Papers by Gianni Royer Carfagni
In structural design the bending strength of heat-treated glass is in general calculated as the s... more In structural design the bending strength of heat-treated glass is in general calculated as the simple sum of the characteristic values of the strength of annealed glass and of the thermally-induced prestress, considered as the 5% quantiles of the corresponding statistical distributions. However, the probability that two stochastic variables attain small values simultaneously is quite low; therefore, it is expected that the 5% quantile of the heat-treated glass strength is higher than the simple sum of the 5% quantiles of the two constituent distributions. Here, we theoretically confirm this result by assuming a two-parameter Weibull distribution for the population of annealed glass strengths and a Gaussian distribution for the thermal stresses. Although recent studies have confirmed that the two-parameter Weibull distribution cannot properly interpret the left-hand-side-tail of the annealed-glass strength population, it is here shown that the statistical competition with the surfac...
The term 'flexural tensegrity' applies to beam-like structures composed by segments in un... more The term 'flexural tensegrity' applies to beam-like structures composed by segments in unilateral contact, whose integrity under flexion is provided by tendons (cables), tensioned and later anchored at the end segments. Besides the cable tension, the constitutive response depends upon the shape of the contact surfaces between consecutive segments, identified by the corresponding pitch lines and constructed with a double couple of conjugate profiles, so to achieve an internal constraint equivalent to a spring hinge. The response is non-local in type, because the cable elongation, and consequently the stiffness of the spring hinges, depends upon the rotations of all the segments, but this effect becomes negligible under moderate deflections. In this case, the structure can be approximated with an <i>elastica</i> in the continuum limit. Testing of prototypes, manufactured with a 3D printer, shows a very good agreement with the theoretical predictions for different designs of the spring hinges. The system, whose stiffness can be functionally graded and actively controlled, can be packaged when the cable is slack and deployed by pulling the cable at one extremity. It appears particularly suitable to build soft arms for robotics or deployable compliant booms for aerospace applications.
Engineering Structures, 2021
There is an increasing need to define the capacity of glazed surfaces under impulsive dynamic act... more There is an increasing need to define the capacity of glazed surfaces under impulsive dynamic actions, such as those transmitted by a soft-body impactor as required by new regulations. The dynamic problem is first analyzed with a simple approach based upon an equivalent linear and non-linear 2-DOF system. The time-history analysis is complemented with energetic considerations that, with reasonable assumptions, can directly provide the maximum stress in the panel through the definition of an equivalent static load. Furthermore, an advanced FEM tool has been developed, which uses non-linear unilateral beam elements available in the library of a commercial software for structural analysis and, therefore, has a wide range of applicability. The comparison of the predictions from the proposed methods with results obtained from experiments and other advanced software, indicates the accuracy of the proposed approaches and their range of applicability.
Computers & Structures, 2017
A Non-Smooth Contact Dynamic (NSCD) formulation is used to analyze complex assemblies of rigid bl... more A Non-Smooth Contact Dynamic (NSCD) formulation is used to analyze complex assemblies of rigid blocks, representative of real masonry structures. A model of associative friction sliding is proposed, expressed through a Differential Variational Inequality (DVI) formulation, relying upon the theory of Measure Differential Inclusion (MDI). A regularization is used in order to select a unique solution and to avoid problems of indeterminacy in redundant contacts. This approach, complemented with an optimized collision detection algorithm for convex contacts, results to be reliable for dynamic analyses of masonry structures under static and dynamic loads. The approach is comprehensive, since we implement a custom NSCD simulator based on the Project Chrono C++ framework, and we design custom tools for pre-and post-processing through a user-friendly parametric design software. Representative examples confirm that the method can handle 3-D complex structures, as typically are architectural masonry constructions, under both static and dynamic loading.
International Journal of Mechanical Sciences, 2013
Laminated glass is a layered sandwich structures composed of elastic glass plies bonded by viscoe... more Laminated glass is a layered sandwich structures composed of elastic glass plies bonded by viscoelastic polymeric interlayers, which produce the mechanical shear-coupling of the plies under flexural loads. Here, we analytically solve the time-dependent problem of a simply-supported three-layered sandwich-beam with linear-viscoelastic interlayer under a loading/unloading history, showing that its gross response is strongly affected by the rheological properties of the polymer, here modeled by Wiechert-Maxwell units. The results, confirmed by numerical simulations, are compared with those obtainable with an approximate solution, commonly used in the design practice, where the interlayer is modeled by an equivalent linear-elastic material, whose properties are calibrated according to temperature and characteristic duration of the applied loads. For this, practical design rules to account for superimposition of applied loads are proposed. The qualitative properties of the two approaches are analytically discussed, evidencing those loadhistories under which the approximate solution is, or is not, conservative for what stress and deflection evaluation is concerned.
AutoCAD file used for the 3D printing of the prototype for the sub-linear case.
Proceedings. Mathematical, Physical, and Engineering Sciences, 2020
The proposed theory defines a relative index of epidemic lethality that compares any two configur... more The proposed theory defines a relative index of epidemic lethality that compares any two configurations in different observation periods, preferably one in the acute and the other in a mild epidemic phase. Raw mortality data represent the input, with no need to recognize the cause of death. Data are categorized according to the victims’ age, which must be renormalized because older people have a greater probability of developing a level of physical decay (human damage), favouring critical pathologies and co-morbidities. The probabilistic dependence of human damage on renormalized age is related to a death criterion considering a virus spread by contagion and our capacity to cure the disease. Remarkably, this is reminiscent of the Weibull theory of the strength of brittle structures containing a population of crack-like defects, in the correlation between the statistical distribution of cracks and the risk of fracture at a prescribed stress level. Age-of-death scaling laws are predic...
The Gecko system is a patented innovative point-fixing device of laminated glass for frameless ... more The Gecko system is a patented innovative point-fixing device of laminated glass for frameless glazing, fully exploiting a new structural ionoplast polymeric interlayer. Here, we record the results of destructive tests performed on laminated panels attached with this system under either wind pressure or dead loads. In the pre-glass-brakeage phase, the panel exhibits a monolithic response confirmed by a full 3D viscoelastic FEM model. The post-glass-brakeage phase has been studied analyzing the cases when either just one or all the glass plies composing the laminated panel are broken. In both cases, glass fragments remain attached to the interlayer after breakage and, consequently, the system can preserve a certain load bearing capacity avoiding sudden collapse (fail-safe response). What is more, even after complete fragmentation of glass, the fixing devices firmly hold the interlayer, which acts as a confining membrane.
International Journal of Engineering Science, 2020
A given symmetric and compatible linear transformation field D determines, through Cesaro represe... more A given symmetric and compatible linear transformation field D determines, through Cesaro representation theorem, a vector field v whose symmetric gradient ∇ s v equals D , up to an additive vector field v h satisfying ∇ s v h = 0. If D represents an infinitesimal strain field, then v h is an infinitesimal rigid-body displacement. If D represents a stretching field, then v h is a rigid-body velocity which characterizes a rate of translation and rotation of the whole (fluid or solid) body. If D is compatible in regions separated by a smooth singular surface across which D suffers a jum p, then in our main Theorem 2.3 we show that the associated vector field v must satisfy the Hadamard rank 1 compatibility condition across the surface, i.e., the jump ∇v is rank 1 of the form d n , where n is a unit normal to the surface, if and only if ∇v is constant across the singular surface. Importantly, no a priori stated restriction on the skewsymmetric part of ∇v is needed. We, then, record two corollaries that characterize the possible jump behavior at a corner line where two smooth singular surfaces meet, discussing how our results apply in two example elementary flow problems in classical fluid dynamics.
Latin American Journal of Solids and Structures, 2018
The peridynamic theory is an extension of the classical continuum mechanics theory. The peridynam... more The peridynamic theory is an extension of the classical continuum mechanics theory. The peridynamic governing equations involve integrals of interaction forces between near particles separated by finite distances. These forces depend upon the relative displacements between material points within a body. On the other hand, the classical governing equations involve the divergence of a tensor field, which depends upon the spatial derivatives of displacements. Thus, the peridynamic governing equations are valid not only in the interior of a body, but also on its boundary, which may include a Griffith crack, and on interfaces between two bodies with different mechanical properties. Near the boundary, the solution of a peridynamic problem may be very different from the classical solution. In this work, we investigate the behavior of the displacement field of a unidimensional linearly elastic bar of length L near its ends in the context of the peridynamic theory. The bar is in equilibrium without body force, is fixed at one end, and is subjected to an imposed displacement at the other end. The bar has micromodulus C, which is related to the Young's modulus E in the classical theory and is given by different expressions found in the literature. We find that, depending on the expression of C, the displacement field may be singular near the ends, which is in contrast to the linear behavior of the displacement field observed in the classical linear elasticity. In spite of the above, we show that the peridynamic displacement field converges to its classical counterpart as a length scale, called peridynamic horizon, tends to zero.
Journal of the European Ceramic Society, 2017
The macroscopic strength of float glass is governed by the presence of micro-cracks, whose size, ... more The macroscopic strength of float glass is governed by the presence of micro-cracks, whose size, orientation and distribution affects the corresponding statistics. A micro-mechanically motivated model is here proposed, which spells out the connection between crack population and strength statistics, leading to generalized distributions of the Weibull type. Aging in the form of corrosion or abrasion can produce a variation of the defectiveness scenario originally present on the pristine glass surface, and we discuss how such a modification can statistically affect the macroscopic strength. A practical application is made to justify the change in strength experimentally observed passing from the "air" to the "tin" side of float glass. Assuming that the contact with the tin bath and the rollers produce a damage equivalent to the abrasion of the glass surface, we theoretically derive a bimodal Weibull statistics that agrees with the experimental evidence.
International Journal of Solids and Structures, 2016
Abstract The contact stresses in a bonded joint due to differential thermal expansions are calcul... more Abstract The contact stresses in a bonded joint due to differential thermal expansions are calculated by considering the adhesive as an elastic rectangle confined by plates representing the adherends. The interface is cohesive in type, so that the contact area is a perfectly adherent region surrounded by cohesive areas where slip occurs at constant shear-stress. The problem is formulated in terms of Papkovich–Fadle eigenfunctions, which satisfy the boundary conditions on the stress free edges. The resulting integral equations are solved with the Jacobi integration formula. The size of the cohesive zone, which is determined by imposing the finiteness of the contact stresses at the frontier with the bonded region, depends upon the length and height of the joint. In very long joints the result tends to the technical rule of thumb traditionally employed to design such joints, but for intermediate lengths the elastic solution is quite different.
Engineering Structures, 2016
Abstract The macroscopic properties of float glass are governed by the opening of surface cracks ... more Abstract The macroscopic properties of float glass are governed by the opening of surface cracks in mode I. To bypass the influence of crack orientation and defectiveness of the borders (due to the cutting process), in the experimental measurement of the material strength the panacea would be to induce an equibiaxial state of stress in the core of the specimen. The Coaxial Double Ring (CDR) test achieves this ideal condition when geometric non-linearities are of minor importance. To compensate for second-order spurious components, ASTM C1499-09 indicates a CDR configuration with variable geometry according to the specimen thickness, whereas EN 1288-2 proposes the application of an additional overpressure. An analytic theoretical study of the non-linear effects in a CDR test is here presented. Assuming a Weibull statistical distribution of defects, for the CDR configuration with no overpressure, we obtain expressions in closed form for the effective area, a parameter that allows the re-scaling of the experimental data to a reference condition (equibiaxial stress on a unitary area) according to a criterion of equal failure probability. This method is used to propose a new standardized CDR testing method, with fixed geometry and no overpressure. Since the procedure of EN 1288-2 is proved to be ineffective because the induced stress state is not uniform and equibiaxial, a supplementary experimental campaign is reputed necessary, considering that the reference strength of glass in product standards has been determined with this testing method.
Structural and Multidisciplinary Optimization, 2016
Analogical physical models are a preferred technique to intuitively grasp complex engineering pro... more Analogical physical models are a preferred technique to intuitively grasp complex engineering problems. It is well-known that the equilibrium minimal-surface configuration of membranes under equibiaxial tension can be visually represented by the surface of a soap film under equivalent boundary conditions, but this analogy fails when the stress state is not uniform equibiaxial. We extend to this situation the analogy with soap films. The equilibrium state of an orthotropically tensioned membrane is found by geometrically stretching the shape of a soap film, in a precise manner depending upon the applied state of stress. The procedure is easily done by elaborating digital pictures. The method is mathematically justified under the kinematic hypotheses of small strains and large rotations, and further verified in a parametric design environment. It can also provide an insight into the equilibrium configuration of cable-nets, when the stresses in the warp and weft directions are considerably different. Furthermore, this visualization favors implementing transformable shapes for membranes or orthogonal cable nets, as a consequence of a modification of the ratio of the principal stress components.
A practical way to calculate the response of laminated glass is to consider both glass and polyme... more A practical way to calculate the response of laminated glass is to consider both glass and polymeric interlayer as linear elastic materials; the viscoelastic behavior of the polymer is evaluated assuming equivalent elastic moduli, that is, the relaxed moduli under constant strain after a time equal to the duration of the design action. Here, we analytically solve the time-dependent problem of simply-supported laminated-glass beams, modeling the response of the polymer by a Prony’s series of Maxwell elements. The obtained results, in agreement with a full 3-D viscoelastic finite-element numerical analysis, emphasize that there is a noteworthy difference between the state of strain and stress calculated in the full-viscoelastic case or in the aforementioned “equivalent” elastic problem. The second approach gives in general results that are on the side of safeness, but the design may be too conservative for short-time actions, whose duration depends upon the polymer type.
Journal of Applied Mechanics, 2016
We extend the classical J-integral approach to calculate the energy release rate of cracks by pro... more We extend the classical J-integral approach to calculate the energy release rate of cracks by prolonging the contour path of integration across a traction-transmitting interphase that accounts for various phenomena occurring within the gap region defined by the nominal crack surfaces. Illustrative examples show how the closed contours, together with a proper definition of the energy momentum tensor, account for the energy dissipation associated with material separation. For cracks surfaces subjected to cohesive forces, the procedure directly establishes an energetic balance à la Griffith. For cracks modeled as phase-fields, for which no neat material separation occurs, integration of a generalized energy momentum (GEM) tensor along the closed contour path that traverses the damaged material permits the calculation of the energy release rate and the residual elasticity of the completely damaged material.
Mathematics and Mechanics of Solids, 2016
Using a classical non-linear theory, we analytically investigate possible ways for transforming t... more Using a classical non-linear theory, we analytically investigate possible ways for transforming the shape of a curved elastic membrane while keeping it tensioned and moderately strained. This is a critical issue because, as a rule, membranes must be considerably stretched in order to avoid wrinkling and slackening. If the final configuration is fixed, the membrane can be cut and formed according to the final shape, but this cannot be done if more configurations, considerably distant from one another, have to be achieved. Nevertheless, we propose large transformation movements that can be obtained starting from flat membranes while maintaining their strain as limited. We discuss in detail the paradigmatic example of the hyperbolic-paraboloid-shaped membrane. These opportunities are suitable for applications of transformable architecture because they do not require excessive tensioning, compatible with the strength of materials used for this kind of structures.
International Journal of Mechanical Sciences, 2015
An analytical study is presented for the bent-lamination of curved layered beams, a process consi... more An analytical study is presented for the bent-lamination of curved layered beams, a process consisting in gluing the constituent plies together after they have been elastically bent against a constraining negative mould. Possible applications range from glued laminated timber manufacturing, to cold-lamination-bending of structural glass. After removal of the constraint, the shear coupling through the glue maintains the curvature only partially, because the laminate suffers an initial spring-back followed by a long-term relaxation. The model problem considered here is that of two Euler-Bernoulli beams coupled by a thin viscoelastic adhesive layer. Within a variational approach, we analytically describe the relationship between the mould shape and the shape of the curved beam, which is timedependent due to the viscosity of the adhesive layer. Localized contacts with the mould and stress concentrations may occur, depending upon the type of profile that is initially imposed. Comparison of the cases of instantaneous or gradual release of the contact with the mould, evidences a remarkable reduction of the transient state of stress in the second case.
Journal of Elasticity
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Papers by Gianni Royer Carfagni