Showing papers in "Meccanica in 1995"
TL;DR: In this paper, a structured continuum model is formulated to describe the behavior of block masonry modelled as distinct rigid body systems with elastic interfaces, and a correspondence between the two motions is obtained by postulating a relationship between the displacement fields of the continuum and the discrete models.
Abstract: A structured continuum model is formulated to describe the behaviour of block masonry modelled as distinct rigid body systems with elastic interfaces. A correspondence between the two motions is obtained by postulating a relationship between the displacement fields of the continuum and the discrete models. The constitutive functions for the dynamic actions of the continuum are derived by equating the power of the two models.
70 citations
TL;DR: In this article, the need to improve H-means and semi-classical measures is stressed and relations between young measures and H-measures are described and used to analyze an example from micromagnetics.
Abstract: Young measures and their limitations are discussed. Some relations between Young measures and H-measures are described and used to analyze an example from micromagnetics. The need to improve H-measures and semi-classical measures is stressed.
61 citations
TL;DR: In this paper, the classical results of Stoner and Wohlfarth for the prediction of hysteresis loops in small ferromagnetic particles are extended to specimens of non-ellipsoidal shape, and shown to be a consequence of micromagnetics.
Abstract: The classical results of Stoner and Wohlfarth for the prediction of hysteresis loops in small ferromagnetic particles are extended to specimens of non-ellipsoidal shape, and shown to be a consequence of micromagnetics. The insensitivity to surface roughness is proposed as a possible explanation of the high coercivity behavior of small particles.
58 citations
TL;DR: In this paper, the propagation of nonlinear waves in a region with uniform state is studied by means of an asymptotic approach that has already appeared useful in an investigation on wave propagation in bubbly liquids and in fluid mixtures.
Abstract: The equations of motion for dilatant granular material are obtained from a Hamiltonian variational principle of local type in the conservative case. The propagation of nonlinear waves in a region with uniform state is studied by means of an asymptotic approach that has already appeared useful in an investigation on wave propagation in bubbly liquids and in fluid mixtures. When the grains are assumed to be incompressible, it is shown that the material behaves as a continuum with latent microstructure.
36 citations
TL;DR: In this paper, the authors show that the coherence of certain phase transformations in solids is most vividly expressed using the material manifold and within the kinematic continuum description based on the so-calledinverse motion.
Abstract: First we recognize that the coherence of certain phase transformations in solids is most vividly expressed using the material manifold and within the kinematic continuum description based on the so-calledinverse motion. In this fully dynamical framework the equation of interest is theun-balance of pseudomomentum for thermoelastic conductors. On computing the power developed by the accompanying surface source of quasi-inhomogeneities at the phase-transition front, we show that this relates directly to the normal jump of the Eshelby stress — devoid of any kinetic energy, but computed from the free energy — a scalar quantity which may be referred to as theHugoniot-Gibbs configurational force at the front. The thermodynamic analysis also establishes that this power is dissipated as the material progresses at the front that ishomothermal. The jump relation including this dissipation is that associated with the heat propagation equation valid at regular points. In all, this approach is based on the theory of material uniformity and inhomogeneities as developed in recent years by M. Epstein and the authors. All reasonings are made in full dynamics, for finite strains, and any anisotropy in three dimensions.
35 citations
TL;DR: In this paper, the boundary layer in a power-law fluid flowing in the presence of a transverse variable magnetic field is investigated, assuming the electric conductivity of the fluid is dependent on its velocity, Meksyn's method is used to get an analytical solution for the velocity field and the coefficient of friction.
Abstract: The boundary layer in a power-law fluid flowing in the presence of a transverse variable magnetic field is investigated. Assuming the electric conductivity of the fluid is dependent on its velocity, Meksyn's method is used to get an analytical solution for the velocity field and the coefficient of friction. The effect of the magnetic field is then discussed.
34 citations
TL;DR: In this article, the role of interfacial energy in creating finitescale microstructures, by considering the combined effect of the oscillationinducing and oscillation-inhibiting terms in the energy functional.
Abstract: This paper addresses the non-uniqueness pointed out by Ericksen in his classical analysis of the equilibrium of a one-dimensional elastic bar with non-convex energy [1]. Following some previous work in this area, we suitably regularize the problem in order to investigate this degenerancy. Our approach gives an explicit framework for the the study of the rich variety offinite-scale equilibrium microstructures for the bar in a hard loading device, and their stability properties. In this way we clarify the role of interfacial energy in creating finitescale microstructures, by considering the combined effect of the oscillation-inducing and oscillation-inhibiting terms in the energy functional.
33 citations
TL;DR: In this paper, a procedure for plane higher-curvature path analysis and synthesis is described, which facilitates the numerical computation of Generalized Burmester Points for a moving link of a planar mechanism in a nonsymmetric position.
Abstract: This note describes a procedure for plane higher-curvature path analysis and synthesis. All coefficients have been written in terms of elementary instantaneous invariants. This facilitates the numerical computation of Generalized Burmester Points for a moving link of a planar mechanism in a non-symmetric position. FORTRAN subroutines have been written and a numerical example is provided.
29 citations
TL;DR: In this paper, two types of regularization to the basic quasistatic double-well potential problem in one space dimension are described, one model features a spatially nonlocal term while the other incorporates the use of an order parameter.
Abstract: The paper describes two types of regularization to the basic quasistatic double-well potential problem in one space dimension. One model features a spatially nonlocal term while the other incorporates the use of an order parameter. Some basic existence and regularity results for these modified models are derived and some numerical calculations that show hysteresis and motion of phase boundaries are presented.
28 citations
TL;DR: In this paper, the influence of additional surface energy terms on the existence of stress-free microstructures both in the nonlinear and a geometrically linear setting is discussed.
Abstract: Certain alloys such as In-Tl, Ni-Ti, Ag-Cd or Cu-Al-Ni display remarkable mechanical properties such as the shape memory effect or pseudo-elasticity. This behaviour is related to a solid-solid phase transformation which leads to a complicated microscopic arrangement of different phases. In recent studies such microstructures have been analyzed by the minimization of elastic energy. We discuss the influence of additional surface energy terms on the existence of stress-free microstructures both in the nonlinear and a geometrically linear setting.
26 citations
TL;DR: In this paper, the stress-strain isothermal hysteresis loops due to the incomplete martensitic transformation were analyzed for Ti-Ni shape memory alloys, and the existence of two distinct yield lines for phase transition was shown.
Abstract: The stress-strain isothermal hysteresis loops due to the incomplete martensitic transformation are analysed for Ti-Ni shape memory alloys. Experiments show the existence of two distinct yield lines for phase transition; one for the forward transformation austenite→martensite (A→M), the other for the reverse transformation M→A. The tensile behaviour of single crystals with only one yield line (A↔M) [1] can be considered as an ‘ideal’ case. An extension of a thermodynamic model for pseudoelasticity [2] allows these two yield lines to be taken into account.
TL;DR: In this paper, evolution equations for liquid crystals and for magnetostrictive solids are discussed within the framework of a theory of continua with microstructure that allows for mechanical self-interactions and non-standard inertial terms.
Abstract: Evolution equations for liquid crystals and for magnetostrictive solids are discussed within the framework of a theory of continua with microstructure that allows for mechanical self-interactions and non-standard inertial terms.
TL;DR: In this paper, a neural network model is proposed and studied for the treatment of elastoplastic analysis problems, which are formulated as Q.P.s with inequality subsidiary conditions.
Abstract: A neural network model is proposed and studied for the treatment of elastoplastic analysis problems. These problems are formulated as Q.P.P.s with inequality subsidiary conditions. In order to treat these conditions the Hopfield model is appropriately generalized and a neural model is proposed covering the case of inequalities. Finally, the parameter identification problem is formulated as a supervised learning problem. Numerical applications close the presentation of the theory and the advantages of the neural network approach are illustrated.
TL;DR: In this article, the authors set forth the groundwork for the continuum model and proved the property announced in the title, while intent on proving the property in a more specific and concrete mode.
Abstract: Smectic liquid crystals are quasi solids, which possess microstructure both of the material and local type (the nematic mictrostructure and the lamellae, respectively). They also exhibit phase transitions: from smectic B to smectic A, to nematic, to isotrtopic liquid (see [1], Ch. 7). Their study, though special, might show up general advantages and drawbacks of different types of mathematical models. Here, while intent on proving the property announced in the title, we set forth the groundwork for the continuum model (see, in a more specific and concrete mode [2]).
TL;DR: In this article, the authors investigated the geometrical-mechanical properties of the shakedown load boundary for small displacements and combined time-variable/steady loads.
Abstract: In the hypothesis of small displacements and combined time-variable/steady loads, the geometrical-mechanical properties of the shakedown load boundary are investigated. It is shown that, in the load space, the shakedown load boundary plays the role of yield surface, and that a certain plastic strain accumulation vector—characterizing some impending inadaptation collapse mechanism—obeys the normality rule, whereas a specific form of the maximum plastic work theorem constitutes an effective tool for the evaluation of the shakedown limit load corresponding to a specified inadaptation collapse mode. The equations governing the state of the structure at the shakedown limit are provided and the related collapse mechanism is shown to specify the shape of the steady-state response of the structure to a periodic load enveloping the load domain with an intensity slightly above the shakedown limit.
TL;DR: In this article, an asymptotic analytic solving method for a differential equation with complex function, small nonlinearity and a slow variable parameter is developed, which is an extension of the well known Bogolubov-Mitropolski method.
Abstract: In this paper an asymptotic analytic solving method for a differential equation with complex function, small nonlinearity and a slow variable parameter is developed. The procedure is an extension of the well known Bogolubov-Mitropolski method. The correctness of the procedure is proved by an example. The vibrations of a rotor on which a thin band is wound and on which a small linear damping acts are obtained. The analytical solutions are compared with numerical ones. They are in good agreement.
TL;DR: In this article, an iteration procedure is proposed which uses the output of the RFP technique as a starting estimate, and minimizes the true fitting error, expressed as a first order Taylor expansion of the identified parameters.
Abstract: The rational fraction polynomial (RFP) modal identification procedure is a well known frequency domain fitting technique. To deal with a linear problem, the RFP procedure does not directly minimize the fitting error, i.e. the difference between the experimental and the analytical frequency response function, but a frequency weighted function of it: this causes bias in the modal parameter estimates. In this paper an iteration procedure is proposed which uses the output of the RFP technique as a starting estimate, and minimizes the true fitting error, expressed as a first order Taylor expansion of the identified parameters. Results are quite satisfactory: the fitting error is notably reduced after few iterations. Moreover, less computational modes with respect to the original RFP method are needed to obtain a good fit in a given frequency band.
TL;DR: A numerical approach for structural analysis of masonry walls in plane stress conditions is presented and an accuracy analysis on the integration algorithm employed in the solution of constitutive relations has been carried out.
Abstract: A numerical approach for structural analysis of masonry walls in plane stress conditions is presented. The assumption of a perfectly no-tension material (NTM) constitutive model, whose relevant equations are in the form of classical rate-independent associated flow laws of elastoplastic material, allows one to adopt numerical procedures commonly used in computational plasticity. An accuracy analysis on the integration algorithm employed in the solution of constitutive relations has been carried out. The results obtained for some relevant case-studies and their comparison with data, available in the literature show the effectiveness of the proposed method.
TL;DR: The problem of finding an optimum shape for rotating discs is a classical one and has received considerable attention; in the present paper an attempt to use genetic algorithms is described in this paper.
Abstract: The problem of finding an optimum shape for rotating discs is a classical one and has received considerable attention; in the present paper an attempt to use genetic algorithms is described.
TL;DR: In this article, the authors studied the inversion problem and the quasi-static problem of the constitutive equation in the theory of linear viscoelasticity and showed that both problems admit one solution if the relaxation function satisfies Graffi's inequality.
Abstract: Within the theory of linear viscoelasticity, we seek solutions to the inversion problem of the constitutive equation respectively inL
2 and in the spaceS′ of the tempered distributions. Successively we study the quasi-static problem inS′. Both problems admit one and only one solution if the relaxation function satisfies Graffi's inequality. Finally we show that the inversion problem and the quasi-static one are deeply connected and that every counterexample about the existence or uniqueness of the solutions for the first problem also provides a counterexample for the latter.
TL;DR: In this article, pseudoelasticity in tensile experiments has been treated thermodynamically under the assumption that the relevant constitutive ingredients are a nonconvex free energy;
Abstract: In some previous papers [1], [2] pseudoelasticity in tensile experiments has been treated thermodynamically under the assumption that the relevant constitutive ingredients are
(i)
a non-convex free energy;
(ii)
coherency between the austenitic and martensitic phase.
TL;DR: In this paper, the torsion of a hollow cylinder with an elongated cross-section was studied theoretically by an efficient eigenfunction expansion and modified point-match method, and the effects of geometric parameters on torsional rigidity and maximum shear stress were determined.
Abstract: The torsion of a hollow cylinder with elongated cross-section is studied theoretically by an efficient eigenfunction expansion and modified point-match method. The effects of the geometric parameters on torsional rigidity and maximum shear stress are determined.
TL;DR: The step-wise martensite to austenite reversible transformation (SMART) as mentioned in this paper is a martensitic thermoelastic transformation where a stepwise kinetics is induced by a partial cycling procedure within the hysteresis cycle (incomplete cycle on heating (ICH) procedure).
Abstract: The step-wise martensite to austenite reversible transformation (SMART) in shape memory alloys (SMA) is a martensitic thermoelastic transformation where a step-wise kinetics is induced by a partial cycling procedure within the hysteresis cycle (incomplete cycle on heating (ICH) procedure). The ICH procedure has been proved effective in inducing a reversible microstructural modification of the martensitic phase. Results till now obtained both on the SMART behaviour and on the effects of the ICH procedure are reviewed here: the hypotheses advanced till now are discussed to explain experimental evidences.
TL;DR: In this article, a turbulent boundary layer manipulated by outer-layer devices has been studied in the 0.70 by 0.50 m2 low speed wind tunnel of the ‘Modesto Panetti’ Aeronautical Laboratory of the Politecnico di Torino.
Abstract: A turbulent boundary layer manipulated by outer-layer devices has been studied. Experiments have been conducted in the 0.70 by 0.50 m2 low speed wind tunnel of the ‘Modesto Panetti’ Aeronautical Laboratory of the Politecnico di Torino. Mean values and turbulent quantities measured in the natural and manipulated boundary layers are shown for comparison. The mechanisms to explain the observed skin friction and turbulence reduction are discussed. The manipulator wake effect, consisting in decoupling the wall-region from the boundary layer outer-region, is stressed in the present results.
TL;DR: In this article, the rotation number of the magnetic spherical pendulum on a torus corresponds to a regular value of the energy momentum mapping, which is based on the idea of Montgomery.
Abstract: This article gives two formulae for the rotation number of the flow of the magnetic spherical pendulum on a torus corresponding to a regular value of the energy momentum mapping. One of these formulae is nonclassical and is based on an idea of Montgomery.
TL;DR: In this article, the Laplace and Korteweg theories of isothermal material interfaces were revisited for the stability of microscopic droplets, based on the classical instability results for a large droplet of liquid (vapor) imbedded in a vapor (liquid).
Abstract: This paper reconsiders the Laplace and Korteweg theories of isothermal material interfaces. After rederiving the classical instability results for a large droplet of liquid (vapor) imbedded in a vapor (liquid) we consider the stability of microscopic droplets. On this scale the revised Laplace and Korteweg theories predict critical stability of the droplet.
TL;DR: In this article, an atomistic model for the potential energy of Ni-Al alloys based on the Embedded Atom Method was discussed, and the potential was applied in a Molecular Dynamics and Quasi Harmonic investigation of the Martensitic Transformation (MT) that occurs in Ni x Al1−x for compositions 0.61
Abstract: We discuss an atomistic model for the potential energy of Ni-Al alloys based on the Embedded Atom Method. The potential is applied in a Molecular Dynamics and Quasi Harmonic investigation of the Martensitic Transformation (MT) that occurs in Ni x Al1−x for compositions 0.61
TL;DR: In this paper, a new potential-vorticity decomposition is proposed to derive an exact representation of the effects of the vorticity on the external flow, and the relationship between approximate transpiration-velocity representation and the exact one presented here is analyzed.
Abstract: The Lighthill transpiration-velocity correction is commonly used in the analysis of viscous flows of aeronautical interest, in order to take into account the perturbation to the potential flow caused by the presence of the vorticity in the boundary layer. This correction consists of considering the boundary as a permeable surface from which the fluid flows through the boundary surface, with a velocity (named the transpiration velocity) determined on the basis of the local boundary-layer characteristics. Here, we use a new potential-vorticity decomposition in order to derive an exact representation of the effects of the vorticity on the external flow. The relationship between approximate transpiration-velocity representation and the exact one presented here is analyzed: it is shown that, under typical boundary-layer assumptions, the new representation reduces to that by Lighthill, except for a corrective field term. Finally, in order to quantify, in a simple case, the contribution of the corrective terms which arise in the new formulation, we examine, as a numerical test case, the problem of an attached boundary-layer flow over a flat plate: the numerical results indicate that the corrective term is negligible for Reynolds numbers above 104.
TL;DR: In this paper, a boundary-independent integral in finite elasticity from which Bui's result follows as a particular case is established, which is based on the complementary stress energy density.
Abstract: A path-independent integral has been stated by Bui in the presence of a straight crack in a two-dimensional deformation field. Such an integral isdual to the Rice integral in the sense that it is based on the complementary stress energy density. Here we establish a boundary-independent integral in finite elasticity from which Bui's result follows as a particular case.
TL;DR: In this paper, the authors propose a notion of internal work for a generalized hyperelastic material, taking into account the topological structure of its singular locus via the Maslov class.
Abstract: We propose a notion of internal work for a generalized hyperelastic material, taking into account the topological structure of its singular locus via the Maslov class. This is based on the interpretation of the crossing of the singular locus as a phase transition.