In this volume a survey of the most relevant nonlinear crack models is provided, with the purpose of analyzing the nonlinear mechanical effects occurring at the tip of macrocracks in quasi-brittle materials - such as concrete, rocks, ceramics, polymers, high-strength metallic alloys - and in brittle-matrix fibre-reinforced composites. Such local effects, as, for example, plastic deformation, yielding, strain-hardening, strain-softening, mechanical damage, matrix microcracking, aggregate debonding, fibre bridging, fibre slippage, crazing, and so on, are properly described through different simplified models, representing the peculiarities of the phenomena involved. The models are introduced and described separately and then compared in the last part of the book. This volume will be of interest to students, professionals and researchers in the field of nonlinear fracture mechanics.

In this volume on the mechanics of fracture of Portland cement concrete, the general theme is the connection between microstructural phenomena and macroscopic models. The issues addressed include techniques for observation over a wide range of scales, the influence of .microcracking on common measures of strength and de formability , and ultimately, the relationship between microstructural changes in concrete under load and its resistance to cracking. It is now commonly accepted that, in past attempts to force-fit the behavior of concrete into the rules of linear elastic fracture mechanics, proper attention has not been paid to scale effects. Clearly, the relationships among specimen size, crack length and opening, and characteristic material fabric dimensions have been, in comparison to their counterparts in metals, ceramics, and rocks, abused in concrete. Without a fundamental understanding of these relationships, additional testing in search of the elusive, single measure of fracture toughness has spawned additional confusion and frustration. No one is in a better position to document this observation than Professor Mindess.

Design, Assessment and Retrofitting of RC Structures is the second volume of the Proceedings of the 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS-6, Catania, Italy, 17-22 June 2007), and is divided into four parts: (1) Theoretical and Experimental Investigation on the Mechanical Behaviour of RC Structures; (2) Practical Problems in RC Structural Applications; (3) Monitoring and Assessment of RC Structures; (4) Maintenance and Retrofitting of RC Structures.

Fracture Mechanics is used to interpret different problems: anchor fastening; plastic rotation capacity in RC beams; minimum reinforcement and ductility. It is also relevant to questions of size effect; flexural-shear-crushing failure mode transition; cohesive crack modelling; and rebar corrosion. Traditional problems arising in RC structures are also reconsidered and re-interpreted: crack width evaluation; dynamic and impact loading; fire and thermal degradation; fatigue strength assessment; as well as punching and spalling. Monitoring and assessment issues in RC structures come under discussion, such as acoustic emission and ultra sound. Maintenance and retrofitting techniques are treated, including the increasingly popular technique of fibre-reinforced polymer sheets used as wrapping around cracked structures, for example, to strengthen beams and columns.

The other two volumes comprising the Proceedings of the 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures are: New Trends in Fracture Mechanics of Concrete; and High-Performance Concrete, Brick-Masonry and Environmental Aspects. They present a wealth of information, and will be useful to professional civil engineers, postgraduate students and researchers.

Design, Assessment and Retrofitting of RC Structures

New Trends in Fracture Mechanics of Concrete contains Volume 1 of the Proceedings of the 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures (FraMCoS-6, Catania, Italy, 17-22 June 2007). It is divided into four parts: (1) Theoretical and Numerical Methods in Fracture Mechanics of Concrete; (2) Experimental Methods in Fracture Mechanics of Concrete; (3) Constitutive Damage Modelling of Concrete; (4) Time Effects in the Damage and Fracture of Concrete. Over the last twenty years, many theoretical, numerical and experimental methods have evolved in the field of Fracture Mechanics of Concrete. These have led to practical applications in reinforced-concrete design, assessment, monitoring and retrofitting, as well as innovative high-performance and durable cementitious materials. Although Fracture Mechanics of Concrete is now mature as a framework for defining and solving a variety of engineering problems, there is still much work to be done in improving previous theoretical and numerical models, and for re-interpreting established phenomena. In particular, there are new developments in the treatment of scale effects; the implementation of 3D-discretisation; and the combination of continuous and discontinuous models. Other areas of rapid progress are the development of innovative testing techniques; the proposal of non-local and anisotropic constitutive laws; the formulation of lattice and multiscale models, and the development of coupled multifield theories. The other two volumes comprising the Proceedings of the 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures are Design, Assessment and Retrofitting of RC Structures; and High-Performance Concrete, Brick-Masonry and Environmental Aspects. The set presents a wealth of information, and will be useful to professional civil engineers, postgraduate students and researchers.

This text presents a complete treatment of the fundamental themes of structural mechanics, from the traditonal to the most advanced. It covers: the mechanics of linear elastic solids, theory of beam systems and phenomena of structural failure. Structural symmetry is considered in one chapter and dynamics are dealt with at various points. The book is intended as a text for students and a reference for research workers and practising engineers. Logical presentation allows the clear introduction of topics such as finite element methods, automatic calculation of framed beam systems, dynamics, theory of plasticity and fracture mechanics. Key features of the text include: coverage of statics, dynamic, automatic computation of framed structures and the finite element method; an explicit consideration of all the static and dynamic operators of structural mechanics with their dual character; discussion of instability, plasticity and fracture; and examples and exercises with complete solutions.

Invited international contributions to this exciting new research field are included in this volume. It contains the specially selected papers from 45 key specialists given at the Symposium held under the auspices of the prestigious International Union of Theoretical and Applied Mechanics at Turin in October 1994.

Following Volumes III and IV that dealt with the fracture mechanics of concrete emphasizing both material testing and structural application in general, it was felt that specimen size and loading rate effects for concrete require further attention. The only criterion that has thus far successfully linearized the highly nonlinear crack growth data of concrete is the strain energy density theory. In particular, the crack growth resistance curves plotting the strain energy density factor versus crack growth known as the SR.curves are straight lines as specimen size and loading steps or rates are altered. This allows the extrapolation of data and provides a useful design methodology. This book is unique in that it is devoted specifically to the application of the strain energy density theory to civil engineering structural members made of concrete. Analyzed in detail is the strain softening behavior of concrete for a variety of different components including the influence of steel reinforcement. Permanent damage of the material is accounted for each increment of loading by invoking the mechanism of elastic unloading. This assumption is justified in concrete structures where the effective stiffness depends primarily on the crack growth rate and load history. Crack growth data are presented in terms of SR-curves with emphases placed on scaling specimen size which alone can change the mode of failure from plastic collapse to brittle fracture. Loading rate effects can also be scaled to control failure by yielding and fracture."

This volume emphazises the most early 1990s advances in fracture mechanics as specifically applied to steel bar reinforced concrete. Fracture mechanics has been applied to plain and fibre reinforced concrete with increasing success over recent years. This workshop extended these concepts to steel bar reinforced and pre-stressed concrete design. Particularly for high strength concrete, which is a very brittle material, and in the case of large structural members, the application of fracture mechanics appears to be very useful for improving the present design rules. The participants at the Turin workshop contributed expert opinions in four selected areas for which a rational approach, using fracture mechanics, could introduce variations into the concrete design codes: size effects; anchorage and bond; minimum reinforcement for elements in flexure; and shear resistance. The 23 chapters logically address these themes and demonstrate the unique ability of fracture mechanics to capture all the experimentally observed characteristics.

This work reviews methods for the experimental determination of concrete toughness and presents theories and models suitable for describing cracking and fracturing phenomena in plain and reinforced concrete. Test methods based on classsical linear fracture mechanics cannot be applied to laboratory sized concrete specimens. The book compares the currently used methods and presents recommended test procedures for mode I fracture/toughness using notched beam and other specimens. Crack propagation under mixed-mode loading (Mode II) is discussed and current test methods are extensively reviewed. Effects of loading rate, temperature and humidity effects are treated in a separate chapter. The book concludes with descriptions and recommendations of techniques for detecting the fracture process zone in concrete, in particular, pulse velocity and laser interferometry techniques. The introduction of the concepts of fracture toughness and fracture energy into structural concrete design codes means that the experimental determination of fracture porperties is ceasing to be an academic exercise and is becoming a technical need. This book has been prepared by RILEM Technical committee 89-FMT and

Contained in the volume are the papers presented at an International Symposium on Advanced Technology for Design and Fabrication of Composite Materials and Structures. The Symposium was organized by Consorzio per la Ricerca e l'Educazione Permanente; Institute of Fracture and Solid Mechanics, Lehigh University, Pennsylvania USA; Dipartimento di Ingegneria Strutturale del Politecnico di Torino; and Dipartimento di Ingegneria Aeronautica e Spaziale del Politecnico di Torino. It was held at the Politecnico di Torino in Italy, May 24-28, 1993. The support from the various organizations is acknowledged as follows: * Consiglio N azionale delle Ricerche * ALENIA SP AZIO * AGUST A * CIRA * AERMACCHI * Centro Ricerche FIAT * ALENIA (formerly AERITALIA) * Collegio Costruttori Edili della Provincia di Torino As new knowledge is being accumulated on the design and fabrication of advanced composite systems in different sectors of the world, there is the need not only to exchange new ideas but also to disseminate the information from the researchers to the users. The theme of this Symposium is particularly relevant to the automobile, marine, aerospace and construction industry where the competitive edge lies on improved processing and/or manufacturing of the products. Technological advances have been and will continue to depend strongly on the development of new materials and their effective use in design. Empirical trial-and- error methods could no longer be considered economically feasible when applied to usage-specific materials such as composites.

The book explores the two opposite natural trends of composite systems: (i) order and structure emerging from heterogeneity and randomness, and (ii) instability and chaos arising from simple nonlinear rules. Providing insights into the rapidly growing field of complexity sciences, the book focuses on the role of complexity in fracture mechanics. It firstly discusses the occurrence of self-similarity and fractal patterns in deformation, damage, fracture, and fragmentation of heterogeneous materials and the apparent scaling of the nominal mechanical properties of disordered materials, as well as of the time-to-failure after fatigue and creep loading. Then the book addresses criticality in the acoustic emissions from damaged structures and tectonic faults. Further, it examines the snap-back instability in the structural behavior of relatively large composite structures in the framework of catastrophe theory, and lastly describes the transition toward chaos in the dynamics of cracked elements.

This volume emphazises the most recent advances in fracture mechanics as specifically applied to steel bar reinforced concrete. Fracture mechanics has been applied to plain and fibre reinforced concrete with increasing success over recent years. This workshop extended these concepts to steel bar reinforced and pre-stressed concrete design. Particularly for high strength concrete, which is a very brittle material, and in the case of large structural members, the application of fracture mechanics appears to be very useful for improving the present design rules. The pre-eminent participants at the Turin workshop contributed extensive expert opinions in four selected areas for which a rational approach, using fracture mechanics, could introduce variations into the concrete design codes: size effects; anchorage and bond; minimum reinforcement for elements in flexure; and shear resistance. The 23 chapters logically address these themes and demonstrate the unique ability of fracture mechanics to capture all the experimentally observed characteristics. The book is primarily directed to the researchers in universities and institutions and will be of value to consultants and engineering companies.

Compares currently used methods in determining concrete toughness and presents recommended test procedures with theories and models for describing cracking and fracturing phenomena. Effects of loading rate, temperature and humidity are also examined. Well referenced and illustrated, this book is filled with practical technical information for materials and structural engineers.

This book presents a complete and unified treatment of the fundamental themes of structural mechanics, ranging from the traditional to the most advanced topics, covering mechanics of linear elastic solids, theory of beam systems, and phenomena of structural failure. The book considers explicitly all the static and kenetic operators of structural mechanics with their dual character. Topics relating to structural symmetry are covered in a single chapter while dynamics is dealt with at various points. The logical presentation allows the clear introduction of topics such as finite element methods, automatic calculation of framed beam systems, plate and shell theory, theory of plasticity, and fracture mechanics. Numerous worked examples, exercises with complete solutions and illustrations make it accessible both as a text for students and as a reference for research workers and practicing engineers.

Structural Mechanics Fundamentals gives you a complete and uniform treatment of the most fundamental and essential topics in structural mechanics. Presenting a traditional subject in an updated and modernized way, it merges classical topics with ones that have taken shape in more recent times, such as duality. This book is extensively based on the introductory chapters to the author's Structural Mechanics: A Unified Approach. Coverage includes: The basic topics of geometry of areas and of kinematics and statics of rigid body systems The mechanics of linear elastic solids-beams, plates, and three-dimensional solids-examined using a matrix approach The analysis of strain and stress around a material point The linear elastic constitutive law, with related Clapeyron's and Betti's theorems Kinematic, static, and constitutive equations The implication of the principle of virtual work The Saint Venant problem The theory of beam systems-statically determinate or indeterminate Methods of forces and energy for the examination of indeterminate beam systems The book draws on the author's many years of teaching experience and features a wealth of illustrations and worked examples to help explain the topics clearly yet rigorously. The book can be used as a text for senior undergraduate or graduate students in structural engineering or architecture and as a valuable reference for researchers and practicing engineers.

This book is a spin-off from the International Journal of Fracture and collects lectures and papers presented at the 11th International Conference on Fracture (ICF11), March 20-25, 2005. Included in this volume are introductory addresses, as well as remarks on the presentation of honorary degrees. A collection of papers follows, including presentations by such eminent scientists as B.B. Mandelbrot, G.I. Barenblatt, and numerous others, reviewing advanced research in fracture.

Building on the author's Structural Mechanics Fundamentals, this text presents a complete and uniform treatment of the more advanced topics in structural mechanics, ranging from beam frames to shell structures, from dynamics to buckling analysis, from plasticity to fracture mechanics, from long-span to high-rise civil structures. Plane frames Statically indeterminate beam systems: Method of displacements Plates and shells Finite element method Dynamics of discrete systems Dynamics of continuous elastic systems Buckling instability Long-span structures High-rise structures Theory of plasticity Plane stress and plane strain conditions Mechanics of fracture This book serves as a text for graduate students in structural engineering, as well as a reference for practising engineers and researchers.

Earthquakes are caused by the sudden release of energy during the fracture of stressed rock within the Earth's crust. This phenomenon is similar to that which occurs in materials under load, and although they take place on very different scales, these two phenomena - earthquakes in geophysics and damage in structural materials - have similarities. In both cases, there is a release of elastic energy from sources located inside a medium. These are selected papers from special sessions at the 11th International Conference on Fracture, held in Turin in 2005. They provide an outline of topics related to earthquakes and Acoustic Emission, and discuss the latest developments in this area. The papers have been divided into two categories: Seismic Mechanics & Earthquakes and Structural Failure & Acoustic Emission. Earthquakes and Acoustic Emission will serve as a useful supplementary textbook for postgraduates, while being of special interest to professionals in the field of earthquakes and acoustic emission.

High-Performance Concrete, Brick-Masonry and Environmental Aspects constitutes Volume 3 of the Proceedings of the 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures (Catania, Italy, 17-22 June 2007). It is divided into four parts: (1) High-Performance Concrete; (2) Fiber-Reinforced Concrete; (3) Brick-Masonry and other Quasi-Brittle Materials; and (4) Environmental Issues. Concrete technology has developed at a fast pace during the last two decades and material performance has been significantly improved. High-performance concrete (HPC) is now a reality. Initially, attention focused on compressive strength and the enhanced concrete was named "high-strength concrete" (HSC). Later, however, other issues arose, such as workability and durability. There was an increasing demand for enhanced rheology (in terms of flowability and cohesion, i.e. no segregation effects) in the fresh state, and compactness in the hardened state. Researchers responded with the development of self-consolidating concrete (SCC). Since higher strength generally implies higher brittleness, fibre-reinforced concrete (FRC) has generated considerable interest for its enhanced toughness under both static and dynamic loading, as well as for its ability to control concrete cracking. Nowadays, there are many types of fibre on the market, with different material and geometric qualities. The remarkable toughness of FRC, due to its fracture energy, combined with advances of nonlinear fracture-mechanics in modelling the structural behaviour, means that the advantages of incorporating fibres can be fully exploited. Furthermore, by adopting optimized mix-designs (in terms of fibre content and type, and of pozzolanic or hydraulically-active adjuncts) the increasingly important requirements of durability can be met, even under the most severe environmental conditions (like chemical aggression, high and low temperatures, and fatigue). Recently, the field of fracture mechanics has extended to other brittle or quasi-brittle materials, such as brick-masonry, glass, polymers and ice, and a more realistic evaluation of the safety level of structures has been obtained. The other two volumes comprising the Proceedings of the 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures are New Trends in Fracture Mechanics of Concrete; and Design, Assessment and Retrofitting of RC Structures. this set presents a wealth of information, and will be useful to professional civil engineers, postgraduate students and researchers.

In this volume a survey of the most relevant nonlinear crack models is provided, with the purpose of analyzing the nonlinear mechanical effects occurring at the tip of macrocracks in quasi-brittle materials - such as concrete, rocks, ceramics, polymers, high-strength metallic alloys - and in brittle-matrix fibre-reinforced composites. Such local effects, as, for example, plastic deformation, yielding, strain-hardening, strain-softening, mechanical damage, matrix microcracking, aggregate debonding, fibre bridging, fibre slippage, crazing, and so on, are properly described through different simplified models, representing the peculiarities of the phenomena involved. The models are introduced and described separately and then compared in the last part of the book. This volume will be of interest to students, professionals and researchers in the field of nonlinear fracture mechanics.

Structural Mechanics Fundamentals gives you a complete and uniform treatment of the most fundamental and essential topics in structural mechanics. Presenting a traditional subject in an updated and modernized way, it merges classical topics with ones that have taken shape in more recent times, such as duality. This book is extensively based on the introductory chapters to the author s Structural Mechanics: A Unified Approach.

Coverage includes:

• The basic topics of geometry of areas and of kinematics and statics of rigid body systems
• The mechanics of linear elastic solids beams, plates, and three-dimensional solids examined using a matrix approach
• The analysis of strain and stress around a material point
• The linear elastic constitutive law, with related Clapeyron s and Betti s theorems
• Kinematic, static, and constitutive equations
• The implication of the principle of virtual work
• The Saint Venant problem
• The theory of beam systems statically determinate or indeterminate
• Methods of forces and energy for the examination of indeterminate beam systems

The book draws on the author s many years of teaching experience and features a wealth of illustrations and worked examples to help explain the topics clearly yet rigorously. The book can be used as a text for senior undergraduate or graduate students in structural engineering or architecture and as a valuable reference for researchers and practicing engineers.

In this volume on the mechanics of fracture of Portland cement concrete, the general theme is the connection between microstructural phenomena and macroscopic models. The issues addressed include techniques for observation over a wide range of scales, the influence of .microcracking on common measures of strength and de formability , and ultimately, the relationship between microstructural changes in concrete under load and its resistance to cracking. It is now commonly accepted that, in past attempts to force-fit the behavior of concrete into the rules of linear elastic fracture mechanics, proper attention has not been paid to scale effects. Clearly, the relationships among specimen size, crack length and opening, and characteristic material fabric dimensions have been, in comparison to their counterparts in metals, ceramics, and rocks, abused in concrete. Without a fundamental understanding of these relationships, additional testing in search of the elusive, single measure of fracture toughness has spawned additional confusion and frustration. No one is in a better position to document this observation than Professor Mindess.

This book is a spin-off from the International Journal of Fracture and collects lectures and papers presented at the 11th International Conference on Fracture (ICF11), March 20-25, 2005. Included in this volume are introductory addresses, as well as remarks on the presentation of honorary degrees. A collection of papers follows, including presentations by such eminent scientists as B.B. Mandelbrot, G.I. Barenblatt, and numerous others, reviewing advanced research in fracture.

Following Volumes III and IV that dealt with the fracture mechanics of concrete emphasizing both material testing and structural application in general, it was felt that specimen size and loading rate effects for concrete require further attention. The only criterion that has thus far successfully linearized the highly nonlinear crack growth data of concrete is the strain energy density theory. In particular, the crack growth resistance curves plotting the strain energy density factor versus crack growth known as the SR.curves are straight lines as specimen size and loading steps or rates are altered. This allows the extrapolation of data and provides a useful design methodology. This book is unique in that it is devoted specifically to the application of the strain energy density theory to civil engineering structural members made of concrete. Analyzed in detail is the strain softening behavior of concrete for a variety of different components including the influence of steel reinforcement. Permanent damage of the material is accounted for each increment of loading by invoking the mechanism of elastic unloading. This assumption is justified in concrete structures where the effective stiffness depends primarily on the crack growth rate and load history. Crack growth data are presented in terms of SR-curves with emphases placed on scaling specimen size which alone can change the mode of failure from plastic collapse to brittle fracture. Loading rate effects can also be scaled to control failure by yielding and fracture."

Contained in the volume are the papers presented at an International Symposium on Advanced Technology for Design and Fabrication of Composite Materials and Structures. The Symposium was organized by Consorzio per la Ricerca e l'Educazione Permanente; Institute of Fracture and Solid Mechanics, Lehigh University, Pennsylvania USA; Dipartimento di Ingegneria Strutturale del Politecnico di Torino; and Dipartimento di Ingegneria Aeronautica e Spaziale del Politecnico di Torino. It was held at the Politecnico di Torino in Italy, May 24-28, 1993. The support from the various organizations is acknowledged as follows: * Consiglio N azionale delle Ricerche * ALENIA SP AZIO * AGUST A * CIRA * AERMACCHI * Centro Ricerche FIAT * ALENIA (formerly AERITALIA) * Collegio Costruttori Edili della Provincia di Torino As new knowledge is being accumulated on the design and fabrication of advanced composite systems in different sectors of the world, there is the need not only to exchange new ideas but also to disseminate the information from the researchers to the users. The theme of this Symposium is particularly relevant to the automobile, marine, aerospace and construction industry where the competitive edge lies on improved processing and/or manufacturing of the products. Technological advances have been and will continue to depend strongly on the development of new materials and their effective use in design. Empirical trial-and- error methods could no longer be considered economically feasible when applied to usage-specific materials such as composites.