| Title:
|
On a 1-D model of stress relaxation in an annealed glass (English) |
| Author:
|
Janovský, Vladimír |
| Author:
|
Just, David |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
47 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
115-125 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
viscoelasticity |
| Keyword:
|
relaxation functions |
| Keyword:
|
method of lines |
| MSC:
|
65M20 |
| MSC:
|
74D05 |
| MSC:
|
74F05 |
| MSC:
|
74S30 |
| idZBL:
|
Zbl 1090.74017 |
| idMR:
|
MR1894664 |
| DOI:
|
10.1023/A:1021781001389 |
| . |
| Date available:
|
2009-09-22T18:09:11Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134489 |
| . |
| Reference:
|
[1] J. M. Golden, G. A. C. Graham: Boundary Value Problems in Linear Viscoelasticity.Springer, Berlin, 1988. MR 0958684 |
| Reference:
|
[2] V. Janovský, S. Shaw, M. K. Warby and J. R. Whiteman: Numerical methods for treating problems of viscoelastic isotropic solid deformation.J. Com. Appl. Math. 63 (1995), 91–107. MR 1365554 |
| Reference:
|
[3] D. Just: Mathematical model of the origin and relaxation of the stress in glass.Diploma Thesis, MFF UK Praha, 2000. (Czech) |
| Reference:
|
[4] E. H. Lee, T. G. Rogers and T. C. Woo: Residual stresses in glass plate cooled symmetrically from both surfaces.J. Amer. Cer. Soc. 48 (1965), 480–487. |
| Reference:
|
[5] O. S. Narayanaswamy: A model of structural relaxation in glass.J. Amer. Cer. Soc. 54 (1981), 491–498. |
| Reference:
|
[6] S. Shaw, M. K. Warby, J. R. Whiteman, C. Dawson and M. F. Wheeler: Numerical techniques for the treatment of quasistatic viscoelastic stress problemes in linear isotropic solids.Comput. Methods Appl. Mech. Engng. 18 (1994), 211–237. MR 1298954 |
| Reference:
|
[7] S. Shaw, M. K. Warby and J. R. Whiteman: 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. MR 1291218 |
| Reference:
|
[8] F. Shill: Cooling of Glass.Informatorium, Praha, 1993. (Czech) |
| . |
