Francesco Genna

On the elastic behavior of syntactic foams

Abstract This work concerns composite materials called “syntactic foams”, i.e., materials made by a polymeric matrix filled with hollow solid inclusions. Explicit formulae for the homogenized values of the elastic moduli of these materials are derived, by means of the physical model and the corresponding elastic solution used by Herve and Pellegrini [Herve, E., Pellegrini, O., 1995. Archives Mechanics. 47 (2), 223–246.]. The morphologically representative patterns theory of Bornert et al. [Bornert, M., Stolz, C., Zaoui, A., 1996. Journal of the Mechanics and Physics of Solids 44, 307–331.] is used to take into account both the influence of the filler gradation and the presence of “unwanted” voids in the matrix, factors that are shown to be important in characterizing the mechanical behavior of syntactic foams. Comparisons with both experimental and numerical results show that the techniques used are capable of predicting, with good accuracy, the elastic moduli of real syntactic foams, i.e., those arising from an actual production process.

Elastic design of syntactic foamed sandwiches obtained by filling of three-dimensional sandwich-fabric panels

A non-conventional sandwich, made by a fabric panel core filled by a syntactic foam, and by resin-impregnated fiberglass skins, is studied in the elastic range, with the aim of giving guidelines to its minimum weight design. Standard homogenization techniques are employed to compute the elastic moduli of the skins, whereas a specifically developed homogenization method has been used to obtain the elastic moduli of the core. A simple but accurate relationship for computing the shear stiffness of the sandwich was used in conjunction with the well-known formulae for the bending stiffness. Comparisons with both experiments and numerical predictions show good accuracy of both the proposed homogenization methods and the overall stiffness evaluation procedure.

An Interface Model for the Periodontal Ligament

A nonlinear interface constitutive law is formulated for modeling the mechanical behavior of the periodontal ligament. This gives an accurate interpolation of the few available experimental results and provides a reasonably simple model for mechanical applications. The model is analyzed from the viewpoints of both mathematical consistency and effectiveness in numerical calculations. In order to demonstrate the latter, suitable two- and three-dimensional nonlinear interface finite elements have been implemented.

Numerical analysis of old masonry buildings : a comparison among constitutive models

Abstract This paper makes reference to several constitutive models developed for the analysis of structures made of components weak in tension. These models are applied to the study of a real structural problem which exhibits characteristics of complexity different from those usually found in laboratory specimens, in that it specifically involves the influence of the construction details on the overall structural resistance. The study of the model structure—a part of an old Monastery whose monitoring and restoration was entrusted to the Department of Civil Engineering in Brescia—has been performed by coupling in situ investigations with numerical analyses.

On the Effects of Cyclic Transversal Forces on Osseointegrated Dental Implants: Experimental and Finite Element Shakedown Analyses

This paper is concerned with the mechanical strength of fixed osseointegrated dental implants subjected to cyclic external loads, applied mainly in a direction orthogonal to their axis. Such a loading condition, seen as a basic design action for the implant, has been given little attention so far. Experimental results and numerical simulations, performed on two- and three-dimensional Finite Element models, are discussed. The shakedown theory is used to show that a common implant design (threaded fixture-abutment-connection screw) is susceptible of low-cycle fatigue failure under loading conditions well within the working range, even if the same design is able to withstand loading of the same type, but applied monotonically, much in excess of the working values. The shakedown analyses give an indication of several possible failure modalities: the low-cycle fatigue either of the implant or of the connection screw, or the loosening of the connection screw itself. Experimental and numerical results are in good qualitative agreement, and both suggest that the issue of transversal cyclic loading on fixed dental implants should be carefully reconsidered in the design phase.

Mechanical response of bone under short-term loading of a dental implant with an internal layer simulating the nonlinear behaviour of the periodontal ligament.

We consider a non-standard design for a fixed dental implant, incorporating a soft layer which simulates the presence of the periodontal ligament (PDL). Instead of being aimed at causing an a priori defined stress/strain field within the surrounding bone, upon loading, such a design simply tries to better reproduce the natural tooth–PDL configuration. To do this, the mechanical properties of the internal layer match those of the PDL, determined experimentally to be strongly nonlinear. Three-dimensional finite element analyses show that the presence of such a layer produces (i) a prosthesis mobility very similar to that of a healthy tooth, for several loading conditions, and (ii) a stress/strain distribution substantially different from that arising, upon loading, around a conventional implant. The lack of knowledge of the real mechanical fields existing, under loading, in the bone around a healthy tooth makes it very difficult to state that the stress distribution produced by the modified implant is “better” than that produced by the standard one. Nevertheless, the comparison of the results obtained here, with those of previous refined analyses of the tooth–PDL–bone system, indicates that the modified implant tends to produce a stress distribution in the bone, upon loading, closer to “natural” than that given by the standard one, within the limits imposed by the presence of threads coupling the implant with the bone.

Some variational formulations for continuum nonlinear dynamics

Abstract A modification of a theory developed by Tonti (1984) for obtaining extremal formulations of a generic nonlinear problem is applied to derive several variational formulations for the nonlinear continuum dynamic problem with prescribed initial conditions. Such a problem does not admit “classical” variational statements, owing to its lack of symmetry with respect to “classical” bilinear forms. However, Tontis theory, with some developments introduced first by Carini, and then in this work, allows the systematic derivation of variational statements which may prove helpful both in understanding theoretical aspects and in devising numerical integration schemes.

Anomalous elastic-plastic responses to short pulse loading of circular plates

Abstract It is shown that a circular plate with fully fixed boundary may exhibit anomalous nonlinear elastic, perfectly plastic response behaviours of the same type that have been shown to occur in a beam whose ends are fixed against both axial and transverse displacements. “Anomalous” here means that the final deflection may be either in the direction of the applied external force during the pulse, or in the opposite (“negative”) direction. When the plate is modelled with two or more degrees of freedom the response may be chaotic and the final deflection unpredictable because of extreme sensitivity to parameters. In this paper results are shown of calculations by the general purpose finite element code ABAQUS and by Galerkin models of one, two, three, and eight degrees of freedom. For simplicity the assumption of sandwich plate behaviour is adopted, but comparisons are also shown for plates of uniform section.

Newmark's time integration method from the discretization of extended functionals

In this note we illustrate how to obtain the full family of Newmark s time integration algorithms within a rigorous variational framework, i.e., by discretizing suitably defined extended functionals, rather than by starting from a weak form (for instance, of the Galerkin type), as done in the past. The availability of functionals as a starting point is useful both as a tool to obtain new families of time integration methods, and as a theoretical basis for error estimates. To illustrate the first issue, here we provide some examples of how to obtain modified algorithms, in some cases significantly more accurate than the basic Newmark one despite having a comparable computational cost.

Time integration errors and some new functionals for the dynamics of a free mass

Abstract We study the numerical integration of the Poisson second-order ordinary differential equation which describes, for instance, the dynamics of a free mass. Classical integration algorithms, when applied to such an equation, furnish solutions affected by a significant “drift” error, apparently not studied so far. In the first part of this work we define measures of such a drift. We then proceed to illustrate how to construct both classical and extended functionals for the equation of motion of a free mass with given initial conditions. These tools allow both the derivation of new variationally-based time integration algorithms for this problem, and, in some cases, the theoretical isolation of the source of the drift. While we prove that this particular error is unavoidable in any algorithmic solution of this problem, we also provide some new time integration algorithms, extensions at little added cost of classical methods, which permit to substantially improve numerical predictions.