Abstract
This paper investigates the influence of uncertain spatially varying material properties on the fracture behavior of structures with softening materials. Structural failure is modeled using the sequentially linear analysis (SLA) proposed by Rots (Sequentially linear continuum model for concrete fracture. In: de Borst R, Mazars J, Pijaudier-Cabot G, van Mier J (eds) Fracture mechanics of concrete structures. Balkema, Lisse, 2001, pp 831–839), which replaces the incremental nonlinear finite element analysis by a series of scaled linear analyses and the nonlinear stress-strain law by a saw-tooth curve. In this work, SLA is implemented in the framework of a stochastic setting. The proposed approach constitutes an efficient procedure avoiding the convergence problems encountered in regular nonlinear FE analysis. The effect of uncertain material properties (Young’s modulus, tensile strength, fracture energy) on the variability of the load-displacement curves and crack paths is examined. The uncertain properties are described by homogeneous stochastic fields using the spectral representation method in conjunction with translation field theory. The response variability is computed by means of direct Monte Carlo simulation. The influence of the variation of each random parameter as well as of the coefficient of variation and correlation length of the stochastic fields is quantified in a numerical example. It is shown that the load-displacement curves, the crack paths and the failure probability are affected by the statistical characteristics of the stochastic fields.
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Acknowledgements
This work is implemented within the framework of the research project “MICROLINK: Linking micromechanics-based properties with the stochastic finite element method: a challenge for multiscale modeling of heterogeneous materials and structures” – Action “Supporting Postdoctoral Researchers” of the Operational Program “Education and Lifelong Learning” (Action’s Beneficiary: General Secretariat for Research and Technology), and is co-financed by the European Social Fund (ESF) and the Greek State. The provided financial support is gratefully acknowledged. M. Papadrakakis acknowledges the support from the European Research Council Advanced Grant “MASTER-Mastering the computational challenges in numerical modeling and optimum design of CNT reinforced composites” (ERC-2011-ADG 20110209).
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Stefanou, G., Georgioudakis, M., Papadrakakis, M. (2014). Sequentially Linear Analysis of Structures with Stochastic Material Properties. In: Papadrakakis, M., Stefanou, G. (eds) Multiscale Modeling and Uncertainty Quantification of Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-06331-7_2
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DOI: https://doi.org/10.1007/978-3-319-06331-7_2
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