Itou, Hiromichi; Kovtunenko, Victor A.; Rajagopal, Kumbakonam R. On the states of stress and strain adjacent to a crack in a strain-limiting viscoelastic body. (English) Zbl 1404.74028 Math. Mech. Solids 23, No. 3, 433-444 (2018). Summary: The viscoelastic Kelvin-Voigt model is considered within the context of quasi-static deformations and generalized with respect to a nonlinear constitutive response within the framework of limiting small strain. We consider a solid possessing a crack subject to stress-free faces. The corresponding class of problems for strain-limiting nonlinear viscoelastic bodies with cracks is considered within a generalized formulation stated as variational equations and inequalities. Its generalized solution, relying on the space of bounded measures, is proved rigorously with the help of an elliptic regularization and a fixed-point argument. Cited in 17 Documents MSC: 74D10 Nonlinear constitutive equations for materials with memory 74R20 Anelastic fracture and damage 74H20 Existence of solutions of dynamical problems in solid mechanics Keywords:Kelvin-Voigt viscoelastic solid; limiting small strain; crack; variational problem; generalized solution PDFBibTeX XMLCite \textit{H. Itou} et al., Math. Mech. Solids 23, No. 3, 433--444 (2018; Zbl 1404.74028) Full Text: DOI References: [1] [1] Rajagopal, KR . On implicit constitutive theories. Appl Math 2003; 28: 279-319. · Zbl 1099.74009 [2] [2] Rajagopal, KR . On the nonlinear elastic response of bodies in the small strain range. Acta Mech 2014; 225: 1545-1553. · Zbl 1401.74045 [3] [3] Bulicek, M, Malek, J, Rajagopal, KR. On Kelvin-Voigt model and its generalizations. AIMS Evol Eq Control Theory 2012; 1: 17-42. · Zbl 1371.74067 [4] [4] Merodio, J, Rajagopal, KR. On constitutive equations for anisotropic nonlinearly viscoelastic solids. 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