Abstract
Failure in quasi-brittle materials comes under an intermediate category of fracture failure, which includes different stages, i.e., micro-cracks nucleation, growth, and coalescence into a macroscopic crack. The different stages of failure result in a tension-softening structural response, which can be accurately modeled using the conventional gradient damage models. However, due to a constant interacting domain throughout the load history, conventional gradient damage models suffer from various drawbacks which limits their application to simulate the final stages of quasi-brittle failure process. In this contribution, the present work illustrates a thermodynamically consistent localizing gradient damage model, which successfully overcomes the drawbacks of conventional gradient damage models. The localizing gradient damage model uses an interaction function definition in the constitutive framework to take into account the diminishing nonlocal interactions, thus attaining a macroscopic crack in the form of a localized damage profile during the last stages of failure. The numerical accuracy of the model is tested against both mode-I and mode-II types of failure problems and compared with the experimental results.
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References
Kumar S, Singh IV, Mishra BK (2015) A homogenized XFEM approach to simulate fatigue crack growth problems. Comput Struct 150:1–22. https://doi.org/10.1016/j.compstruc.2014.12.008
Meschke G, Dumstorff P (2007) Energy-based modeling of cohesive and cohesionless cracks via X-FEM. Comput Methods Appl Mech Eng 196(21–24):2338–2357. https://doi.org/10.1016/j.cma.2006.11.017
Peerlings RD, De Borst R, Brekelmans WD, De Vree JHP (1996) Gradient enhanced damage for quasi-brittle materials. Int J Numer Meth Eng 39(19):3391–3403. https://doi.org/10.1002/(SICI)1097-0207(19961015)39:19%3c3391:AID-NME7%3e3.0.CO;2-D
Peerlings RHJ (1999) Enhanced damage modelling for fracture and fatigue. Doctoral dissertation, Technische Universiteit Eindhoven
Pijaudier‐Cabot G, Bažant ZP (1987) Nonlocal damage theory. J Eng Mech 113(10):1512–1533. https://doi.org/10.1061/(asce)0733-9399(1987)113:10(1512)
Simone A, Askes H, Sluys LJ (2004) Incorrect initiation and propagation of failure in non-local and gradient-enhanced media. Int J Solids Struct 41(2):351–363. https://doi.org/10.1016/j.ijsolstr.2003.09.020
Poh LH, Sun G (2016) Localizing gradient damage model with decreasing interactions. Int J Numer Meth Eng 110(6):503–522. https://doi.org/10.1002/nme.5364
Coleman BD, Noll W (1963) The thermodynamics of elastic materials with heat conduction and viscosity. Arch Ration Mech Anal 13(1):167–178. https://doi.org/10.1007/bf01262690
Bažant ZP, Gettu R, Kazemi MT (1991) Identification of nonlinear fracture properties from size effect tests and structural analysis based on geometry-dependent R-curves. Int J Rock Mech Min Sci Geomech Abstr 28(1):43–51. https://doi.org/10.1016/0148-9062(91)93232-u
Khoramishad H, Akbardoost J, Ayatollahi M (2013) Size effects on parameters of cohesive zone model in mode I fracture of limestone. Int J Damage Mech 23(4):588–605. https://doi.org/10.1177/1056789513504319
Giry C, Dufour F, Mazars J (2011) Stress-based nonlocal damage model. Int J Solids Struct 48(25–26):3431–3443. https://doi.org/10.1016/j.ijsolstr.2011.08.012
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Negi, A., Kumar, S. (2020). Crack Growth Simulation in Quasi-brittle Materials Using a Localizing Gradient Damage Model. In: Maity, D., Siddheshwar, P., Saha, S. (eds) Advances in Fluid Mechanics and Solid Mechanics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-0772-4_20
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