Variational regularization of damage models based on the emulated RVE
- 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.
Author: | Stephan SchwarzGND, Philipp JunkerORCiDGND, Klaus HacklORCiDGND |
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URN: | urn:nbn:de:hbz:294-80540 |
DOI: | https://doi.org/10.1007/s00161-020-00886-0 |
Parent Title (English): | Continuum mechanics and thermodynamics |
Publisher: | Springer Nature |
Place of publication: | Berlin |
Document Type: | Article |
Language: | English |
Date of Publication (online): | 2021/04/29 |
Date of first Publication: | 2020/05/24 |
Publishing Institution: | Ruhr-Universität Bochum, Universitätsbibliothek |
Tag: | Damage; Quasiconvex envelope; Relaxation; Variational methods |
Volume: | 33 |
First Page: | 69 |
Last Page: | 95 |
Note: | Dieser Beitrag ist auf Grund des DEAL-Springer-Vertrages frei zugänglich. |
Institutes/Facilities: | Lehrstuhl für Mechanik - Materialtheorie |
Lehrstuhl für Mechanik - Kontinuumsmechanik | |
Dewey Decimal Classification: | Technik, Medizin, angewandte Wissenschaften / Ingenieurbau, Umwelttechnik |
open_access (DINI-Set): | open_access |
faculties: | Fakultät für Bau- und Umweltingenieurwissenschaften |
Licence (English): | Creative Commons - CC BY 4.0 - Attribution 4.0 International |