| Title:
|
Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem (English) |
| Author:
|
Rosca, Ioan |
| Author:
|
Sofonea, Mircea |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
6 |
| Year:
|
1994 |
| Pages:
|
401-414 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper deals with an initial and boundary value problem describing the quasistatic evolution of rate-type viscoplastic materials. Using a fixed point property, an iterative method in the study of this problem is proposed. A concrete algorithm as well as some numerical results in the one-dimensional case are also presented. (English) |
| Keyword:
|
rate-type models |
| Keyword:
|
viscoelasticity |
| Keyword:
|
viscoplasticity |
| Keyword:
|
fixed point |
| Keyword:
|
iterative method |
| Keyword:
|
error estimates |
| Keyword:
|
finite element method |
| MSC:
|
65M15 |
| MSC:
|
74C10 |
| MSC:
|
74S05 |
| idZBL:
|
Zbl 0814.73064 |
| idMR:
|
MR1298730 |
| DOI:
|
10.21136/AM.1994.134268 |
| . |
| Date available:
|
2009-09-22T17:45:27Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134268 |
| . |
| Reference:
|
[1] H. Geiringer and A. M. Freudenthal: The mathematical theories of the inelastic continuum.Handbuch der Physik, Springer-Verlag, Berlin, 1958. MR 0093963 |
| Reference:
|
[2] N. Cristescu and I. Suliciu: Viscoplasticity.Martinus Nijhoff, The Netherlands and Ed. Tehnica, Bucarest, 1982. MR 0691135 |
| Reference:
|
[3] I. Suliciu: Some energetic properties of smooth solutions in rate-type viscoelasticity.Internat. J. Nonlin. Mech. 19(6) (1984), 325–344. Zbl 0553.73026, MR 0769360, 10.1016/0020-7462(84)90049-0 |
| Reference:
|
[4] I. R. Ionescu and M. Sofonea: Quasistatic processes for elastic-visco-plastic materials.Quart. Appl. Math. 2 (1988), 229–243. MR 0950599, 10.1090/qam/950599 |
| Reference:
|
[5] I. R. Ionescu: Error estimates of an Euler method for a quasistatic elastic-visco-plastic problem.ZAMM, Z. angew. Math. Mech. 3 (1990), 173–180. Zbl 0712.73028, MR 1047857, 10.1002/zamm.19900700304 |
| Reference:
|
[6] S. Djabi and M. Sofonea: A fixed point method in quasistatic rate-type viscoplasticity.To appear in Appl. Math. and Comp. Sci. 3(1) (1993). MR 1248215 |
| Reference:
|
[7] J. Nečas and I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies: an introduction.Elsevier, Amsterdam, 1981. MR 0600655 |
| Reference:
|
[8] J. Kratochvíl and J. Nečas: On the existence of the solution of boundary-value problems for elastic-inelastic solids.Comment. Math. Univ. Carolinae 14 (1973), 755–760. MR 0337100 |
| Reference:
|
[9] O. John: On the solution of displacement boundary-value problem for elastic-inelastic materials.Appl. Maths. 19 (1974), 65–71. MR 0347200 |
| Reference:
|
[10] P. Laborde: Problèmes quasivariationnels en visco-plasticité avec écrouissage.C.R. Acad. Sci. Paris, Série A 283 (1976), 393–396. |
| Reference:
|
[11] P. Laborde: On visco-plasticity with hardening.Numerical Functional Analysis and Optimization 1(3) (1979), 315–339. Zbl 0462.73015, MR 0537835, 10.1080/01630567908816019 |
| Reference:
|
[12] P. Ciarlet: The finite element method for elliptic problem.North-Holland, Amsterdam, 1978. MR 0520174 |
| . |
