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

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

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

6. Assumptions & Limitations
Continuous damage mechanics
“ continuous defect field “
damage
Where is εp ? What about crack?

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

8. 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

9. Micriomechanics of damage
Strain localization
Micro-Macro relationships
Size effect

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

11. 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

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

13. 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

14. 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