| Title:
|
Modelling of singularities in elastoplastic materials with fatigue (English) |
| Author:
|
Krejčí, Pavel |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
137-160 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The hypothesis that, on the macroscopic level, the accumulated fatigue of an elastoplastic material with kinematic hardening can be identified from the mathematical point of view with the dissipated energy, is used for the construction of a new constitutive elastoplastic fatigue model. Its analytical investigation characterizes conditions for the formation of singularities in a finite time. The corresponding constitutive law is then coupled with the dynamical equation of motion of a one-dimensional continuum and the resulting hyperbolic problem is solved via space-discretization method. (English) |
| Keyword:
|
hysteresis |
| Keyword:
|
elastoplasticity |
| Keyword:
|
fatigue |
| Keyword:
|
hyperbolic system |
| MSC:
|
35L67 |
| MSC:
|
73M10 |
| MSC:
|
74R99 |
| idZBL:
|
Zbl 0804.73043 |
| idMR:
|
MR1258189 |
| DOI:
|
10.21136/AM.1994.134250 |
| . |
| Date available:
|
2009-09-22T17:43:30Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134250 |
| . |
| Reference:
|
[1] A. Beste, K. Dressler, H. Kötzle, W. Krüger, B. Maier, J. Petersen: Multiaxial rainflow (preprint).. |
| Reference:
|
[2] J. Betten: Elastizitäts- und Plastizitätslehre.Vieweg, 1986. (German) |
| Reference:
|
[3] M. Brokate, K. Dressler, P. Krejčí: On the Mróz model.Preprint no. 74, Universität Kaiserslautern, 1992. MR 1419644 |
| Reference:
|
[4] M. Brokate, K. Dressler, P. Krejčí: Rainflow counting and energy dissipation for hysteresis models in elastoplasticity.(to appear). MR 1412202 |
| Reference:
|
[5] T. H. Hildebrandt: Introduction to the theory of integration.Academic Press, 1963. Zbl 0112.28302, MR 0154957 |
| Reference:
|
[6] M. A. Krasnoselskii, A.V. Pokrovskii: Systems with hysteresis.Nauka, Moscow, 1983. (Russian) MR 0742931 |
| Reference:
|
[7] P. Krejčí: On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case.Apl. Mat. 34 (1989), 364–374. MR 1014077 |
| Reference:
|
[8] P. Krejčí: Vector hysteresis models.Euro. Jnl. Appl. Math. 2 (1991), 281–292. MR 1123144, 10.1017/S0956792500000541 |
| Reference:
|
[9] P. Krejčí: Vector hysteresis models II. Shape dependence.(to appear). MR 1123144 |
| Reference:
|
[10] P. Krejčí: Global behaviour of solutions to the wave equation with hysteresis.Adv. Math. Sci. Appl. 2 (1993), 1–23. |
| Reference:
|
[11] J. Lemaitre, J.-L. Chaboche: Mechanics of solid materials.Cambridge Univ. Press, 1990. |
| Reference:
|
[12] M. Matsuishi, T. Endo: Fatigue of metals subjected to varying stress.Proc. Kyushi Branch JSME, 1968, pp. 37–40. |
| Reference:
|
[13] A. Visintin: Differential models of hysteresis.Springer, to appear. Zbl 0820.35004, MR 1329094 |
| Reference:
|
[14] H. Ziegler: An introduction to thermomechanics, 2${}^{\text{nd}}$ edition.North-Holland, 1983. MR 0732945 |
| . |
