Well-posedness of a one-dimensional nonlinear kinematic hardening model

David Melching; Ulisse Stefanelli

doi:10.3934/dcdss.2020188

Article Contents

2020, Volume 13, Issue 8: 2271-2284. Doi: 10.3934/dcdss.2020188

This issue Previous Article Fractional Cauchy problems and applications Next Article Polarization dynamics in a resonant optical medium with initial coherence between degenerate states

Well-posedness of a one-dimensional nonlinear kinematic hardening model

David Melching^1, and
Ulisse Stefanelli^1,2,

1.
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
2.
Istituto di Matematica Applicata e Tecnologie Informatiche E. Magenes, v. Ferrata 1, 27100 Pavia, Italy

Received: March 2018

Revised: October 2018

Early access: November 2019

Published: May 2020

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Abstract

We investigate the quasistatic evolution of a one-dimensional elastoplastic body at small strains. The model includes general nonlinear kinematic hardening but no nonlocal compactifying term. Correspondingly, the free energy of the medium is local but nonquadratic. We prove that the quasistatic evolution problem admits a unique strong solution.

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Mathematics Subject Classification: 74C05, 49J40.

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References

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