Spatial Estimates for the Constrained Anisotropic Elastic Cylinder

This paper establishes spatial estimates in a prismatic (semi-infinite) cylinder occupied by an anisotropic homogeneous linear elastic material, whose elasticity tensor is strongly elliptic. The cylinder is maintained in equilibrium under zero body force, zero displacement on the lateral boundary and pointwise specified displacement over the base. The other plane end is subject to zero displacement (when the cylinder is finite, say). The limiting case of a semi-infinite cylinder is also considered and zero displacement on the remote end (at large distance) is not assumed in this case. A first approach is developed by considering two mean-square cross-sectional measures of the displacement vector whose spatial evolution with respect to the axial variable is studied by means of a technique based on a second-order differential inequality. Conditions on the elastic constants are derived that show the cross-sectional measures exhibit alternative behaviour and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay. A second approach considers cross-sectional integrals involving the displacement and its gradient and furnishes information upon the spatial evolution, without restricting the range of strongly elliptic elastic constants. Such models are principally based upon a first-order differential inequality as well as on one of second order. The general results are explicitly presented for transversely isotropic materials and graphically illustrated for a cortical bone.     

Some finite extremum principles in piecewise linear elasto-plasticity

Summary The paper discusses the boundary value problem for isotropic continua with elastic-linear hardening stress-strain laws of conventional deformation theory. A pair of dual extremum theorems are proven: the first, which takes as variables stresses and plastic strains, reduces the problem to the minimization of a quadratic functional subject to convex quadratic inequalities and linear equalities; the latter, which takes as variables displacements and plastic strains, reduces the problem to the minimization of a non-quadratic functional subject to linear equalities. In absence of hardening the first principle reduces to the well-known Haar-Kármán theorem for elastic perfectly plastic bodies. Some extensions of the above principles to piecewise linear hardening bodies and the connections of the deformation theory with the flow theory of linear kinematic hardening are reported at the end of the paper.

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Sommario Si discute il problema dell'analisi elastoplastica dei mezzi isotropi dotati d'incrudimento lineare adottando le ipotesi della teoria della deformazione.Vengono dimostrati due principi di estremo duali che consentono di ricondurre la soluzione dei problemi al contorno alla minimizzazione di opportuni funzionali.Il primo di tali principii, in assenza d'incrudimento, si riduce al ben noto teorema di Haar-Karman che viene quindi generalizzato ai mezzi incrudenti.Viene discussa anche l'estensione di quanto sopra accennato al caso d'incrudimento lineare a tratti e la Nota è chiusa da alcune considerazioni in merito alla connessione fra la teoria della deformazione e la teoria incrementale dell'incrudimento cinematico.

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The results presented in this paper were obtained in the course of research sponsored by the National (Italian) Research Council (C.N.R.).     

From 3-D Nonlinear Elasticity Theory to 1-D Bars with Nonconvex Energy

This paper represents a first attempt to derive one-dimensional models with non-convex strain energy starting from “genuine” three-dimensional, nonlinear, compressible, elasticity theory. Following the usual method of obtaining beam theories, we show here for a constrained kinematics appropriate for long cylinders governed by a polyconvex, objective, stored energy function, that the bar model originally proposed by Ericksen [3] is obtainable but enriched by an additional term in the strain gradient. This term, characteristic of nonsimple grade-2 materials, penalizes interfacial energies and makes single-interface two-phase solutions preferred. The resulting model has been proposed by a number of authors to describe the phenomenon of necking and cold drawing in polymeric fibers and, here, we discuss its suitability to interpret also the elastic-plastic behavior of metallic tensile bars under monotone loading.     

Development and Validation of Hierarchical Models for the Design of Engine Control Strategies

The development of mathematical models for the design of controlstrategies for spark ignition automotive engines is described. The objectiveof the models, used for both simulation and optimization analysis, is theprediction of the effects of control strategies on fuel consumption andemissions of a vehicle over arbitrary driving cycles. In order to achievethe best compromise between precision, experimental costs, computationaltime and flexibility, a mixed modelling approach is used, withphenomenological and input-output models integrated within a hierarchicalsystem.Mean value models have been used to describe the most significant dynamiceffects: (i) air flow. (ii) two phases fuel flow in the intake manifold, and(iii) thermal flow in the cylinder walls. Stochastic effects due to sensorsand actuators can be also predicted.Two-zone and multizone thermodynamic models for the prediction ofpressure cycle sub-models for engine emissions (HC, CO, andNO _x and mechanical losses have been developed. Experimentaldesign techniques are also under development to optimize the interactionsbetween experimental analysis and models. Most of the models have beenintegrated in a computer code, used by a major automotive supplier.     

The Kinematics of Plate Models: A Geometrical Deduction

We present a deduction of the Kirchhoff–Love and Reissner–Mindlin kinematics of a simply-connected plate by using the formal asymptotic development method applied to the compatibility conditions of Saint-Venant and the formula of Cesàro–Volterra. This formal deduction is purely geometrical because we do not use any information coming from the loading or the constitutive behavior.      

Thermal stresses in plane elasticity: Numerical solutions based only on harmonic functions

Summary A theoretical treatment is outlined allowing solution of thermal stress problems in plane elasticity by using only numerical methods suited to solving — in 2 D — the Laplace equation. Only one type of element matrix (supposing for the sake of simplicity F.E.M.s are used) and only one mesh would thus be required, both for the determination of the thermal field and of the displacement/stress field. The numerical solutions required in the plane domain of interest entail, consequently, only one variable per node in place of two. Even if numerous unit solutions are required in order to impose arbitrary boundary conditions, this reduction of nodal variables allows to spend less computation time in solving linear systems, at least for problems of a certain extent.

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Sommario Si delinea una tecnica che permette di risolvere i problemi di coazioni termiche in elasticità piana facendo uso solo di metodi numerici atti a risolvere l'equazione di Laplace. Un solo tipo di matrice degli elementi (nel caso si usi una formulazione a E. F.) e una sola reticolazione sono pertanto richiesti tanto per il problema termico come per quello elastico. Ne consegue altresì il vantaggio che le soluzioni numeriche richieste nel dominio di interesse cornportano una sola variabile per nodo, anzichè due; anche tenuto conto che sono richieste numerose soluzioni unitarie per poter imporre condizioni al contorno comunque definite, ne deriva per problemi di una certa ampiezza una riduzione del tempo di calcolo speso nella soluzione di sistemi.

     

Hexametaphosphate‐Capped Silica Mesoporous Nanoparticles Containing CuII Complexes for the Selective and Sensitive Optical Detection of Hydrogen Sulfide in Water

Cu^II‐macrocycle functionalized hexametaphosphate‐capped silica mesoporous nanoparticles have been prepared and used for the selective and sensitive detection of hydrogen sulfide in aqueous environments. The possibility of using different metal complexes combined with different capping anions and choice of different dyes or other sensing molecules as indicators makes this new protocol highly appealing for the preparation of new sensing systems for sulfide detection in different environments.