On a 1-D model of stress relaxation in an annealed glass

Vladimír Janovský; David Just

Applications of Mathematics (2002)

  • Volume: 47, Issue: 2, page 115-125
  • ISSN: 0862-7940

Abstract

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A 1-D model of a slab of glass of a small thickness is considered. The governing equations are those of the classical 1-D linear viscoelasticity. A load due to the temperature gradients is assumed. The aim is to model the process called annealing. It is shown that an additional load due to structural strain is crucial for the success of the model. Algorithms of a numerical solution of the governing equations are proposed. Numerical results are presented and commented.

How to cite

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Janovský, Vladimír, and Just, David. "On a 1-D model of stress relaxation in an annealed glass." Applications of Mathematics 47.2 (2002): 115-125. <http://eudml.org/doc/33107>.

@article{Janovský2002,
abstract = {A 1-D model of a slab of glass of a small thickness is considered. The governing equations are those of the classical 1-D linear viscoelasticity. A load due to the temperature gradients is assumed. The aim is to model the process called annealing. It is shown that an additional load due to structural strain is crucial for the success of the model. Algorithms of a numerical solution of the governing equations are proposed. Numerical results are presented and commented.},
author = {Janovský, Vladimír, Just, David},
journal = {Applications of Mathematics},
keywords = {viscoelasticity; relaxation functions; method of lines; glass annealing; viscoelasticity; thermal load; structural relaxation; nonlinear heat convection; method of lines},
language = {eng},
number = {2},
pages = {115-125},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a 1-D model of stress relaxation in an annealed glass},
url = {http://eudml.org/doc/33107},
volume = {47},
year = {2002},
}

TY - JOUR
AU - Janovský, Vladimír
AU - Just, David
TI - On a 1-D model of stress relaxation in an annealed glass
JO - Applications of Mathematics
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 2
SP - 115
EP - 125
AB - A 1-D model of a slab of glass of a small thickness is considered. The governing equations are those of the classical 1-D linear viscoelasticity. A load due to the temperature gradients is assumed. The aim is to model the process called annealing. It is shown that an additional load due to structural strain is crucial for the success of the model. Algorithms of a numerical solution of the governing equations are proposed. Numerical results are presented and commented.
LA - eng
KW - viscoelasticity; relaxation functions; method of lines; glass annealing; viscoelasticity; thermal load; structural relaxation; nonlinear heat convection; method of lines
UR - http://eudml.org/doc/33107
ER -

References

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  1. Boundary Value Problems in Linear Viscoelasticity, Springer, Berlin, 1988. (1988) MR0958684
  2. Numerical methods for treating problems of viscoelastic isotropic solid deformation, J. Com. Appl. Math. 63 (1995), 91–107. (1995) MR1365554
  3. Mathematical model of the origin and relaxation of the stress in glass, Diploma Thesis, MFF UK Praha, 2000. (Czech) (2000) 
  4. Residual stresses in glass plate cooled symmetrically from both surfaces, J. Amer. Cer. Soc. 48 (1965), 480–487. (1965) 
  5. A model of structural relaxation in glass, J. Amer. Cer. Soc. 54 (1981), 491–498. (1981) 
  6. Numerical techniques for the treatment of quasistatic viscoelastic stress problemes in linear isotropic solids, Comput. Methods Appl. Mech. Engng. 18 (1994), 211–237. (1994) MR1298954
  7. Numerical techniques for problems of quasistatic and dynamic viscoelasticity, In: The Mathematics of Finite Elements and Applications. Proceedings of MAFELAP 1993 (Chapter  3), Academic Press, Chichester, 1994. (1994) MR1291218
  8. Cooling of Glass, Informatorium, Praha, 1993. (Czech) (1993) 

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