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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
Theory of plasticity Non-linearity in concrete –where does it come from? Plastic flow in quasibrittle material? damage ε = εe + εp….( +εω )
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Assumptions & Limitations
Continuous damage mechanics “ continuous defect field “ damage Where is εp ? What about crack?
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Brittle-Elastic-Plastic Model
σ R Dragon A., Mroz Z. (1979) εp ε ε ω
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Assumptions & Limitations
Fracture mechanics ...Stability conditions of one single crack in undamaged – mechanically intact material KIc – critical stress intensity factor KIca – aggregate KIcc – cement paste KIcif – interface KIca >> KIcc > 2 KIcif
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Micriomechanics of damage
Strain localization Micro-Macro relationships Size effect
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Micromechanics of damage
Preexisting microcracks (“technological damage”) No loading is applied 1. Stress concentrators 2. Interaction 3. “Continuum” with discontinuity
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Strain localization The process physically is not clear enough
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 NDT not able to capture 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 (1) theory based on energetic-statistical scaling,
An evidence: Strength of quasibrittle materials (as the concrete), depends significantly of the size of the specimen (1) theory based on energetic-statistical scaling, (2) theory based on the fractal geometry
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Instead of conclusions
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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