Details
| Original language | English |
|---|---|
| Pages (from-to) | 69-95 |
| Number of pages | 27 |
| Journal | Continuum Mechanics and Thermodynamics |
| Volume | 33 |
| Issue number | 1 |
| Early online date | 24 May 2020 |
| Publication status | Published - Jan 2021 |
Abstract
Material models exhibiting softening effects due to damage or localization share the problem of leading to ill-posed boundary value problems that lead to physically meaningless, mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior, described, e.g., by internal variables, at a spatial level. The common way to do this is to take into account higher gradients of the field variables, thus introducing an internal length scale. In this paper, we suggest a different approach to regularization that does not make use of any nonlocal enhancement like the inclusion of higher gradients or integration over local sub-domains nor of any classical viscous effects. Instead we perform an appropriate relaxation of the (condensed) free energy in a time-incremental setting which leads to a modified energy that is coercive and satisfies quasiconvexity in an approximate way. Thus, in every time increment a regular boundary value problem is solved. The proposed approach holds the same advantage as other methods, but with less numerical effort. We start with the theoretical derivation, discuss a rate-independent version of the proposed model and present details of the numerical treatment. Finally, we give finite element results that demonstrate the efficiency of this new approach.
Keywords
- Damage, Quasiconvex envelope, Relaxation, Variational methods
ASJC Scopus subject areas
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In: Continuum Mechanics and Thermodynamics, Vol. 33, No. 1, 01.2021, p. 69-95.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Variational regularization of damage models based on the emulated RVE
AU - Schwarz, S.
AU - Junker, Philipp
AU - Hackl, K.
PY - 2021/1
Y1 - 2021/1
N2 - Material models exhibiting softening effects due to damage or localization share the problem of leading to ill-posed boundary value problems that lead to physically meaningless, mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior, described, e.g., by internal variables, at a spatial level. The common way to do this is to take into account higher gradients of the field variables, thus introducing an internal length scale. In this paper, we suggest a different approach to regularization that does not make use of any nonlocal enhancement like the inclusion of higher gradients or integration over local sub-domains nor of any classical viscous effects. Instead we perform an appropriate relaxation of the (condensed) free energy in a time-incremental setting which leads to a modified energy that is coercive and satisfies quasiconvexity in an approximate way. Thus, in every time increment a regular boundary value problem is solved. The proposed approach holds the same advantage as other methods, but with less numerical effort. We start with the theoretical derivation, discuss a rate-independent version of the proposed model and present details of the numerical treatment. Finally, we give finite element results that demonstrate the efficiency of this new approach.
AB - Material models exhibiting softening effects due to damage or localization share the problem of leading to ill-posed boundary value problems that lead to physically meaningless, mesh-dependent finite element results. It is thus necessary to apply regularization techniques that couple local behavior, described, e.g., by internal variables, at a spatial level. The common way to do this is to take into account higher gradients of the field variables, thus introducing an internal length scale. In this paper, we suggest a different approach to regularization that does not make use of any nonlocal enhancement like the inclusion of higher gradients or integration over local sub-domains nor of any classical viscous effects. Instead we perform an appropriate relaxation of the (condensed) free energy in a time-incremental setting which leads to a modified energy that is coercive and satisfies quasiconvexity in an approximate way. Thus, in every time increment a regular boundary value problem is solved. The proposed approach holds the same advantage as other methods, but with less numerical effort. We start with the theoretical derivation, discuss a rate-independent version of the proposed model and present details of the numerical treatment. Finally, we give finite element results that demonstrate the efficiency of this new approach.
KW - Damage
KW - Quasiconvex envelope
KW - Relaxation
KW - Variational methods
UR - http://www.scopus.com/inward/record.url?scp=85085307520&partnerID=8YFLogxK
U2 - 10.1007/s00161-020-00886-0
DO - 10.1007/s00161-020-00886-0
M3 - Article
VL - 33
SP - 69
EP - 95
JO - Continuum Mechanics and Thermodynamics
JF - Continuum Mechanics and Thermodynamics
SN - 0935-1175
IS - 1
ER -