Quasi-brittle damage modeling based on incremental energy relaxation combined with a viscous-type regularization
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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.
KeywordsConvexity Damage Rate-dependency Regularization Relaxation-based
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- 5.Hertzberg, R.W.: Deformation and Fracture Mechanics of Engineering Materials. Wiley, London (1989)Google Scholar
- 12.Lemaitre, J., Desmorat, R.: Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer, Berlin (2005)Google Scholar
- 14.Dimitrijevic, B.J., Hackl, K.: A method for gradient enhancement of continuum damage models. Technische Mechanik 28(1), 43–52 (2008)Google Scholar
- 21.Forest, S., Lorentz, E.: Local Approach to Fracture, Presse des Mines (2004) (Ch. 11)Google Scholar
- 28.Kachanov, L.M.: Time of the rupture process under creep conditions. Otdelenie Teckhnicheskikh Nauk, Izvestiia Akademii Nauk SSSR 8, 26–31 (1958)Google Scholar
- 31.Mosler, J.: On variational updates for non-associative kinematic hardening of armstrong-frederick-type. Technische Mechanik 30(1–3), 244–251 (2010)Google Scholar
- 38.Junker, P.: Simulation of Shape Memory Alloys—Material Modeling using the Principle of Maximum Dissipation. Ph.d. thesis, Ruhr-Universität Bochum (2011)Google Scholar
- 39.Radulovic, R.: Numerical Modeling of Localized Material Failure by Means of Strong Discontinuities at Finite Strains. Ph.d. thesis, Ruhr-Universität Bochum (2010)Google Scholar