Time/Temperature-Dependent Finite Element Model of Laminated Glass Beams
The polymer foil used for manufacturing of
laminated glass members behaves in a viscoelastic manner with
temperature dependance. This contribution aims at incorporating
the time/temperature-dependent behavior of interlayer to our earlier
elastic finite element model for laminated glass beams. The model
is based on a refined beam theory: each layer behaves according
to the finite-strain shear deformable formulation by Reissner and
the adjacent layers are connected via the Lagrange multipliers
ensuring the inter-layer compatibility of a laminated unit. The
time/temperature-dependent behavior of the interlayer is accounted
for by the generalized Maxwell model and by the time-temperature
superposition principle due to the Williams, Landel, and Ferry.
The resulting system is solved by the Newton method with
consistent linearization and the viscoelastic response is determined
incrementally by the exponential algorithm. By comparing the model
predictions against available experimental data, we demonstrate that
the proposed formulation is reliable and accurately reproduces the
behavior of the laminated glass units.
[1] R. A. Behr, J. E. Minor, and H. S. Norville, “Structural behavior of
architectural laminated glass,” Journal of Structural Engineering, vol.
119, no. 1, pp. 202–222, 1993.
[2] T. Serafinaviˇciusa, J. Lebeta, C. Loutera, T. Lenkimasc, and
A. Kuranovasb, “Long-term laminated glass four point bending test
with PVB, EVA and SG interlayers at different temperatures,” Procedia
Engineering, vol. 57, pp. 996–1004, 2013.
[3] S. J. Bennison, A. Jagota, and C. A. Smith, “Fracture of Glass/Poly(vinyl
butyral) (Butacite R ) laminates in biaxial flexure,” Journal of the
American Ceramic Society, vol. 82, no. 7, pp. 1761–1770, 1999.
[4] F. Pelayo, M. L´opez-Aenlle, L. Hermans, and A. Fraile, “Modal
scaling of a laminated glass plate,” 5th International Operational Modal
Analysis Conference, pp. 1–10, 2013.
[5] C. V. G. Vallabhan, Y. C. Das, M. Magdi, M. Asik, and J. R. Bailey,
“Analysis of laminated glass units,” Journal of Structural Engineering,
vol. 119, no. 5, pp. 1572–1585, 1993.
[6] A. V. Duser, A. Jagota, and S. J. Bennison, “Analysis of glass/polyvinyl
butyral laminates subjected to uniform pressure,” Journal of Engineering
Mechanics, vol. 125, no. 4, pp. 435–442, 1999.
[7] A. Zemanov´a, J. Zeman, and M. ˇ Sejnoha, “Numerical model of elastic
laminated glass beams under finite strain,” Archives of Civil and
Mechanical Engineering, vol. 14, no. 4, pp. 734–744, 2014.
[8] S. T. Mau, “A refined laminated plate theory,” Journal of Applied
Mechanics–Transactions of the ASME, vol. 40, no. 2, pp. 606–607, 1973.
[9] M. Z. As¸ık and S. Tezcan, “A mathematical model for the behavior of
laminated glass beams,” Computers & Structures, vol. 83, no. 21–22,
pp. 1742–1753, 2005.
[10] M. Z. As¸ık, “Laminated glass plates: revealing of nonlinear behavior,”
Computers & Structures, vol. 81, no. 28–29, pp. 2659–2671, 2003.
[11] C. V. G. Vallabhan, Y. C. Das, and M. Ramasamudra, “Properties of
PVB interlayer used in laminated glass,” Journal of Materials in Civil
Engineering, vol. 4, no. 1, pp. 71–76, 1992.
[12] A. K. Dhaliwal and J. N. Hay, “The characterization of polyvinyl
butyral by thermal analysis,” Thermochimica Acta, vol. 391, no. 1-2,
pp. 245–255, 2002.
[13] R. Christensen, Theory of Viscoelasticity: An Introduction, 2nd ed.
Elsevier, 1982.
[14] M. Williams, R. Landel, and J. Ferry, “The temperature dependence of
relaxation mechanisms in amorphous polymers and other glass-forming
liquids,” Journal of the American Chemical Society, vol. 77, no. 14, pp.
3701–3707, 1955.
[15] O. C. Zienkiewicz, M. Watson, and I. P. King, “A numerical method
of visco-elastic stress analysis,” International Journal of Mechanical
Sciences, vol. 10, no. 10, pp. 807–827, 1968. [16] J. C. Simo and T. J. R. Hughes, Computational Inelasticity. Springer,
1998.
[17] A. Zemanov´a, “Numerical modeling of laminated glass structures,”
Ph.D. dissertation, Faculty of Civil Engineering, CTU, Prague, 2014.
[18] M. L´opez-Aenlle, F. Pelayo, A. Fern´andez-Canteli, and M. A.
Garc´ıa Prieto, “The effective-thickness concept in laminated-glass
elements under static loading,” Engineering Structures, vol. 56, pp.
1092–1102, 2013.
[1] R. A. Behr, J. E. Minor, and H. S. Norville, “Structural behavior of
architectural laminated glass,” Journal of Structural Engineering, vol.
119, no. 1, pp. 202–222, 1993.
[2] T. Serafinaviˇciusa, J. Lebeta, C. Loutera, T. Lenkimasc, and
A. Kuranovasb, “Long-term laminated glass four point bending test
with PVB, EVA and SG interlayers at different temperatures,” Procedia
Engineering, vol. 57, pp. 996–1004, 2013.
[3] S. J. Bennison, A. Jagota, and C. A. Smith, “Fracture of Glass/Poly(vinyl
butyral) (Butacite R ) laminates in biaxial flexure,” Journal of the
American Ceramic Society, vol. 82, no. 7, pp. 1761–1770, 1999.
[4] F. Pelayo, M. L´opez-Aenlle, L. Hermans, and A. Fraile, “Modal
scaling of a laminated glass plate,” 5th International Operational Modal
Analysis Conference, pp. 1–10, 2013.
[5] C. V. G. Vallabhan, Y. C. Das, M. Magdi, M. Asik, and J. R. Bailey,
“Analysis of laminated glass units,” Journal of Structural Engineering,
vol. 119, no. 5, pp. 1572–1585, 1993.
[6] A. V. Duser, A. Jagota, and S. J. Bennison, “Analysis of glass/polyvinyl
butyral laminates subjected to uniform pressure,” Journal of Engineering
Mechanics, vol. 125, no. 4, pp. 435–442, 1999.
[7] A. Zemanov´a, J. Zeman, and M. ˇ Sejnoha, “Numerical model of elastic
laminated glass beams under finite strain,” Archives of Civil and
Mechanical Engineering, vol. 14, no. 4, pp. 734–744, 2014.
[8] S. T. Mau, “A refined laminated plate theory,” Journal of Applied
Mechanics–Transactions of the ASME, vol. 40, no. 2, pp. 606–607, 1973.
[9] M. Z. As¸ık and S. Tezcan, “A mathematical model for the behavior of
laminated glass beams,” Computers & Structures, vol. 83, no. 21–22,
pp. 1742–1753, 2005.
[10] M. Z. As¸ık, “Laminated glass plates: revealing of nonlinear behavior,”
Computers & Structures, vol. 81, no. 28–29, pp. 2659–2671, 2003.
[11] C. V. G. Vallabhan, Y. C. Das, and M. Ramasamudra, “Properties of
PVB interlayer used in laminated glass,” Journal of Materials in Civil
Engineering, vol. 4, no. 1, pp. 71–76, 1992.
[12] A. K. Dhaliwal and J. N. Hay, “The characterization of polyvinyl
butyral by thermal analysis,” Thermochimica Acta, vol. 391, no. 1-2,
pp. 245–255, 2002.
[13] R. Christensen, Theory of Viscoelasticity: An Introduction, 2nd ed.
Elsevier, 1982.
[14] M. Williams, R. Landel, and J. Ferry, “The temperature dependence of
relaxation mechanisms in amorphous polymers and other glass-forming
liquids,” Journal of the American Chemical Society, vol. 77, no. 14, pp.
3701–3707, 1955.
[15] O. C. Zienkiewicz, M. Watson, and I. P. King, “A numerical method
of visco-elastic stress analysis,” International Journal of Mechanical
Sciences, vol. 10, no. 10, pp. 807–827, 1968. [16] J. C. Simo and T. J. R. Hughes, Computational Inelasticity. Springer,
1998.
[17] A. Zemanov´a, “Numerical modeling of laminated glass structures,”
Ph.D. dissertation, Faculty of Civil Engineering, CTU, Prague, 2014.
[18] M. L´opez-Aenlle, F. Pelayo, A. Fern´andez-Canteli, and M. A.
Garc´ıa Prieto, “The effective-thickness concept in laminated-glass
elements under static loading,” Engineering Structures, vol. 56, pp.
1092–1102, 2013.
@article{"International Journal of Earth, Energy and Environmental Sciences:70045", author = "Alena Zemanová and Jan Zeman and Michal Šejnoha", title = "Time/Temperature-Dependent Finite Element Model of Laminated Glass Beams", abstract = "The polymer foil used for manufacturing of
laminated glass members behaves in a viscoelastic manner with
temperature dependance. This contribution aims at incorporating
the time/temperature-dependent behavior of interlayer to our earlier
elastic finite element model for laminated glass beams. The model
is based on a refined beam theory: each layer behaves according
to the finite-strain shear deformable formulation by Reissner and
the adjacent layers are connected via the Lagrange multipliers
ensuring the inter-layer compatibility of a laminated unit. The
time/temperature-dependent behavior of the interlayer is accounted
for by the generalized Maxwell model and by the time-temperature
superposition principle due to the Williams, Landel, and Ferry.
The resulting system is solved by the Newton method with
consistent linearization and the viscoelastic response is determined
incrementally by the exponential algorithm. By comparing the model
predictions against available experimental data, we demonstrate that
the proposed formulation is reliable and accurately reproduces the
behavior of the laminated glass units.", keywords = "Laminated glass, finite element method, finite-strain
Reissner model, Lagrange multipliers, generalized Maxwell model,
Williams-Landel-Ferry equation, Newton method.", volume = "9", number = "6", pages = "643-7", }
