Numerical analysis of the equations of small strains quasistatic elastoviscoplasticity

D. Blanchard; P. Le Tallec

doi:10.1007/BF01390427

Numerical analysis of the equations of small strains quasistatic elastoviscoplasticity

D. Blanchard
, P. Le Tallec

Laboratoire Central des Ponts et Chaussées

Research output: Contribution to journal › Article › peer-review

Abstract

The present paper deals with the mathematical and the numerical analysis of small strains elastoviscoplasticity. By considering the problem as an evolution equation whose only unknown is the stress field, the quasistatic elastoviscoplastic evolution problem is proved to be well-posed, consistent mixed finite element approximations are introduced, and classical numerical algorithms are interpreted. In particular, augmented Lagrangian methods operating on the velocity appear as standard alternating-directions time-integrations of this stress evolution problem.

Original language	English
Pages (from-to)	147-169
Number of pages	23
Journal	Numerische Mathematik
Volume	50
Issue number	2
DOIs	https://doi.org/10.1007/BF01390427
Publication status	Published - 1 Mar 1986
Externally published	Yes

Keywords

Subject Classifications: AMS(MOS): 65N30, CR: G1.8

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10.1007/BF01390427

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abstract = "The present paper deals with the mathematical and the numerical analysis of small strains elastoviscoplasticity. By considering the problem as an evolution equation whose only unknown is the stress field, the quasistatic elastoviscoplastic evolution problem is proved to be well-posed, consistent mixed finite element approximations are introduced, and classical numerical algorithms are interpreted. In particular, augmented Lagrangian methods operating on the velocity appear as standard alternating-directions time-integrations of this stress evolution problem.",

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N2 - The present paper deals with the mathematical and the numerical analysis of small strains elastoviscoplasticity. By considering the problem as an evolution equation whose only unknown is the stress field, the quasistatic elastoviscoplastic evolution problem is proved to be well-posed, consistent mixed finite element approximations are introduced, and classical numerical algorithms are interpreted. In particular, augmented Lagrangian methods operating on the velocity appear as standard alternating-directions time-integrations of this stress evolution problem.

AB - The present paper deals with the mathematical and the numerical analysis of small strains elastoviscoplasticity. By considering the problem as an evolution equation whose only unknown is the stress field, the quasistatic elastoviscoplastic evolution problem is proved to be well-posed, consistent mixed finite element approximations are introduced, and classical numerical algorithms are interpreted. In particular, augmented Lagrangian methods operating on the velocity appear as standard alternating-directions time-integrations of this stress evolution problem.

KW - Subject Classifications: AMS(MOS): 65N30, CR: G1.8

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DO - 10.1007/BF01390427

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JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 2

ER -

Numerical analysis of the equations of small strains quasistatic elastoviscoplasticity

Abstract

Keywords

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