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OPEN PROBLEMS IN MODELING FRACTURE PROCESS IN CONCRETE Miodrag Pavisic Structural Engineer

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1.Theory of Plasticity 2.Fracture Mechanics 3.Continuous Damage Mechanics

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Assumptions & Limitations Assumptions & Limitations Theory of plasticity Theory of plasticity Non-linearity in concrete –where does it come from? Plastic flow in quasibrittle material? damage damage ε = ε ε = ε e + ε p …. ( +ε ω )

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Assumptions & Limitations Continuous damage mechanics Continuous damage mechanics continuous defect field damage Where is ε p ?What about crack?

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Brittle-Elastic-Plastic Model σ R Dragon A., Mroz Z. (1979) σ R Dragon A., Mroz Z. (1979) ε p ε 0 ε ε p ε 0 ε ω

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Assumptions & Limitations Fracture mechanics...Stability conditions of one single crack in undamaged – mechanically intact material K Ic – critical stress intensity factor K Ic a – aggregate K Ic c – cement paste K Ic if – interface K Ic a >> K Ic c > 2 K Ic if

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1. 1.Micriomechanics of damage 2. 2.Strain localization Micro-Macro relationships 4. 4.Size effect

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Micromechanics of damage Preexisting microcracks Preexisting microcracks (technological damage) No loading is applied 1. Stress concentrators 2. Interaction 3. Continuum with discontinuity

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Strain localization An evidence: With the load increased enough microcracs and microvoids propagation and interaction concentrate – localize in a close area just before a single macro crack take place The process physically is not clear enough The process physically is not clear enough NDT not able to capture NDT not able to capture Computer simulation limited Computer simulation limited

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Micro-macro relationships Concrete material is not continuum - Micro scale - Meso scale - Macro scale Measure of discontinuity: Microcracks density - Phenomenological approach - Statistical approach

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Size effect An evidence: Strength of quasibrittle materials (as the concrete), depends significantly of the size of the specimen (1) theory based on energetic-statistical scaling, (1) theory based on energetic-statistical scaling, (2) theory based on the fractal geometry (2) theory based on the fractal geometry

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Instead of conclusions Why the combined approach? Why the combined approach? Initially: - Material is not continuum When the loading is applied and gradually increased: 1. Damage – microcracks and microvoids propagation 2. Plasticity – non-linearity 3. Macro crack – in damaged material Fracture of concrete

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