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Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials: A 3D study. (English) Zbl 1194.74313
Summary: In a recent publication [Z. J. Yang et al., Int. J. Solids Struct. 46, No. 17, 3222–3234 (2009; Zbl 1167.74565)], we developed a finite element method capable of modelling complex two-dimensional (2D) crack propagation in quasi-brittle materials considering random heterogeneous fracture properties. The present study extends the method to model three-dimensional (3D) problems. First, 3D cohesive elements are inserted into the initial mesh of solid elements to model potential crack surfaces by a specially designed, flexible and efficient algorithm and corresponding computer program. The softening constitutive laws of the cohesive elements are modelled by spatially-varying 3D Weibull random fields. Monte Carlo simulations are then carried out to obtain statistical information of structural load-carrying capacity. A concrete cube under uniaxial tension was analysed as an example. It was found that as the 2D heterogeneous model, the 3D model predicted realistic, complicated fracture processes and load-carrying capacity of little mesh-dependence. Increasing heterogeneity in terms of the variance in the tensile strength random fields resulted in lower mean and higher standard deviation of peak loads. Due to constraint effects and larger areas of unsmooth, non-planar fracture surfaces, 3D modelling resulted in higher mean and lower standard deviation of peak loads than 2D modelling.

74R10 Brittle fracture
74S60 Stochastic and other probabilistic methods applied to problems in solid mechanics
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[1] ABAQUS 6.7, 2007. User documentation. Dessault systems.
[2] Barenblatt, G. I.: The formation of equilibrium cracks during brittle fracture: general ideas and hypothesis, axially symmetric cracks, Applied mathematics and mechanics 23, 622-636 (1959) · Zbl 0095.39202
[3] Bažant, Z. P.; Pang, S.; Vorechovský, M.; Novák, D.: Energetic-statistical size effect simulated by SFEM with stratified sampling and crack band model, International journal for numerical methods in engineering 71, 1297-1320 (2007) · Zbl 1194.74362
[4] Bažant, Z. P.; Vorechovský, M.; Novák, D.: Asymptotic prediction of energetic-statistical size effect from deterministic finite element solutions, Journal of engineering mechanics – ASCE 133, No. 2, 153-162 (2007)
[5] Bruggi, M.; Casciati, S.: Cohesive crack propagation in a random elastic medium, Probabilistic engineering mechanics 23, No. 1, 23-35 (2008)
[6] BSI, 2001. BS EN 206-1:2000 Concrete Part I: Specification, Performance, Production and Conformity.
[7] Carpinteri, A., 1984. Interpretation of the Griffith instability as a bifurcation of the global equilibrium. In: Shah, S.P. (Ed.), Application of Fracture Mechanics to Cementitious Composites. Proceedings of a NATO Advanced Research Workshop, Evanston, USA, 1984, pp. 284 – 316.
[8] Carpinteri, A.; Chiaia, B.; Invernizzi, S.: Three-dimensional fractal analysis of concrete fracture at the meso-level, Theoretical and applied fracture mechanics 31, 163-172 (1999)
[9] Dugdale, D. S.: Yielding of steel sheets containing slits, Journal of mechanics of physics and solids 8, 100-104 (1960)
[10] Most, T., 2005. Stochastic crack growth simulation in reinforced concrete structures by means of coupled finite element and meshless methods. Ph.D. Thesis, Bauhaus-Universität Weimar.
[11] Vorechovský, M.: Interplay of size effects in concrete specimens under tension studied via computational stochastic fracture mechanics, International journal of solids and structures 44, 2713-2715 (2007) · Zbl 1178.74144
[12] Xu, X.F., 2005. Morphological and multiscale modeling of stochastic complex materials. Ph.D. Thesis, The Johns Hopkins University.
[13] Yang, Z.; Xu, X. F.: A heterogeneous cohesive model for quasi-brittle materials considering spatially varying random fracture properties, Computer methods in applied mechanics and engineering 197, No. 45 – 48, 4027-4039 (2008) · Zbl 1194.74316
[14] Yang, Z. J.; Su, X. T.; Chen, J. F.; Liu, G. H.: Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials, International journal of solids and structures 46, 3222-3234 (2009) · Zbl 1167.74565
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