Kunin, A. B.; Zuo, Q. H. Stability and well-posedness of a rate-dependent damage model for brittle materials based on crack mechanics. (English) Zbl 1459.74160 Appl. Math. Modelling 40, No. 5-6, 3801-3811 (2016). Summary: This paper presents an investigation of the stability and well-posedness of a rate-dependent damage model for brittle materials. The model is based on the response of an ensemble of distributed microcracks under a general, three-dimensional state of stress. The stability and well-posedness of the model are studied by examining the behavior of dynamic perturbations to the steady-state solution of uniaxial-stress loading. It is shown that as a result of incorporating the strain-rate effect in the model, perturbations of all wave lengths remain bounded for finite times, making the problem well-posed. It is also shown that the corresponding rate-independent model is ill-posed in that perturbations grow unbounded with the wave number, even for finite times. MSC: 74R05 Brittle damage 74H55 Stability of dynamical problems in solid mechanics 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35B35 Stability in context of PDEs 35Q74 PDEs in connection with mechanics of deformable solids Keywords:stability analysis; well-posedness; material model; brittle materials; damage mechanics; micromechanics PDFBibTeX XMLCite \textit{A. B. Kunin} and \textit{Q. H. Zuo}, Appl. Math. Modelling 40, No. 5--6, 3801--3811 (2016; Zbl 1459.74160) Full Text: DOI References: [1] Dubé, J. F.; Pijaudier-Cabot, G.; La Borderie, C., Rate dependent damage model for concrete in dynamics, J. Eng. Mech., 122, 10, 939-947 (1996) [2] Zhang, Y. Q.; Hao, H.; Lu, Y., Anisotropic dynamic damage and fragmentation of rock materials under explosive loading, Int. J. Eng. Sci., 41, 9, 917-929 (2003) [3] Zhang, Q. B.; Zhao, J., A review of dynamic experimental techniques and mechanical behaviour of rock materials, Rock Mech. 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