Geodesic
Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem
Applications of Mathematics, Tome 39 (1994) no. 6, pp. 401-414
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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.
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.
DOI : 10.21136/AM.1994.134268
Classification : 65M15, 74C10, 74S05
Keywords: rate-type models; viscoelasticity; viscoplasticity; fixed point; iterative method; error estimates; finite element method 
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Rosca, Ioan; Sofonea, Mircea. Error estimates of an iterative method for a quasistatic elastic-visco-plastic problem. Applications of Mathematics, Tome 39 (1994) no. 6, pp. 401-414. doi: 10.21136/AM.1994.134268

[1] H. Geiringer and A. M. Freudenthal: The mathematical theories of the inelastic continuum. Handbuch der Physik, Springer-Verlag, Berlin, 1958. | MR

[2] N. Cristescu and I. Suliciu: Viscoplasticity. Martinus Nijhoff, The Netherlands and Ed. Tehnica, Bucarest, 1982. | MR

[3] I. Suliciu: Some energetic properties of smooth solutions in rate-type viscoelasticity. Internat. J. Nonlin. Mech. 19(6) (1984), 325–344. | DOI | MR | Zbl

[4] I. R. Ionescu and M. Sofonea: Quasistatic processes for elastic-visco-plastic materials. Quart. Appl. Math. 2 (1988), 229–243. | DOI | MR

[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. | DOI | MR | Zbl

[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

[7] J. Nečas and I. Hlaváček: Mathematical theory of elastic and elasto-plastic bodies: an introduction. Elsevier, Amsterdam, 1981. | MR

[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

[9] O. John: On the solution of displacement boundary-value problem for elastic-inelastic materials. Appl. Maths. 19 (1974), 65–71. | MR

[10] P. Laborde: Problèmes quasivariationnels en visco-plasticité avec écrouissage. C.R. Acad. Sci. Paris, Série A 283 (1976), 393–396.

[11] P. Laborde: On visco-plasticity with hardening. Numerical Functional Analysis and Optimization 1(3) (1979), 315–339. | DOI | MR | Zbl

[12] P. Ciarlet: The finite element method for elliptic problem. North-Holland, Amsterdam, 1978. | MR

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