Fractional Interior Differentiability of the Stress Velocities to Elastic Plastic Problems with Hardening

Jens Frehse; Maria Specovius-Neugebauer

Bollettino dell'Unione Matematica Italiana (2012)

  • Volume: 5, Issue: 3, page 469-494
  • ISSN: 0392-4041

Abstract

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We consider classical variational inequalities modeling elastic plastic problems with kinematic and isotropic hardening. It is shown that the stress velocities have fractional derivatives of order 1/2-\delta in L^{2} in time direction on the whole existence interval. In space direction an analogous result holds in the interior of the domain. In the case of kinematic hardening, these results are also true for the strain velocity.

How to cite

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Frehse, Jens, and Specovius-Neugebauer, Maria. "Fractional Interior Differentiability of the Stress Velocities to Elastic Plastic Problems with Hardening." Bollettino dell'Unione Matematica Italiana 5.3 (2012): 469-494. <http://eudml.org/doc/290864>.

@article{Frehse2012,
abstract = {We consider classical variational inequalities modeling elastic plastic problems with kinematic and isotropic hardening. It is shown that the stress velocities have fractional derivatives of order $1/2 - \delta$ in $L^2$ in time direction on the whole existence interval. In space direction an analogous result holds in the interior of the domain. In the case of kinematic hardening, these results are also true for the strain velocity.},
author = {Frehse, Jens, Specovius-Neugebauer, Maria},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {469-494},
publisher = {Unione Matematica Italiana},
title = {Fractional Interior Differentiability of the Stress Velocities to Elastic Plastic Problems with Hardening},
url = {http://eudml.org/doc/290864},
volume = {5},
year = {2012},
}

TY - JOUR
AU - Frehse, Jens
AU - Specovius-Neugebauer, Maria
TI - Fractional Interior Differentiability of the Stress Velocities to Elastic Plastic Problems with Hardening
JO - Bollettino dell'Unione Matematica Italiana
DA - 2012/10//
PB - Unione Matematica Italiana
VL - 5
IS - 3
SP - 469
EP - 494
AB - We consider classical variational inequalities modeling elastic plastic problems with kinematic and isotropic hardening. It is shown that the stress velocities have fractional derivatives of order $1/2 - \delta$ in $L^2$ in time direction on the whole existence interval. In space direction an analogous result holds in the interior of the domain. In the case of kinematic hardening, these results are also true for the strain velocity.
LA - eng
UR - http://eudml.org/doc/290864
ER -

References

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  1. ALBER, H.-D., Materials with memory, volume 1682 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1998. Initial-boundary value problems for constitutive equations with internal variables. MR1619546DOI10.1007/BFb0096273
  2. ALBER, H.-D. - NESENENKO, S., Local H^{1}-regularity and H^{1/3-\delta}-regularity up to the boundary in time dependent viscoplasticity. Asymptot. Anal., 63 (3) (2009),151-187. MR2541125
  3. FREHSE, J. - LÖBACH, D., Hölder continuity for the displacements in isotropic and kinematic hardening with von Mises yield criterion. ZAMM Z. Angew. Math. Mech., 88 (8) (2008), 617-629. MR2442283DOI10.1002/zamm.200700137
  4. FREHSE, J. - LÖBACH, D., Regularity results for three-dimensional isotropic and kinematic hardening including boundary differentiability. Math. Models Methods Appl. Sci., 19 (12) (2009), 2231-2262. Zbl1248.35207MR2599660DOI10.1142/S0218202509004108
  5. FREHSE, J. - LÖBACH, D., Improved L^{p}-estimates for the strain velocities in hardening problems. GAMM-Mitteilungen, 34 (2011), 10-20. MR2843966DOI10.1002/gamm.201110002
  6. FREHSE, J. - SPECOVIUS-NEUGEBAUER, M., Fractional differentiability for the stress velocities to the solution of the Prandtl-Reuss problem. To appear in ZAMM Z. Angew. Math. Mech. Zbl1380.74019MR2897423DOI10.1002/zamm.201100023
  7. GRUBER, P. - KNEES, D. - NESENENKO, S. - THOMAS, M., Analytical and numerical aspects of time-dependent models with internal variables. ZAMM Z. Angew. Math. Mech., 90 (10-11, Special Issue: On the Occasion of Zenon Mroz' 80th Birthday) (2010), 861-902. MR2760795DOI10.1002/zamm.200900387
  8. JOHNSON, C., Existence theorems for plasticity problems. J. Math. Pures Appl. (9), 55 (4) (1976), 431-444. Zbl0351.73049MR438867
  9. JOHNSON, C., On plasticity with hardening. J. Math. Anal. Appl., 62(2) (1978), 325- 336. Zbl0373.73049MR489198DOI10.1016/0022-247X(78)90129-4
  10. KNEES, D., On global spatial regularity and convergence rates for time dependent elasto-plasticity. M3AS, 20 (2010), 1823-1858. Zbl1207.35083MR2735915DOI10.1142/S0218202510004805
  11. LIONS, J.-L. - MAGENES, E., Non-homogeneous boundary value problems and applications. Vol. I. Springer-Verlag, New York, 1972. Translated from the French by P. Kenneth, Die Grundlehren der mathematischen Wissenschaften, Band 181. Zbl0227.35001MR350177
  12. LÖBACH, D., On regularity for plasticity with hardening. Technical Report 388, Bonner Mathematische Schriften, 2008. MR2414270
  13. SERËGIN, G. A., Differential properties of solutions of evolution variational inequalities in the theory of plasticity. J. Math. Sci., 72 (6) (1994), 3449-3458. MR1317379DOI10.1007/BF01250434

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