Course Summary

The course intends to provide the fundamental concepts of Nonlinear Fracture Mechanics as well as of Fractal Fracture Mechanics. Although this two advanced topics are both connected with Linear Elastic Fracture Mechanics, a specific and extended knowledge of the latter is not required to the attendants. On the other hand, the nonlinear and the fractal aspects are both very important for practical applications and may be treated in the framework of Complexity Sciences.

As a matter of fact, from simple nonlinear rules a catastrophic and/or chaotic mechanical behaviour may derive. Two significant examples are provided by the cohesive constitutive law and by the unilateral constraint condition between the crack faces. The former produces ductile versus brittle size-scale transitions, where the brittle crack propagation is described by cusp catastrophe or snap-back load versus deflection branches. The latter produces nonlinear or chaotic vibrations.

On the other hand, from apparently disordered or chaotic situations a relatively ordered and regular condition may emerge, if we consider the multi-scale and fractal character of damage, cracking and deformation. Renormalized or fractal quantities may be defined, which present anomalous and noninteger physical dimensions and represent the real scale-independent properties. The nominal quantities obey, on the other hand, scaling power-laws where the exponent reflects the fractal dimension of the set over which the same quantity is defined. In this context, damage, cracking and final rupture are seen as critical phenomena.

Training Objectives
The course is addressed to Master and Ph.D. students, post-doctoral fellows, young researchers, specialists in Fracture Mechanics working in the industry. A widening of knowledge is intended towards nonlinear fracture phenomena and statistical and disordered damage processes.

Prerequisites
A specific and extended preparation in Linear Elastic Fracture Mechanics is not explicitly required. On the other hand, basic concepts of solid and structural mechanics are necessary.

Topic list

1. Crackling, brittle ruptures and Catastrophe Theory
2. Instability phenomena (snap-back and snapthrough) in fibrereinforced materials
3. Period doubling and deterministic chaos in the vibration of cracked elements
4. Multi-scale and fractal character of the internal material structure
5. Renormalisation groups and scaling laws for stress, deformation and strain energy density
6. Multifractal scaling laws for tensile strenght and fracture energy
7. Fractional calculus and static-kinematic duality in the mechanics of fractal media
8. Acoustic emission and critical phenomena in structural and seismic engineering

Author’s Curriculum:

Prof. Dr. Alberto CARPINTERI Chair of Structural Mechanics Politecnico di Torino 10129 - Torino - Italy

Academic Positions:

• Professor of Structural Mechanics, Politecnico di Torino, Torino-Italy, 1986-.
• Director Dept. Structural Engineering, Politecnico di Torino, Torino-Italy, 1989-1995.
• Founding Member and Director – Graduate School in Structural Engineering, Politecnico di Torino, Torino-Italy, 1990-.
• Visiting Professor, Lehigh University, Bethlehem-Pennsylvania, USA, 1982-1983.
• Member of the New York Academy of Sciences (founded in 1817), New York, USA, 1997-.
• Member of the American Association for the Advancement of Science (founded in 1848 at the Academy of Natural Sciences in Philadelphia, Pennsylvania, USA), 1999-.
• Member of the American Academy of Mechanics, USA, 2003-.
• Fellow of the Turin Academy of Sciences (founded by G.L. Lagrange in 1783), Torino-Italy,2005-; Member, 1995-2005.
• Member of the Istituto Lombardo – Accademia di Scienze e Lettere, Milano-Italy, 2006-.
• Member of the Accademia Teatina per le Scienze, Chieti-Italy, 2006-.

Scientific Activity:

• President of the European Structural Integrity Society (ESIS), 2002-2006.
• President of the International Association of Fracture Mechanics for Concrete and Concrete Structures (IA-FraMCoS), 2004-2007.
• President of the Italian Group of Fracture (IGF), 1998-2005.
• Senior Vicepresident of the International Congress on Fracture (ICF), 2005-2009.
• Vicepresident of the National Research Institute of Metrology (INRIM), 2006-2009.
• Chairman of the Organizing Committee of the 11th International Conference on Fracture (ICF11), Torino, Italy, March 20-25, 2005.
• Member of the Congress Committee of the International Union of Theoretical and Applied Mechanics (IUTAM), 2004-2008.
• Co-Editor of the International Journal “Strength, Fracture & Complexity”, 2003-;
• Member of the Editorial Board of six international journals.
• Author of over 500 papers on fracture mechanics, material fatigue, thermoelasticity, seismic structures, reinforced concrete, structural monitoring, contact mechanics, fragmentation and comminution, drilling.
• Author or Editor of 38 volumes.

Honours and Awards:

• Recipient of Robert l'Hermite International Prize, RILEM, Paris, France, 1982.
• Recipient of JSME Medal, Japan Society of Mechanical Engineers, Tokyo, Japan, 1993.
• Doctor of Physics Honoris Causa, The Constantinian University, Cranston-Rhode Island, USA, 1994.
• Recipient of International Cultural Diploma of Honor, American Biographical Institute, 1995.
• Honorary Professor, Nanjing Architectural & Civil Engineering Institute, Nanjing, China, 1996.
• Honorary Professor, Albert Schweitzer University, Geneva, Switzerland, 2000.
• Recipient of WIT Eminent Scientist Award, Wessex Institute of Technology, Southampton, U.K., 2000.

This course is an outcome of the ILTOF - Innovative Learning and Training on Fracture project. The course is maintained free of charge by the TCN Consortium for higher education. The ILTOF project has been funded with support from the European Commission. This publication reflects the views only of the Author(s), and the Commission cannot be held responsible for any use which may be made of the information contained therein.