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We present a novel low mass drift chamber concept, developed in order to fulfill the stringent requirements imposed by the experiments for extremely rare processes, which require high resolutions (order of 100–200 keV/c) for particle momenta in a range (50–100 MeV/c) totally dominated by the multiple scattering contribution. We describe a geometry optimization procedure and a new wiring strategy with a feed-through-less wire anchoring system developed and tested on a drift chamber prototype under completion at INFN-Lecce .

Following up to a previous investigation, this paper proposes a strategy to deal with frictionless contact problems involving large penetrations, in the context of the node-to-segment formulation and of the pen- alty method. The rationale is based on two main considerations: the first one is that, within an iteration scheme, the use of consistent linearization is only convenient when the field of the unknowns is suffi- ciently close to the solution point; the second one is that, if the order of magnitude of the maximum con- tact pressure can be estimated a priori, this information can be exploited to approach the solution in a faster and more reliable way. Beside being very effective in case of large initial penetrations, where con- vergence using the standard algorithms would either not be achieved at all, or achieved with a large num- ber of iterations, the strategy can also be used to increase the convergence rate in contact problems with penetrations of usual magnitude. The proposed strategy is based on a check of the nodal contact pressure, to select the technique that has to be used to perform each iteration. If the contact pressure is smaller than a predefined limit, the prob- lem is solved in the standard way, using consistent linearization and Newton’s method. When the contact pressure exceeds the limit, a modified method is used. This one is based on the enforcement of a contact pressure limit and on the use of a simplified secant stiffness, where the geometric stiffness term is dis- regarded. The strategy has to be integrated with a specific ‘‘safeguard algorithm’’ to guarantee conver- gence to the correct solution also in cases where the maximum contact pressure has been underestimated. Two alternative procedures for this purpose are proposed. The solution strategy can be used with any contact formulation. Here, the efficiency and stability of the strategy is illustrated within the framework of the well-known node-to-segment formulation with a 2D implementation. Several example problems are presented.

Following up to a previous investigation, this paper proposes a strategy to deal with frictionless contact problems involving large penetrations, in the context of the node-to-segment formulation and of the penalty method. The rationale is based on two main considerations: the first one is that, within an iteration scheme, the use of consistent linearization is only convenient when the field of the unknowns is sufficiently close to the solution point; the second one is that, if the order of magnitude of the maximum contact pressure can be estimated a priori, this information can be exploited to approach the solution in a faster and more reliable way. The proposed strategy is based on a check of the nodal contact pressure, to select the technique that has to be used to perform each iteration. If the contact pressure is smaller than a predefined limit, the problem is solved in the standard way, using consistent linearization and Newton’s method. When the contact pressure exceeds the limit, a modified method is used. This one is based on the enforcement of a contact pressure limit and on the use of a simplified secant stiffness, where the geometric stiffness term is disregarded. The strategy has to be integrated with a specific “safeguard algorithm” to guarantee convergence to the correct solution also in cases where the maximum contact pressure has been underestimated. Two alternative procedures for this purpose are proposed.

It is well known that the classical one-pass node-to-segment algorithms for the enforcement of contact constraints fail the contact patch test. The situation is particularly critical when using the penalty method. In a recent study, the authors proposed a modified one-pass node-to-segment algorithm able to pass the contact patch test also in conjunction with the penalty method. However, in a general situation the pressure distribution transferred across a contact surface is non-uniform. Hence, even for a contact element which passes the contact patch test under a uniform distribution of the contact pressures, the transfer of a non-uniform state of stress across the contact surface may give rise to disturbances related to the discretization. Such disturbances introduce local solution errors and ultimately affect the accuracy of the analysis. This paper, following on from the previous study, develops an enhanced node-to-segment formulation able to pass a modified version of the contact patch test whereby a linear distribution of pressures has to be transmitted across the contact surface.

From the content: Contact Modelling in Entangled Fibrous Materials.- 3D Contact Smoothing Method Based on Quasi-C1 Interpolation.- On a Geometrically Exact Theory for Contact Interactions.- Finite Deformation Contact Based on a 3D Dual Mortar and Semi-Smooth Newton Approach.- The Contact Patch Test for Linear Contact Pressure Distributions in 2D Frictionless Contact.

The well-known Greenwood and Williamson contact theory for microscopically homogeneous rough surfaces is generalized by considering functionally graded elastic rough surfaces. In particular, two distinct cases giving rise to a non-constant Young’s modulus with depth are considered: (I) an initially plane layered (or graded) solid which is non-uniformly eroded, so that the final product is a rough surface with asperities having an elastic modulus depending on the height; (II) an initially homogeneous rough surface which receives a surface treatment or a chemical degradation which modify the elastic properties of the asperities as a function of the depth from the exposed surface. These Functionally Graded Surfaces (FGS) can be observed both in biological systems and in mechanical components. The effects of graded elasticity on the relationship between real contact area versus applied load, and on the plasticity index are quantified and illustrated with numerical examples. It will be shown that the contact response may differ up to one order of magnitude with respect to that of a homogeneous surface. Comparison between Case I and Case II also shows that, for special surface properties, the two types of grading can provide the same mechanical response.

A contact element which deals with mechanical and thermal fields is presented. The geometrically linear formulation leads to an algorithm which is on the one hand very simple to code, but on the other hand very efficient and yields deep insight into the real physical behaviour of contact conductance. The presented formulation permits the addition of the contact algorithm to any finite element code.

This paper is focused on the analytical modeling of the interface between a rigid substrate with constant curvature and a thin bonded plate. In a previous investigation, an analytical cohesive zone (CZ) model capable of predicting the interfacial behavior prior to the onset of debonding has been proposed by the authors. As a follow-up, this paper presents a new analytical model, which is able to predict both the load at onset of debonding and the subsequent evolution of the debonding process. The study clarifies the essential differences in behavior between joints with flat and curved substrates during debonding. The new analytical model is based on linear-elastic fracture mechanics (LEFM) and is developed under two distinct assumptions: a mode-independent fracture energy, and a fracture energy dependent on the mode mixity, according to a simple mixed-mode fracture criterion. The model is applied to the determination of the load at onset of debonding, and to the prediction of the load–displacement behavior during the entire debonding process. The relationship between the predictions of the CZ and LEFM models regarding the load at initiation of debonding is also established.

The solution of contact problems involves great numerical efforts to satisfy non-penetration conditions. The search for numerical efficiency hence has limited the modelling of the real physical interface behaviour. Up to now mainly simple laws, usually formulated using constant coefficients, have been available to study contact problems in uncoupled from. Here a thermomechanically coupled contact element is presented which accounts for the real microscopic shape of the surfaces, the microscopic mechanism of force transmission and heat exchange. The contact element geometrical behaviour has been put together with experimental and theoretical well founded micro-mechanical and micro-thermal laws adapted to Finite Element Method (FEM) necessities. Based on these laws the macroscopic related stiffnesses are calculated and continuously updated taking into account changes in significant parameters. The linearization of the set of equations has been obtained using a consistent technique which implies computational efficiency.

This paper focuses on the analytical and numerical modeling of the interface between a rigid substrate with simple constant curvature and a thin bonded plate. The interfacial behavior is modeled by independent cohesive laws in the normal and tangential directions, coupled with a mixed-mode fracture criterion. The newly developed analytical model determines the interfacial shear and normal stress distributions as functions of the substrate curvature, during the various behavioral stages of the interface prior to the initiation of debonding. The model is also able to predict the debonding load and the effective bond length. In the numerical model the interface is modeled by zero-thickness node-to-segment contact elements, in which both the geometrical relationships between the nodes of the discretized problem and the interface constitutive laws are suitably defined. Numerical results and comparisons between the predictions of the two models are presented.

The so-called node-to-segment (NTS) algorithm is probably the most widely used discretization tech- nique for large deformation contact between surfaces with non-matching meshes. Despite the classical NTS contact element has been available in the literature for a long time, its detailed description appears to be currently disseminated in several papers. Moreover, the classical NTS formulation presents some limitations which are well known but have been the subject of limited investigations. In particular, the algorithm presents severe problems in dealing with some special cases, in which the identification of the master segment related to a slave-node is either ambiguous or impossible. The objectives of this paper are to provide a careful review of the classical formulation, and to propose new techniques for the treatment of the aforementioned special cases. The paper is composed of three parts. In the first one the classical formulation of the NTS algorithm in two dimensions and in the frictionless case is reviewed in detail. The main geometric relationships are presented, and the contact contributions to the stiffness matrix and to the residual vector are derived. The second part is devoted to the treatment of the special cases. Some algorithms specially developed to deal with such cases are illustrated. Finally, the third part presents some numerical examples which show the effectiveness of the proposed algorithms.

An algorithm to calculate shape function values at specific points is presented. It applies to three‐dimensional serendipity elements with variable node numbers per side and, as a particular case, to plane and truss elements. The procedure is shown for the two‐dimensional case using the natural orthogonal reference system of the element and is then generalized to the three‐dimensional case. The source code of the described algorithms written in Fortran 77 is included.

We describe an outbreak of trichinellosis in Verona, Italy, in early 2008 that was imported from Romania.

The assumption of perfectly flat surfaces within the context of the contact problems constitutes very often an oversimplification of the reality. In fact, when real surfaces are examined more in details, roughness can be found at different scale lengths. This fundamental feature poses enormous difficulties on the mathematical modeling of the physics of the contact problems. Nevertheless, the study of the effect of the multiscale roughness on the contact predictions is crucial from the engineering point of view. To deal with this problem several micromechanical contact models have been developed since the middle of the 19th Century. Such models are based on very different mathematical frameworks, with a consequent lack of standardization. The recent perspective to apply such models to smaller and smaller scale lengths, down to the nanoscale, makes the reliability of these models a still open issue. The basic aim of this chapter is to provide a detailed review of the most popular contact models available in the literature. Moreover we focus one the crucial intent of providing a degree of confidence about the differences between the contact predictions provided by the models. For this purpose a critical comparison of the outcomes of such models by applying them to numerically generated rough surfaces is then proposed.

In this paper a finite element formulation for frictionless contact problems with non-matching meshes in the contact interface is presented. It is based on a non-standard variational formulation due to Nitsche and leads to a matrix formulation in the primary variables. The method modifies the unconstrained functional by adding extra terms and a stabilization which is related to the classical penalty method. These new terms are characterized by the presence of con- tact forces that are computed from the stresses in the contin- uum elements. They can be seen as a sort of Lagrangian-type contributions. Due to the computation of the contact forces from the continuum elements, some additional degrees-of- freedom are involved in the stiffness matrix parts related to contact. These degrees-of-freedom are associated with nodes not belonging to the contact surfaces.

Temperatures and stress transients due to hydration process in concrete casting for dam constructions and to thermal exchanges between concrete and its surrounding environment are analysed. The problem under investigation is highly nonlinear due to different reasons. Placing technique of concrete is carried out by means of large block castings which are superimposed at different times. Concrete surfaces may be cooled using water at ambient temperature or at a lesser temperature; thermal exchanges between concrete and external ambient are affected by the increasing extension of casting surface, by solar radiation and wind action. Thermal stresses due to the temperature transients are produced and cracks may appear in massive concrete. The numerical analysis of corresponding complex phenomena is carried out according to the following lines. Temperature field is calculated at each time step taking into account the above mentioned nonlinearities, then for each time step equilibrium is imposed for finding displacements and stresses using maturity dependent constitutive relationships. Time integration of the nonlinear equation of heat transport is carried out using a two-level scheme with variable step sizes. Thermal and mechanical fields are then found for the whole time transient.

The problem of interface decohesion in laminated beams is addressed with reference to the double cantilever beam (DCB) geometry. The paper deals with the analysis of the influence of non-uniform bonding properties or interfacial defects on the crack propagation process and its stability. In spite of the relative simplicity of the considered case study, which is under pure Mode I deformation, a contact problem takes place due to the decohesion. The occurrence of contact makes the problem highly non-linear, since the extension of the contact area is a priori unknown. The finite element method with a generalized interface constitutive law is used to enforce the contact constraint along the interface and to model the progress of the delamination process.

In this study we deal with the problem of normal contact between rough surfaces. A power spectral density of the asperity heights which obeys a power-law within a given range of wavelengths has been considered. Hence, the resolution dependence of the statistical parameters computed according to the random process theory, of the plasticity index and of the contact predictions provided by stochastic and fractal contact models is discussed and emphasized. It is demonstrated that the plasticity index diverges to infinity when the lower cut-off length of the system vanishes, whereas the slope of the real contact area versus normal load curve tends to zero. In this limit case stochastic and fractal approaches predict either a vanishing real contact area or an infinite normal pressure, regardless of the asperity deformation assumptions. On the other hand, when a non-zero lower cut-off length exists, finite contact predictions can be obtained by applying the contact models at that scale length. This possibility is numerically investigated and, comparing contact results of several models, it is shown that the plasticity index plays an important role for the characterization of the interface mechanical response.

The currently available formulations for contact between beams are based on the identification of the minimal distance points along the beam axes, followed by some tuning in case of non-circular beam cross-sections. Up to now a suitable implementation within the framework of the Finite Element Method is available both for the frictionless and for the frictional case. The procedure requires the explicit computation of the virtual work contribution due to the contacts. In such a context for solving the problem with implicit schemes, the formulation has also to be consistently linearized. With this respect both the frictionless and the frictional formulation present severe problems. To overcome all the cited problems a generalized formulation is proposed, which deals with contact between circular beams. It has to be remarked that the contact problem is treated first in a completely generic framework, and only in a second step the results are particularized to the FE formulation. For such purpose the centroids of the beams in the 3-D space are considered as parametric functions. The framework for the consistent linearization is developed in a very rigorous and systematic way, providing evidence of the symmetry of the operators. The procedure is quite cumbersome, hence here only the most heavy part, related to the computation of all the fundamental geometrical terms involved, is presented.

A unified interface constitutive law for the description of contact and decohesion at bi-material interfaces is proposed. To this aim, a synthesis of the nonlinear models pertaining to Fracture and Contact Mechanics is presented. The issues pertinent to the implementation within the FE discretization framework are also discussed in detail. Finally, a numerical example of fatigue modeling at the mesoscopical level in a fiber-reinforced composite is provided.

Previous results indicate that fibers in ribbons are sometimes affected by systematic birefringence superimposed on the random one, their relative weights depending on fiber position in the ribbon. We report new theoretical and experimental results on stress distribution in ribbons, which is shown to depend on thermal and mechanical properties of the common coating. Numerical simulations are based on the theory of elasticity and the finite-element method (FEM). Polarization dispersion measurements vs. temperature match very well with numerical results, and indicate that central fibers in the ribbon exhibit significantly larger birefringence than lateral ones.

The progress in advanced technology fields requires more and more sophisticated formulations to consider contact problems properly. This paper is devoted to the development of a new constitutive model for electrostatic-mechanical contacts, based on a micro–macro approach to describe the contact behaviour. The electric-mechanical contact constitutive law is obtained considering the real microscopic shape of the contacting surfaces, the microscopic behaviour of force transmission and current flow. Some thermo-mechanical macroscopic models based on microscopic characterizations have already been developed to compute the normal and tangential contact stiffness and the thermal contact resistance. On the basis of such macroscopic models, a similar model, suitable for the electric-mechanical field, is developed. With reference to the thermal constriction resistance the electric contact resistance is studied, assuming a flux tube around each contacting asperity, and choosing a suitable geometry for its narrowing at the contact zone. The contact element geometry is based on well known theoretical and experimental micro-mechanical laws, suitably adapted for the FEM formulation. The macroscopic stiffness matrix is calculated on the basis of the microscopic laws and it is continuously updated as a function of the changes in the mechanical and electric significant parameters. A consistent linearization of the set of equations is developed to improve the computational speed, within the framework of implicit methods. Copyright © 2005 John Wiley & Sons, Ltd.

This paper describes modern techniques used to solve contact problems within Computational Mechanics. On the basis of a continuum description of contact, the mathematical structure of the contact formulation for finite element methods is derived. Emphasis is also placed on the constitutive behavior at the contact interface for normal and tangential (frictional) contact. Furthermore, different discretization schemes currently applied to solve engineering problems are formulated for small and finite strain problems. These include isoparametric interpolations, node-to-segment discretizations and also mortar and Nitsche techniques. Furthermore, several algorithms related to spatial contact search and fulfillment of the inequality constraints at the contact interface are discussed. Here, especially the penalty and Lagrange multiplier schemes are considered and also SQP- and linear-programming methods are reviewed. Keywords: contact mechanics; friction; penalty method; Lagrange multiplier method; contact algorithms; finite element method; finite deformations; discretization methods

In this paper a comparison among several micromechanical contact models is presented. The aim of the research is to provide a degree of confidence about the differences between the predictions of the contact behavior provided by the models. For this purpose some ideal microscopically rough surfaces with self-affine topography have been generated by means of a numerical algorithm. From such surfaces all the parameters needed to characterize them from the statistical viewpoint have been extracted. The predictions provided by the models with increasing normal load for the evolution of the real contact area, the number of contact points and other useful parameters have been outlined with diagrams, clearly showing the existing differences.

The interaction of the cutting tools with different geological settings determines a different wear and consequently different economical costs for the excavation. We apply here a strategy for soil modelling which is based on dis- cretization of the continuum with rigid disks and suitable contact models. We concentrate at contact level the real mechanical behaviour of the soil. In order to carry out this strategy a ”micro” and a ”macro” level are established. This paper focuses on the micromechanical model.

In this paper a model to deal with electric-mechanical contact problems in the framework of the FEM is presented. On the basis of some micro-mechanical studies, a new approach is developed to define the non-linear constitutive law that governs the normal force-displacement behaviour and the electric resistance of the contacting surfaces.

Cables where several fibers (typically, 4-16) are collected in a ribbon allow cost reduction and mass splicing. Their wide use in the access network and, in perspective, in long-haul links, has drawn attention on all factors affecting their performance. Polarization mode dispersion (PMD) in fibers embedded in ribbons has already been investigated, but with contradictory results. All previous results appear to indicate that birefringence in fibers belonging to ribbons can be significantly affected by stress distribution in the ribbon itself, which depends on thermal and mechanical properties of the coating. We report new theoretical and experimental results, which reconfirm this conjecture. Birefringence is shown to depend strongly on the fiber position in the ribbon. Theoretical results are based on a finite-element-method numerical simulation, based on the theory of elasticity, and apply over the temperature range (15-31/spl deg/C) where viscosity in all materials can be ignored. Central fibers are found to be under compression in the ribbon plane, while lateral fibers do not experience significant compression, as the ribbon coating is softer than silica. Birefringence can be estimated in a simple way from the stress distribution. To validate the predictions experimentally, PMD measurements were performed on a 4-fiber ribbon.

The paper presents a procedure for the numerical computation of the global interstrand resistances measured between strands of superconducting multistrand cables. The procedure is based on a geometrical reconstruction of the cable strands geometries, which are used to generate an electrical equivalent DC lumped network. In this network, the strands are represented by ideal short circuits and the geometrical points of contact between the strands correspond to lumped conduc- tances. The network is completed with a suitable arrangement of connections between strands and DC power supplies. The network equations are then solved numerically and the strand currents are evaluated together with the interstrand voltages. The accuracy of the procedure is discussed through a comparison with experimental results.

Wear-mechanism maps for different materials, actually steel on steel, are being modeled with FEM. A microthermo-mechanical approach has been used in order to model accurately the macroscopic phenomena of wear. A plastic law for the normal micromechanical contact of asperities has been implemented in FEAP and a slight modification, based on experimental results, is proposed. For the three mechanisms modeled, good correlation between the numerical results of wear and those found in literature has been obtained for a pin-on-disk configuration. The flash temperatures reached in the contact interface have been also studied and fair good agreement with literature is achieved.

In this paper a formulation to deal with the Finite Element modelling of coupled electric-mechanical contact resistance is presented. The electrical contact resistance is based on a micro-macro approach, i.e. the contacting surfaces are not considered as perfectly smooth, but are characterised at the microscopic level by the presence of valleys and peaks. Such roughness reduces the real contact area to a very small percentage of the apparent one. The microscopic geometry thus plays a very important role in perturbing any type of field (mechanical, thermal, electrical etc.) in the contact zone. Some macroscopic models, based on microscopic characterizations, have been proposed to describe the normal and tangential contact stiffness and the thermal contact resistance. Within such models, the surface microrugosity of the asperities in contact is taken into account by replacing each surface by a statistically equivalent one. The load-flattening mechanical behaviour of the contacting asperities is modelled by choosing a perfectly plastic constitutive law as well as an elastic one. In this way the mean plane approach is obtained as a function of the applied load variation.

Numerical treatment of contact problems is more and more growing in complexity, due to the efforts spent to represent real contact mechanisms. Numerical formulations considering adaptation to the Finite Element framework of contact constitutive laws based on microscopical characterisation of contact zones have been proposed recently. Microscopical contact laws actually available consider the mechanisms of force and heat transmission between contacting asperities. The global behaviour of the contact is determined using statistical relationships and mechanical hypotheses.

The detailed discretization of contact zones with contact stiffness based on real physical characteristics of contact surfaces can produce stiffness terms which induce ill-conditioning of the global stiffness matrix. Moreover the consistent treatment of frictional behaviour generates non-symmetric tangent stiffness matrices due to the non-associativity of the slip phase. Other non-symmetries are due to the coupling terms and to the dependencies on various parameters that can be involved. To overcome these difficulties almost consistent techniques based on two-step algorithms have been proposed in the past. Here an augmentation technique is proposed which takes into account micro-mechanical effects, and permits the symmetrization of the tangent stiffness during frictional slip phase.

An fast and effective error check for the FE stresses, based on the unit load theorem is proposed. The relative stress error is estimated by the relative error between displacements obtained by the unit load theorem and by the FE method. Analytical examples and numerical applications are presented.

The use of micromechanically based constitutive equations for contact interfaces leads to technically relevant parameters to ill-conditioned finite-element equations. In the paper an augmented Lagrangian technique is employed to overcome this difficulty and to provide a good converging algorithm.

Tesi di Dottorato in Meccanica delle Strutture

This paper focuses on modeling of the interface between a rigid substrate and a thin elastic adherend subjected to mixed-mode loading in the peel test configuration. The context in which the investigation is situated is the study of bond between fiber-reinforced polymer (FRP) sheets and quasi-brittle substrates, where FRP sheets are used as a strengthening system for existing structures. The problem is approached both analytically and numerically. The analytical model is based on the linear-elastic fracture mechanics energy approach. In the numerical model, the interface is discretized with zero-thickness contact elements which account for both debonding and contact within a unified framework, using the node-to-segment contact strategy. Uncoupled cohesive interface constitutive laws are adopted in the normal and tangential directions. The formulation is implemented and tested using the finite element code FEAP. The models are able to predict the response of the bonded joint as a function of the main parameters, which are identified through dimensional analysis. The main objective is to compute the debonding load and the effective bond length of the adherend, i.e., the value of bond length beyond which a further increase has no effect on the debonding load, as functions of the peel angle. The detailed distributions of interfacial shear and normal stresses are also found. Numerical results and analytical predictions are shown to be in excellent agreement.