solids containing interfaces/holes/cracks/inclusions,” Eng. Anal. Bound. Elem., vol. 35, no. 8, pp. 1010–1018, 2011. DOI: https://doi.org/10.1016/j.enganabound.2011.03.008.
- C. Hwu, Anisotropic Elastic Plates. New York: Springer, 2010.
- C. A. Brebbia, J. C. F. Telles and L. C. Wrobel, Boundary Element Techniques: Theory and Applications in Engineering. Heidelberg: Springer, 1984.