Adaptive probabilistic modeling of localization, failure and size effect of quasi-brittle materials
Final Report Abstract
In structural materials, the presence of fine-scale features with random nature can greatly affect material properties such as stiffness, ultimate strength and the size of the fracture process zone. Unfortunately, if all microscale interactions are minutely taken into account in the numerical analysis, even deterministically, computational models of enormous size and complexity typically emerge. In order to capture the damage process in the microstructure while keeping the complexity of the problem down to manageable levels, we combined the the adaptive finite element method and of random field simulations in a single model. The developed model allowed us to gradually zoom into the fine scale of the material structure with locally increased computational demand in critical regions only. In these areas, the heterogeneity of material described by randomly fluctuating fields is essential for the development of microcracks. This approach employing methods of adaptivity and stochastics will allow us to capture the size effect phenomena in its complexity and to provide a computational tool for robust analysis and reliability assessment of large structures with quasi-brittle material that is hitherto not possible with the currently available methods and tools. The formulation of the algorithm has been accompanied with the generic software implementation. The proposed algorithm has been included in the finite element code as one of “adaptive strategies”. The probabilistic adaptivity was used for prototyping the software design of the general purpose simulation framework with adaptive time-stepping. The available environment can accommodate applications combining several adaptive strategies, including introduction of strong or weak discontinuities or adaptation of the “Ansatz space”. The implemented adaptive strategy is an important component of the modeling framework for modeling of quasi-brittle and quasi-ductile materials used in several running research projects in the area of composite material developments. In particular, the probabilistic adaptivity is being utilized as a tool for the derivation of effective properties (both stiffness and strength) of heterogeneous material structure.
Publications
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Numerical modeling of delayed activation and statistical size effect in multifilament yarns. In Vlastimil Bilek and Zbynek Kersner, editors, 2nd International symposium Nontraditional cement & concrete, pages 439–449, Brno, Czech Republic, 2005. Brno University of Technology
M. Vorechovsky and R. Chudoba
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Statistical length scale for micromechanical model of multifilament yarns and size effect on strength. In G. Augusti, G. I. Schuëller, and M. Ciampoli, editors, ICoSSaR ’05 the 9th International Cone ference on Structural Safety and Reliability, pages 395–401, Rome, Italy, 2005. Millpress Rotterdam, Netherlands
M. Vorechovsky and R. Chudoba
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Adaptive probabilistic modeling of localization, failure and size effect of quasi-brittle materials. In ECCM ’06, 3rd European Conference on Computational Mechanics, Solids, Structures and Coupled Problems in Engineering, Lisabon, Portugal, 2006
M. Vorechovsky, R. Chudoba, and J. Jerabek
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Size effect in concrete specimens under tension: interplay of sources. In Computational Modelling of Concrete Structures, pages 905–914, 2006
M. Vorechovsky and D. Matesova
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Stochastic modeling of multi-filament yarns I: Random properties within the cross section and size effect. International Journal of Solids and Structures, 43(3-4):413–434, 2006
R. Chudoba, M. Vorechovsky , and Martin Konrad
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Stochastic modeling of multi-filament yarns II: Random properties over the length and size effect. International Journal of Solids and Structures, 43(3-4):435–458, 2006
M. Vorechovsky and R. Chudoba
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Adaptive time-stepping algorithm exploiting the combined effect of softening and spatial variability of material parameters. In M. Jirasek, Z. Bittnar, and H. Mang, editors, Modelling of Heterogeneous Materials with Application in Construction and Biomedical Engineering, pages 238–239, Prague, Czech Republic, 2007
J. Jerabek, R. Chudoba, M. Vorechovsky, and M. Mombartz
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Adaptive time-stepping algorithm exploiting the spatial variability of material parameters. In SEMC 2007 The Third International Conference on Structural Engineering, Mechanics and Computation, 2007
R. Chudoba, J. Jerabek, and M. Vorechovsky
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Adaptive time-stepping algorithm for strain-softening materials. In 8th. World Congress on Computational Mechanics & 5th. European Congress on Computational Methods in Applied Sciences and Engineering, Venice, 2008
R. Chudoba and M. Vorechovsky
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Framework for adaptive multi-scale simulation of textile reinforced concrete. PhD thesis, RWTH Aachen University, Germany, 2008
F. Peiffer
