OPEN PROBLEMS IN MODELING OPEN PROBLEMS IN MODELING FRACTURE PROCESS IN FRACTURE PROCESS IN CONCRETECONCRETEMiodrag PavisicMiodrag Pavisic

Structural EngineerStructural Engineer

1.1. Theory of PlasticityTheory of Plasticity

2.2. Fracture MechanicsFracture Mechanics

3.3. Continuous Damage MechanicsContinuous Damage Mechanics

Assumptions & Assumptions & LimitationsLimitations

Theory of plasticityTheory of plasticity

Non-linearity in concrete –where does it come from?Non-linearity in concrete –where does it come from?

Plastic flowPlastic flow in quasibrittle material? in quasibrittle material?

damagedamage

εε = = εεe + εp….( +εω )

Assumptions & Assumptions & LimitationsLimitations

Continuous damage mechanicsContinuous damage mechanics

“ continuous defect field “

damage

Where is εp ? What about crack?

1

s

1

s

1

s

1

s

Brittle-Elastic-Plastic Brittle-Elastic-Plastic ModelModel

σσ RR Dragon A., Mroz Z. Dragon A., Mroz Z. (1979)(1979)

εεp p εε0 0 εε

ωω

Assumptions & Assumptions & LimitationsLimitations

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 >> KIc

c > 2 KIcif

1. Micriomechanics of damage

2. Strain localization

3. Micro-Macro relationships

4. Size effect

Micromechanics of Micromechanics of damagedamage Preexisting microcracksPreexisting microcracks

(“technological damage”)(“technological damage”)

No loading is applied No loading is applied

1. Stress concentrators1. Stress concentrators

2. Interaction2. Interaction

3. “Continuum” with discontinuity3. “Continuum” with discontinuity

Strain localizationStrain localization

An evidenceAn evidence::

““With the load increased enough microcracs and microvoids propagation With the load increased enough microcracs and microvoids propagation and interaction concentrate – localize in a close area just before a single and interaction concentrate – localize in a close area just before a single macro crack take place”macro crack take place”

The process physically is not clear enoughThe process physically is not clear enough NDT not able to capture NDT not able to capture Computer simulation limited Computer simulation limited

Micro-macro Micro-macro relationshipsrelationshipsConcrete material Concrete material is not continuumis not continuum

- - Micro scaleMicro scale

- Meso scale- Meso scale

- - Macro scaleMacro scale

Measure of discontinuityMeasure of discontinuity: : Microcracks densityMicrocracks density

- Phenomenological approach- Phenomenological approach- Statistical approach- Statistical approach

Size effectSize effectAn evidence:An evidence:

Strength of quasibrittle materials (as the concrete), depends Strength of quasibrittle materials (as the concrete), depends significantly of the size of the specimen 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

Instead of conclusionsInstead of conclusions

Why the combined approach?Why the combined approach?

Initially: - Material is not continuumInitially: - Material is not continuum

When the loading is applied and gradually increased:When the loading is applied and gradually increased:

1. Damage – microcracks and microvoids propagation1. Damage – microcracks and microvoids propagation

2. “Plasticity” – non-linearity2. “Plasticity” – non-linearity

3. Macro crack – in damaged material 3. Macro crack – in damaged material

Fracture of concreteFracture of concrete