Marco Paggi | IMT Lucca (original) (raw)

Papers by Marco Paggi

Modeling and Simulation of Tribological Problems in Technology, 2019

This chapter provides a self-consistent introduction to computational methods for the solution of... more This chapter provides a self-consistent introduction to computational methods for the solution of contact problems between bodies separated by rough interfaces. Both frictional and frictionless contact problems are examined. The mathematical formulation of the boundary element method is presented first, with details on the possible algorithmic implementation strategies and their computational efficiency. In the second part of the chapter, the fundamentals of the finite element method for the solution of contact problems are presented, along with an overview on the different strategies available in the literature to accurately discretize the multiscale features of roughness. A synopsis of the major advantages and disadvantages provided by the computational methods based on the boundary element method or the finite element method concludes the chapter, illustrating also perspective research directions.

This chapter provides a self-consistent introduction to computational methods for the solution of... more This chapter provides a self-consistent introduction to computational methods for the solution of contact problems between bodies separated by rough interfaces. Both frictional and frictionless contact problems are examined. Themathematical formulation of the boundary element method is presented first, with details on the possible algorithmic implementation strategies and their computational efficiency. In the second part of the chapter, the fundamentals of the finite element method for the solution of contact problems are presented, along with an overview on the different strategies available in the literature to accurately discretize the multiscale features of roughness. A synopsis of the major advantages and disadvantages provided by the computational methods based on the boundary element method or the finite elementmethod concludes the chapter, illustrating also perspective research directions.

Computational Mechanics, 2019

A novel multi-scale finite element formulation for contact mechanics between nominally smooth but... more A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface interactions at the macro-scale with a boundary element method (BEM) for the solution of the contact problem at the micro-scale. The BEM is used at each integration point to determine the normal contact traction and the normal contact stiffness, allowing to take into account any desirable kind of rough topology, either real, e.g. obtained from profilometric data, or artificial, evaluated with the most suitable numerical or analytical approach. Different numerical strategies to accelerate coupling between FEM and BEM are discussed in relation to a selected benchmark test.

International Journal of Fatigue, 2016

This paper presents the results of an extensive experimental analysis of the fractal properties o... more This paper presents the results of an extensive experimental analysis of the fractal properties of fatigue crack rough surfaces. The analysis of the power-spectral density functions of profilometric traces shows a predominance of the box fractal dimension D = 1.2. This result leads to a particularization of the fatigue crack growth equation based on fractality proposed by the last two authors which is very close to the generalized Frost-Dugdale equation proposed by the first three authors. The two approaches, albeit based on different initial modelling assumptions, are both very effective in predicting the crack growth rate of short cracks.

Cmes-computer Modeling in Engineering & Sciences, Nov 1, 2009

The stick-slip instability is a typical manifestation of the nonlinearity of the frictional respo... more The stick-slip instability is a typical manifestation of the nonlinearity of the frictional response of rough surfaces. As recently demonstrated by several researchers, the problem of contact loss is also inherently connected to the stick-slip instability and it has been detected both in elastically soft materials, such as rubber or gelatine, and in elastic stiff materials, such as for earthquake faults. Treating the problem of tangential contact in the framework of micromechanical contact models, the effect of the phenomenon of contact loss on the micro-slip behavior of rough surfaces is herein investigated. To this aim, the stick and slip components of the total applied tangential force and of the total real contact area are properly determined as functions of the total applied tangential force. A comparison with the behavior of smooth surfaces, such as spheres, cylinders and flat surfaces, is presented. Then, simulating the problem of tangential loading followed by a reduction of the applied normal force, it will be shown that the phenomenon of contact loss gives rise to energy release due to snap-back instability in the diagram relating the tangential force to the sliding displacement. This result provides for the very first time an explanation to the phenomenon of stick-slip according to the Catastrophe Theory, in close analogy with the cusp-catastrophe instability of Mode I crack propagation in cohesive solids.

International Journal of Solids and Structures, 2005

An overview of the classical friction laws holding at the macro-scale and the new developments at... more An overview of the classical friction laws holding at the macro-scale and the new developments at the nano-level are proposed. Furthermore, two opposite phenomena are addressed: the former concerning the apparent weakness of the San Andreas fault, the latter regarding the strong frictional behavior which appears at the nano-scale. An interpretation of these size effects on the friction coefficient is attempted making use of the renormalization group procedure which allows to explain the frictional phenomena over all the scales.

International Journal of Solids and Structures, 2008

The problem of interface decohesion in laminated beams is addressed with reference to the debondi... more The problem of interface decohesion in laminated beams is addressed with reference to the debonding double cantilever beam test geometry (DCB). The paper deals with the analysis of the influence of nonuniform bonding properties or interfacial defects on the crack propagation process and its stability. To this aim, the classical analytical approach based on the Euler-Bernoulli beam on an elastic foundation is extended to the presence of a general distribution of microcracks ahead of the macrocrack tip. The main features and limitations of this approach are carefully analyzed. In particular, it is shown that this simplified approach does not consider the unilateral contact condition along the interface, thus admitting a penetration between the two arms of the beam. A comparison with a finite element formulation is proposed to assess if this violation of the constraints inequalities, usually adopted in the case of uniform bonding, is still acceptable when interfacial defects are present. In order to fully describe the whole nonlinear behavior of the interface, a generalized interface constitutive law is used. The models comparison shows that, in the presence of interfacial defects, the effect of contact plays a crucial role in the description of the mechanical response of the joint.

This article addresses the fundamental issue of shear transfer across rough joints, a problem of ... more This article addresses the fundamental issue of shear transfer across rough joints, a problem of paramount importance in several civil engineering applications. Starting from the examination of the experimental results obtained from shear tests on concrete-concrete joints, rockrock joints and concrete-soil interfaces, the main features of the physical phenomenon are presented. The experimental results are then interpreted according to a novel formulation based on the integration of contact mechanics, suitable for the description of the pre-peak response of the joint, and nonlinear fracture mechanics, for the description of the post-peak softening branch. The proposed treatment fully takes into account the size-scale effects on the shear response of the joints due to interface roughness, providing a significant step forward with respect to the state-of-the-art modelling based on elasto-plasticity with a history dependent friction coefficient.

In this paper the Greenwood and Williamson contact theory for microscopically rough surfaces is g... more In this paper the Greenwood and Williamson contact theory for microscopically rough surfaces is generalized by considering a grading on the elastic modulus of the asperities. This situation can be representative of surfaces receiving superficial treatments or characterized by a chemical degradation. The effect of an exponential grading on the applied normal load, on the relationship between the real contact area and the load, on the plasticity index, as well as on the contact conductance is illustrated with detailed numerical examples.

Instability phenomena occurring in the microstructure of composite materials are investigated. To... more Instability phenomena occurring in the microstructure of composite materials are investigated. To this aim, a complete description of the mechanical behavior of bi-material interfaces in composite materials requires the definition of both a cohesive law involving damage for the debonding stage, and a contact model during the closure of the interface. Both formulations are herein presented and implemented in the FE code FEAP. Numerical examples showing the transition from a snap-back instability to a stable mechanical response are presented.

Journal of Physics D: Applied Physics, 2015

The random process theory (RPT) has been widely applied to predict the joint probability distribu... more The random process theory (RPT) has been widely applied to predict the joint probability distribution functions (PDFs) of asperity heights and curvatures of rough surfaces. A check of the predictions of RPT against the actual statistics of numerically generated random fractal surfaces and of real rough surfaces has been only partially undertaken. The present experimental and numerical study provides a deep critical comparison on this matter, providing some insight into the capabilities and limitations in applying RPT and fractal modeling to antireflective and hydrophobic rough surfaces, two important types of textured surfaces. A multi-resolution experimental campaign by using a confocal profilometer with different lenses is carried out and a comprehensive software for the statistical description of rough surfaces is developed. It is found that the topology of the analyzed textured surfaces cannot be fully described according to RPT and fractal modeling. The following complexities emerge: (i) the presence of cutoffs or bi-fractality in the power-law powerspectral density (PSD) functions; (ii) a more pronounced shift of the PSD by changing resolution as compared to what expected from fractal modeling; (iii) inaccuracy of the RPT in describing the joint PDFs of asperity heights and curvatures of textured surfaces; (iv) lack of resolution-invariance of joint PDFs of textured surfaces in case of special surface treatments, not accounted by fractal modeling.

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2013

A theoretical study based on dimensional analysis and fractal geometry of crack profiles is propo... more A theoretical study based on dimensional analysis and fractal geometry of crack profiles is proposed to establish the relation between their fractal dimension D (1 < D < 2) and the parameters defining the fatigue crack propagation rate. The exponent m of the Paris’ law is found to be an increasing function of the fractal dimension of the crack profile, m = 2 D/(2 − D). This trend is confirmed by a quantitative analysis of fractographic images of titanium alloys with different grain sizes (different roughness of crack profiles), by a new experimental test and by an indirect estimation of D from crack growth equations accounting from crack-size effects in steel and aluminum. The present study can be considered as the first quantitative analysis of fractographic images aiming at relating the morphological features of cracks to their kinetics in fatigue.

Meccanica, 2014

Paris and Wöhler's fatigue curves are intimately connected by the physics of the process of fatig... more Paris and Wöhler's fatigue curves are intimately connected by the physics of the process of fatigue crack growth. However, their connections are not obvious due to the appearance of anomalous specimen-size and crack-size effects. In this study, considering the equations for a notched specimen (or for a specimen where failure is the result of the propagation of a main crack) and the assumption of incomplete self-similarity on the specimen size, the relations between the size-scale effects observed in the Paris and Wöhler's diagrams are explained. In the second part of the work, the behaviour of physically short cracks is addressed and, considering a fractal model for fatigue crack growth, the crack-size effects on the Paris and Wöhler's curves are discussed.

Journal of ASTM International, 2011

In the present paper, generalized Paris and Wö hler equations are derived according to dimensiona... more In the present paper, generalized Paris and Wö hler equations are derived according to dimensional analysis and incomplete similarity concepts. They provide a rational interpretation to a majority of empirical powerlaw criteria used in fatigue. In particular, they are able to model the effects of the grain size, of the initial crack length, as well as of the size-scale of the tested specimen on the crack growth rate and on the fatigue life. Regarding the important issue of crack-size dependencies of the Paris' coefficient C and of the fatigue threshold, an independent approach, based on the application of fractal geometry concepts, is proposed to model such an anomalous behavior. As a straightforward consequence of the fractality of the crack surfaces, the fractal approach provides scaling laws fully consistent with those determined from dimensional analysis arguments. The proposed scaling laws are applied to relevant experimental data related to the crack-size and to the structural-size dependencies of the fatigue parameters in metals and in quasi-brittle materials. Finally, paying attention to the limit points defining the range of validity of the classical Wö hler and Paris power-law relationships, correlations between the so-called cyclic or fatigue properties are proposed, giving a rational explanation to the experimental trends observed in the material property charts.

Journal of Engineering Mechanics, 2010

The problem of end-plate debonding of the external reinforcement in strengthened concrete beams i... more The problem of end-plate debonding of the external reinforcement in strengthened concrete beams is analyzed in this paper. As experimentally observed, this mode of failure is highly brittle and poses severe limitations to the efficacy of the strengthening technique. A numerical analysis of the full-range behavior of strengthened beams in bending is herein proposed to study the stages of nucleation and propagation of interfacial cracks between the external reinforcement and the concrete substrate. This is achieved by modeling the nonlinear interface behavior according to a cohesive law accounting for Mode Mixity. The numerically obtained load versus midspan deflection curves for three-or four-point bending beams show that the process of end-plate debonding is the result of a snap-back instability, which is fully interpreted in the framework of the Catastrophe Theory. To capture the softening branch with positive slope, the interface crack-length control scheme is proposed in the numerical simulations. The results of a wide parametric study exploring the effect of the relative reinforcement length, the mechanical percentage of fiber-reinforced polymer sheets, the beam slenderness, and the ratio between Mode II and Mode I fracture energies are collected in useful diagrams. Finally, an experimental assessment of the proposed model completes the paper.

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2012

The present paper is a state-of-the-art review of the research carried out at the Politecnico di ... more The present paper is a state-of-the-art review of the research carried out at the Politecnico di Torino during the last two decades on the modelling of strain localization. Introducing the elementary cohesive/overlapping models in tension/compression, it will be shown that it is possible to get a deep insight into the ductile-to-brittle transition and into the scaling of the material properties usually detected when testing quasi-brittle material specimens or structures at different size-scales.

International Journal of Heat and Mass Transfer, 2011

The dependence of the contact conductance of self-affine rough surfaces on the applied pressure i... more The dependence of the contact conductance of self-affine rough surfaces on the applied pressure is studied using the electric-mechanical analogy which relates the contact conductance to the normal stiffness. According to dimensional analysis arguments, an efficient dimensionless formulation is proposed which minimizes the number of dimensionless variables governing the phenomenon. Assuming incomplete similarity in the dimensionless pressure, a power-law dependence between contact conductance and mean pressure is proposed. This is confirmed by earlier semi-empirical correlations that are recovered as special cases of the proposed formulation. To compute the exponent b of the power-law, and relate it to the morphological properties of the surfaces, we numerically test self-affine rough surfaces composed of random midpoint displacement (RMD) patches. Such patches are generated using a modified RMD algorithm in order to decouple the effect of the long wavelength cutoff from that due to microscale roughness. Numerical results show that the long wavelength cutoff has an important effect on the contact conductance, whereas the sampling interval and the fractal dimension are less important. The effect of elastic interaction between asperities has also been quantified and it significantly influences the predicted power-law exponent b.

International Journal of Fracture, 2010

In the present paper, a new fracturemechanics based model is proposed for the analysis of reinfor... more In the present paper, a new fracturemechanics based model is proposed for the analysis of reinforced concrete beams in bending describing both cracking and crushing growths taking place during the loading process by means of the concept of strain localization. In particular, the nonlinear behaviour of concrete in compression is modelled by the Overlapping Crack Model, which considers a material interpenetration when the elastic limit is overcome, in close analogy with the Cohesive Crack Model, routinely adopted for modelling the tensile behaviour of concrete. On the basis of different nonlinear contributions due to concrete and steel, a numerical finite element algorithm is proposed. According to this approach, the flexural behaviour of reinforced concrete structural elements is analyzed by varying the main geometrical and mechanical parameters. Particular regard is given to the role of the size-scale effects on the ductility of plastic hinges, which is available at the ultimate load conditions.

Modeling and Simulation of Tribological Problems in Technology, 2019

This chapter provides a self-consistent introduction to computational methods for the solution of... more This chapter provides a self-consistent introduction to computational methods for the solution of contact problems between bodies separated by rough interfaces. Both frictional and frictionless contact problems are examined. The mathematical formulation of the boundary element method is presented first, with details on the possible algorithmic implementation strategies and their computational efficiency. In the second part of the chapter, the fundamentals of the finite element method for the solution of contact problems are presented, along with an overview on the different strategies available in the literature to accurately discretize the multiscale features of roughness. A synopsis of the major advantages and disadvantages provided by the computational methods based on the boundary element method or the finite element method concludes the chapter, illustrating also perspective research directions.

This chapter provides a self-consistent introduction to computational methods for the solution of... more This chapter provides a self-consistent introduction to computational methods for the solution of contact problems between bodies separated by rough interfaces. Both frictional and frictionless contact problems are examined. Themathematical formulation of the boundary element method is presented first, with details on the possible algorithmic implementation strategies and their computational efficiency. In the second part of the chapter, the fundamentals of the finite element method for the solution of contact problems are presented, along with an overview on the different strategies available in the literature to accurately discretize the multiscale features of roughness. A synopsis of the major advantages and disadvantages provided by the computational methods based on the boundary element method or the finite elementmethod concludes the chapter, illustrating also perspective research directions.

Computational Mechanics, 2019

A novel multi-scale finite element formulation for contact mechanics between nominally smooth but... more A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface interactions at the macro-scale with a boundary element method (BEM) for the solution of the contact problem at the micro-scale. The BEM is used at each integration point to determine the normal contact traction and the normal contact stiffness, allowing to take into account any desirable kind of rough topology, either real, e.g. obtained from profilometric data, or artificial, evaluated with the most suitable numerical or analytical approach. Different numerical strategies to accelerate coupling between FEM and BEM are discussed in relation to a selected benchmark test.

International Journal of Fatigue, 2016

This paper presents the results of an extensive experimental analysis of the fractal properties o... more This paper presents the results of an extensive experimental analysis of the fractal properties of fatigue crack rough surfaces. The analysis of the power-spectral density functions of profilometric traces shows a predominance of the box fractal dimension D = 1.2. This result leads to a particularization of the fatigue crack growth equation based on fractality proposed by the last two authors which is very close to the generalized Frost-Dugdale equation proposed by the first three authors. The two approaches, albeit based on different initial modelling assumptions, are both very effective in predicting the crack growth rate of short cracks.

Cmes-computer Modeling in Engineering & Sciences, Nov 1, 2009

The stick-slip instability is a typical manifestation of the nonlinearity of the frictional respo... more The stick-slip instability is a typical manifestation of the nonlinearity of the frictional response of rough surfaces. As recently demonstrated by several researchers, the problem of contact loss is also inherently connected to the stick-slip instability and it has been detected both in elastically soft materials, such as rubber or gelatine, and in elastic stiff materials, such as for earthquake faults. Treating the problem of tangential contact in the framework of micromechanical contact models, the effect of the phenomenon of contact loss on the micro-slip behavior of rough surfaces is herein investigated. To this aim, the stick and slip components of the total applied tangential force and of the total real contact area are properly determined as functions of the total applied tangential force. A comparison with the behavior of smooth surfaces, such as spheres, cylinders and flat surfaces, is presented. Then, simulating the problem of tangential loading followed by a reduction of the applied normal force, it will be shown that the phenomenon of contact loss gives rise to energy release due to snap-back instability in the diagram relating the tangential force to the sliding displacement. This result provides for the very first time an explanation to the phenomenon of stick-slip according to the Catastrophe Theory, in close analogy with the cusp-catastrophe instability of Mode I crack propagation in cohesive solids.

International Journal of Solids and Structures, 2005

An overview of the classical friction laws holding at the macro-scale and the new developments at... more An overview of the classical friction laws holding at the macro-scale and the new developments at the nano-level are proposed. Furthermore, two opposite phenomena are addressed: the former concerning the apparent weakness of the San Andreas fault, the latter regarding the strong frictional behavior which appears at the nano-scale. An interpretation of these size effects on the friction coefficient is attempted making use of the renormalization group procedure which allows to explain the frictional phenomena over all the scales.

International Journal of Solids and Structures, 2008

The problem of interface decohesion in laminated beams is addressed with reference to the debondi... more The problem of interface decohesion in laminated beams is addressed with reference to the debonding double cantilever beam test geometry (DCB). The paper deals with the analysis of the influence of nonuniform bonding properties or interfacial defects on the crack propagation process and its stability. To this aim, the classical analytical approach based on the Euler-Bernoulli beam on an elastic foundation is extended to the presence of a general distribution of microcracks ahead of the macrocrack tip. The main features and limitations of this approach are carefully analyzed. In particular, it is shown that this simplified approach does not consider the unilateral contact condition along the interface, thus admitting a penetration between the two arms of the beam. A comparison with a finite element formulation is proposed to assess if this violation of the constraints inequalities, usually adopted in the case of uniform bonding, is still acceptable when interfacial defects are present. In order to fully describe the whole nonlinear behavior of the interface, a generalized interface constitutive law is used. The models comparison shows that, in the presence of interfacial defects, the effect of contact plays a crucial role in the description of the mechanical response of the joint.

This article addresses the fundamental issue of shear transfer across rough joints, a problem of ... more This article addresses the fundamental issue of shear transfer across rough joints, a problem of paramount importance in several civil engineering applications. Starting from the examination of the experimental results obtained from shear tests on concrete-concrete joints, rockrock joints and concrete-soil interfaces, the main features of the physical phenomenon are presented. The experimental results are then interpreted according to a novel formulation based on the integration of contact mechanics, suitable for the description of the pre-peak response of the joint, and nonlinear fracture mechanics, for the description of the post-peak softening branch. The proposed treatment fully takes into account the size-scale effects on the shear response of the joints due to interface roughness, providing a significant step forward with respect to the state-of-the-art modelling based on elasto-plasticity with a history dependent friction coefficient.

In this paper the Greenwood and Williamson contact theory for microscopically rough surfaces is g... more In this paper the Greenwood and Williamson contact theory for microscopically rough surfaces is generalized by considering a grading on the elastic modulus of the asperities. This situation can be representative of surfaces receiving superficial treatments or characterized by a chemical degradation. The effect of an exponential grading on the applied normal load, on the relationship between the real contact area and the load, on the plasticity index, as well as on the contact conductance is illustrated with detailed numerical examples.

Instability phenomena occurring in the microstructure of composite materials are investigated. To... more Instability phenomena occurring in the microstructure of composite materials are investigated. To this aim, a complete description of the mechanical behavior of bi-material interfaces in composite materials requires the definition of both a cohesive law involving damage for the debonding stage, and a contact model during the closure of the interface. Both formulations are herein presented and implemented in the FE code FEAP. Numerical examples showing the transition from a snap-back instability to a stable mechanical response are presented.

Journal of Physics D: Applied Physics, 2015

The random process theory (RPT) has been widely applied to predict the joint probability distribu... more The random process theory (RPT) has been widely applied to predict the joint probability distribution functions (PDFs) of asperity heights and curvatures of rough surfaces. A check of the predictions of RPT against the actual statistics of numerically generated random fractal surfaces and of real rough surfaces has been only partially undertaken. The present experimental and numerical study provides a deep critical comparison on this matter, providing some insight into the capabilities and limitations in applying RPT and fractal modeling to antireflective and hydrophobic rough surfaces, two important types of textured surfaces. A multi-resolution experimental campaign by using a confocal profilometer with different lenses is carried out and a comprehensive software for the statistical description of rough surfaces is developed. It is found that the topology of the analyzed textured surfaces cannot be fully described according to RPT and fractal modeling. The following complexities emerge: (i) the presence of cutoffs or bi-fractality in the power-law powerspectral density (PSD) functions; (ii) a more pronounced shift of the PSD by changing resolution as compared to what expected from fractal modeling; (iii) inaccuracy of the RPT in describing the joint PDFs of asperity heights and curvatures of textured surfaces; (iv) lack of resolution-invariance of joint PDFs of textured surfaces in case of special surface treatments, not accounted by fractal modeling.

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2013

A theoretical study based on dimensional analysis and fractal geometry of crack profiles is propo... more A theoretical study based on dimensional analysis and fractal geometry of crack profiles is proposed to establish the relation between their fractal dimension D (1 < D < 2) and the parameters defining the fatigue crack propagation rate. The exponent m of the Paris’ law is found to be an increasing function of the fractal dimension of the crack profile, m = 2 D/(2 − D). This trend is confirmed by a quantitative analysis of fractographic images of titanium alloys with different grain sizes (different roughness of crack profiles), by a new experimental test and by an indirect estimation of D from crack growth equations accounting from crack-size effects in steel and aluminum. The present study can be considered as the first quantitative analysis of fractographic images aiming at relating the morphological features of cracks to their kinetics in fatigue.

Meccanica, 2014

Paris and Wöhler's fatigue curves are intimately connected by the physics of the process of fatig... more Paris and Wöhler's fatigue curves are intimately connected by the physics of the process of fatigue crack growth. However, their connections are not obvious due to the appearance of anomalous specimen-size and crack-size effects. In this study, considering the equations for a notched specimen (or for a specimen where failure is the result of the propagation of a main crack) and the assumption of incomplete self-similarity on the specimen size, the relations between the size-scale effects observed in the Paris and Wöhler's diagrams are explained. In the second part of the work, the behaviour of physically short cracks is addressed and, considering a fractal model for fatigue crack growth, the crack-size effects on the Paris and Wöhler's curves are discussed.

Journal of ASTM International, 2011

In the present paper, generalized Paris and Wö hler equations are derived according to dimensiona... more In the present paper, generalized Paris and Wö hler equations are derived according to dimensional analysis and incomplete similarity concepts. They provide a rational interpretation to a majority of empirical powerlaw criteria used in fatigue. In particular, they are able to model the effects of the grain size, of the initial crack length, as well as of the size-scale of the tested specimen on the crack growth rate and on the fatigue life. Regarding the important issue of crack-size dependencies of the Paris' coefficient C and of the fatigue threshold, an independent approach, based on the application of fractal geometry concepts, is proposed to model such an anomalous behavior. As a straightforward consequence of the fractality of the crack surfaces, the fractal approach provides scaling laws fully consistent with those determined from dimensional analysis arguments. The proposed scaling laws are applied to relevant experimental data related to the crack-size and to the structural-size dependencies of the fatigue parameters in metals and in quasi-brittle materials. Finally, paying attention to the limit points defining the range of validity of the classical Wö hler and Paris power-law relationships, correlations between the so-called cyclic or fatigue properties are proposed, giving a rational explanation to the experimental trends observed in the material property charts.

Journal of Engineering Mechanics, 2010

The problem of end-plate debonding of the external reinforcement in strengthened concrete beams i... more The problem of end-plate debonding of the external reinforcement in strengthened concrete beams is analyzed in this paper. As experimentally observed, this mode of failure is highly brittle and poses severe limitations to the efficacy of the strengthening technique. A numerical analysis of the full-range behavior of strengthened beams in bending is herein proposed to study the stages of nucleation and propagation of interfacial cracks between the external reinforcement and the concrete substrate. This is achieved by modeling the nonlinear interface behavior according to a cohesive law accounting for Mode Mixity. The numerically obtained load versus midspan deflection curves for three-or four-point bending beams show that the process of end-plate debonding is the result of a snap-back instability, which is fully interpreted in the framework of the Catastrophe Theory. To capture the softening branch with positive slope, the interface crack-length control scheme is proposed in the numerical simulations. The results of a wide parametric study exploring the effect of the relative reinforcement length, the mechanical percentage of fiber-reinforced polymer sheets, the beam slenderness, and the ratio between Mode II and Mode I fracture energies are collected in useful diagrams. Finally, an experimental assessment of the proposed model completes the paper.

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2012

The present paper is a state-of-the-art review of the research carried out at the Politecnico di ... more The present paper is a state-of-the-art review of the research carried out at the Politecnico di Torino during the last two decades on the modelling of strain localization. Introducing the elementary cohesive/overlapping models in tension/compression, it will be shown that it is possible to get a deep insight into the ductile-to-brittle transition and into the scaling of the material properties usually detected when testing quasi-brittle material specimens or structures at different size-scales.

International Journal of Heat and Mass Transfer, 2011

The dependence of the contact conductance of self-affine rough surfaces on the applied pressure i... more The dependence of the contact conductance of self-affine rough surfaces on the applied pressure is studied using the electric-mechanical analogy which relates the contact conductance to the normal stiffness. According to dimensional analysis arguments, an efficient dimensionless formulation is proposed which minimizes the number of dimensionless variables governing the phenomenon. Assuming incomplete similarity in the dimensionless pressure, a power-law dependence between contact conductance and mean pressure is proposed. This is confirmed by earlier semi-empirical correlations that are recovered as special cases of the proposed formulation. To compute the exponent b of the power-law, and relate it to the morphological properties of the surfaces, we numerically test self-affine rough surfaces composed of random midpoint displacement (RMD) patches. Such patches are generated using a modified RMD algorithm in order to decouple the effect of the long wavelength cutoff from that due to microscale roughness. Numerical results show that the long wavelength cutoff has an important effect on the contact conductance, whereas the sampling interval and the fractal dimension are less important. The effect of elastic interaction between asperities has also been quantified and it significantly influences the predicted power-law exponent b.

International Journal of Fracture, 2010

In the present paper, a new fracturemechanics based model is proposed for the analysis of reinfor... more In the present paper, a new fracturemechanics based model is proposed for the analysis of reinforced concrete beams in bending describing both cracking and crushing growths taking place during the loading process by means of the concept of strain localization. In particular, the nonlinear behaviour of concrete in compression is modelled by the Overlapping Crack Model, which considers a material interpenetration when the elastic limit is overcome, in close analogy with the Cohesive Crack Model, routinely adopted for modelling the tensile behaviour of concrete. On the basis of different nonlinear contributions due to concrete and steel, a numerical finite element algorithm is proposed. According to this approach, the flexural behaviour of reinforced concrete structural elements is analyzed by varying the main geometrical and mechanical parameters. Particular regard is given to the role of the size-scale effects on the ductility of plastic hinges, which is available at the ultimate load conditions.