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Course ILTOF01 - Fracture mechanics and complexity sciences

Course ILTOF01 - Fracture mechanics and complexity sciences

course summary (.pdf).

Lecturer: Prof. Dr. Alberto CARPINTERI

short curriculum

Important: how to access the online lectures

Topic 1: Crackling, brittle ruptures and Catastrophe Theory (2 h)

On the basis of the Cohesive Crack Model, an original representation and interpretation of brittle ruptures is provided. Virtual branches of cusp catastrophe instability are captured by the model. When such branches are not adequately controlled, a snap-back instability occurs with energy release. In the cases of multiple energy releases, crackling noise is acustically emitted.

Lecture 1:

Lecture 2: please register to the website to access this lecture.

Lectures 1, 2: references

Topic 2: Instability phenomena (snap-back and snap-through) in fibre-reinforced materials (2 h)

On the basis of the Bridged Crack Model, snap-through and snap-back instabilities are analyzed in fibre-reinforced materials. The particular case of reinforced concrete is contemplated together with the related condition of minimum reinforcement.

Lectures 3, 4: please register to the website to access these lectures.

Lectures 3, 4: references

Topic 3: Period doubling and deterministic chaos in the vibration of cracked elements (1 h)

Period doubling and transition to deterministic chaos is considered and analyzed in damaged materials and cracked structural elements. The effect of the unilateral constraint between the crack faces in closure is emphasized.

Lecture 5: please register to the website to access this lecture.

Lecture 5: references

Topic 4: Multi-scale and fractal character of the internal material structure (1 h)

The reasons producing the fractal structure of natural objects and materials are presented and explained. In addition to the evident hierarchical features of the components, a more fundamental origin may be found in nonlinear dynamics and fractality of strange attractors.

Lecture 6: please register to the website to access this lecture.

Lecture 6: references

Topic 5: Renormalisation groups and scaling laws for stress, deformation and strain energy density (3 h)

Assuming fractal patterns for damage, cracking and deformation, renormalized or fractal counterparts of stress, strain and fracture energy are defined. Such fractal quantities present anomalous, noninteger physical dimensions and represent the real scale-independent material properties. On the other hand, the usual nominal quantities become scale-dependent and vary with the size according to peculiar power-laws where the scaling exponent is connected to the fractal dimension of the same set over which the quantity is defined.

Lectures 7, 8, 9: please register to the website to access these lectures.

Lectures 7, 8, 9: references

Topic 6: Multifractal scaling laws for tensile strenght and fracture energy (1 h)

The slope of the scaling laws as well as the fractality are maximum at the smallest scales, whereas they tend to vanish at the largest scales. This homogeneization effect is kept by a Multi-Fractal Scaling Law (MFSL), which is working very well for initially uncracked elements. Different well-known scaling laws for tensile strength are discussed and compared to MFSL.

Lecture 10: please register to the website to access this lecture.

Lecture 10: references

Topic 7: Fractional calculus and static-kinematic duality in the mechanics of fractal media (1 h)

The concept of fractional derivative is applied to the equations of an elastic body deformable only over a fractal sub-set. The duality of the static and kinematic fractional operators is shown, as well as an extension of the Virtual Work Principle.

Lecture 11: please register to the website to access this lecture.

Lecture 11: references

Topic 8: Acoustic emission and critical phenomena in structural and seismic engineering (1 h)

Acoustic emission and crackling noise are considered to experimentally detect damage and fracture processes occurring in structural elements or in the Earth crust. Localization, intensity and stability condition of the damage process may be obtained by the proposed method.

Lecture 12: please register to the website to access this lecture.

Lecture 12: references