Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem

Ioan Rosca; Mircea Sofonea

Applications of Mathematics (1994)

  • Volume: 39, Issue: 6, page 401-414
  • ISSN: 0862-7940

Abstract

top
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.

How to cite

top

Rosca, Ioan, and Sofonea, Mircea. "Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem." Applications of Mathematics 39.6 (1994): 401-414. <http://eudml.org/doc/32894>.

@article{Rosca1994,
abstract = {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.},
author = {Rosca, Ioan, Sofonea, Mircea},
journal = {Applications of Mathematics},
keywords = {rate-type models; viscoelasticity; viscoplasticity; fixed point; iterative method; error estimates; finite element method; rate-type materials; fixed point property; one-dimensional case},
language = {eng},
number = {6},
pages = {401-414},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem},
url = {http://eudml.org/doc/32894},
volume = {39},
year = {1994},
}

TY - JOUR
AU - Rosca, Ioan
AU - Sofonea, Mircea
TI - Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem
JO - Applications of Mathematics
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 39
IS - 6
SP - 401
EP - 414
AB - 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.
LA - eng
KW - rate-type models; viscoelasticity; viscoplasticity; fixed point; iterative method; error estimates; finite element method; rate-type materials; fixed point property; one-dimensional case
UR - http://eudml.org/doc/32894
ER -

References

top
  1. The mathematical theories of the inelastic continuum, Handbuch der Physik, Springer-Verlag, Berlin, 1958. (1958) MR0093963
  2. Viscoplasticity, Martinus Nijhoff, The Netherlands and Ed. Tehnica, Bucarest, 1982. (1982) MR0691135
  3. 10.1016/0020-7462(84)90049-0, Internat. J. Nonlin. Mech. 19(6) (1984), 325–344. (1984) Zbl0553.73026MR0769360DOI10.1016/0020-7462(84)90049-0
  4. 10.1090/qam/950599, Quart. Appl. Math. 2 (1988), 229–243. (1988) MR0950599DOI10.1090/qam/950599
  5. 10.1002/zamm.19900700304, ZAMM, Z. angew. Math. Mech. 3 (1990), 173–180. (1990) Zbl0712.73028MR1047857DOI10.1002/zamm.19900700304
  6. A fixed point method in quasistatic rate-type viscoplasticity, To appear in Appl. Math. and Comp. Sci. 3(1) (1993). (1993) MR1248215
  7. Mathematical theory of elastic and elasto-plastic bodies: an introduction, Elsevier, Amsterdam, 1981. (1981) MR0600655
  8. On the existence of the solution of boundary-value problems for elastic-inelastic solids, Comment. Math. Univ. Carolinae 14 (1973), 755–760. (1973) MR0337100
  9. On the solution of displacement boundary-value problem for elastic-inelastic materials, Appl. Maths. 19 (1974), 65–71. (1974) MR0347200
  10. Problèmes quasivariationnels en visco-plasticité avec écrouissage, C.R. Acad. Sci. Paris, Série A 283 (1976), 393–396. (1976) 
  11. 10.1080/01630567908816019, Numerical Functional Analysis and Optimization 1(3) (1979), 315–339. (1979) Zbl0462.73015MR0537835DOI10.1080/01630567908816019
  12. The finite element method for elliptic problem, North-Holland, Amsterdam, 1978. (1978) MR0520174

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.