Quasi-brittle damage modeling based on incremental energy relaxation combined with a viscous-type regularization

authored by: K Langenfeld, Philipp Junker, Joern Mosler
Abstract: This paper deals with a constitutive model suitable for the analysis of quasi-brittle damage in structures. The model is based on incremental energy relaxation combined with a viscous-type regularization. A similar approach—which also represents the inspiration for the improved model presented in this paper—was recently proposed in Junker et al. (Contin Mech Thermodyn 29(1):291–310, 2017). Within this work, the model introduced in Junker et al. (2017) is critically analyzed first. This analysis leads to an improved model which shows the same features as that in Junker et al. (2017), but which (i) eliminates unnecessary model parameters, (ii) can be better interpreted from a physics point of view, (iii) can capture a fully softened state (zero stresses), and (iv) is characterized by a very simple evolution equation. In contrast to the cited work, this evolution equation is (v) integrated fully implicitly and (vi) the resulting time-discrete evolution equation can be solved analytically providing a numerically efficient closed-form solution. It is shown that the final model is indeed well-posed (i.e., its tangent is positive definite). Explicit conditions guaranteeing this well-posedness are derived. Furthermore, by additively decomposing the stress rate into deformation- and purely time-dependent terms, the functionality of the model is explained. Illustrative numerical examples confirm the theoretical findings.
External Organisation(s): Ruhr-Universität Bochum
Type: Article
Journal: Continuum Mechanics and Thermodynamics
Volume: 30
Pages: 1125-1144
No. of pages: 20
ISSN: 0935-1175
Publication date: 01.09.2018
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Materials Science(all), Mechanics of Materials, Physics and Astronomy(all)
Electronic version(s): https://doi.org/10.1007/s00161-018-0669-z (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{1dc1d01d7ab349dda3af29f8f026ded2,
title = "Quasi-brittle damage modeling based on incremental energy relaxation combined with a viscous-type regularization",
abstract = "This paper deals with a constitutive model suitable for the analysis of quasi-brittle damage in structures. The model is based on incremental energy relaxation combined with a viscous-type regularization. A similar approach—which also represents the inspiration for the improved model presented in this paper—was recently proposed in Junker et al. (Contin Mech Thermodyn 29(1):291–310, 2017). Within this work, the model introduced in Junker et al. (2017) is critically analyzed first. This analysis leads to an improved model which shows the same features as that in Junker et al. (2017), but which (i) eliminates unnecessary model parameters, (ii) can be better interpreted from a physics point of view, (iii) can capture a fully softened state (zero stresses), and (iv) is characterized by a very simple evolution equation. In contrast to the cited work, this evolution equation is (v) integrated fully implicitly and (vi) the resulting time-discrete evolution equation can be solved analytically providing a numerically efficient closed-form solution. It is shown that the final model is indeed well-posed (i.e., its tangent is positive definite). Explicit conditions guaranteeing this well-posedness are derived. Furthermore, by additively decomposing the stress rate into deformation- and purely time-dependent terms, the functionality of the model is explained. Illustrative numerical examples confirm the theoretical findings.",
keywords = "Convexity, Damage, Rate-dependency, Regularization, Relaxation-based",
author = "K Langenfeld and Philipp Junker and Joern Mosler",
note = "Publisher Copyright: {\textcopyright} 2018, Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2018",
month = sep,
day = "1",
doi = "10.1007/s00161-018-0669-z",
language = "English",
volume = "30",
pages = "1125--1144",
journal = "Continuum Mechanics and Thermodynamics",
issn = "0935-1175",
publisher = "Springer New York",
number = "5",
}