Abstract: The shock structure problem for Grad 10-moment equations for an inert binary mixture is investigated: necessary conditions for the formation of sub-shocks in fields of only one gas or of both components are rigorously obtained, and a detailed comparison with the shock-wave structure of its principal sub-system (deduced assuming vanishing viscous stress tensors) and of the equilibrium Euler sub-system is performed. Some numerical simulations for a mixture of argon and helium are presented. PubDate: 2015-09-23

Abstract: We propose a model of complex poroelastic media with periodic or locally periodic structures observed at microscopic and mesoscopic scales. Using a two-level homogenization procedure, we derive a model coherent with the Biot continuum, describing effective properties of such a hierarchically structured poroelastic medium. The effective material coefficients can be computed using characteristic responses of the micro- and mesostructures which are solutions of local problems imposed in representative volume elements describing the poroelastic medium at the two levels of heterogeneity. In the paper, we discus various combinations of the interface between the micro- and mesoscopic porosities, influence of the fluid compressibility, or solid incompressibility. Gradient of porosity is accounted for when dealing with locally periodic structures. Derived formulae for computing the poroelastic material coefficients characterize not only the steady-state responses with static fluid, but are relevant also for quasistatic problems. The model is applicable in geology, or in tissue biomechanics, in particular for modeling canalicular-lacunar porosity of bone which can be characterized at several levels. PubDate: 2015-09-04

Abstract: Targeted energy transfer between a main oscillator with a set of parallel Saint-Venant elements and
a nonlinear energy sink with a general nonlinear and odd potential function around 1:1 resonance is studied. The complexified system has been investigated at fast and slow time scales by detecting its invariant manifold, equilibrium and singular points, which can explain bifurcation(s) and different regimes of the system. Then, we introduce an example which treats vibratory energy exchanges between a main oscillator with two parallel Saint-Venant elements and a coupled cubic nonlinear energy sink. Finally, analytical predictions are compared with results obtained by numerical integrations of system equations. PubDate: 2015-09-01

Abstract: A model for lipid membranes with lipid distension is presented. This incorporates the conventional Helfrich-type formulation as a special case. The effects of lipid distension on the shape equation, and the required adjustments to operative edge conditions, are discussed in detail. The model is illustrated through numerical simulations. PubDate: 2015-09-01

Abstract: We study the exterior stress field in a three-phase circular inclusion which is bonded to the surrounding matrix through an intermediate interphase layer. All three phases belong to a particular class of compressible hyperelastic materials of harmonic type. We focus on the design of a harmonic elastic inclusion which by definition, does not disturb the sum of the normal stresses in the surrounding matrix. We show that in order to make the coated inclusion harmonic, certain inequalities concerning the material and geometric parameters of the three-phase composite must first be satisfied. The corresponding remote loading parameters can then be uniquely determined while keeping the associated phase angles arbitrary. Our results allow for both uniform and non-uniform remote loading. We show that the stress field inside the inclusion is uniform when the remote loading is uniform. PubDate: 2015-09-01

Abstract: One century after the seminal work by Leonor Michaelis and Maud Menten devoted to the theoretical study of the enzymatic reactions, in this paper, we give an overview of the most recent trends concerning the mathematical modeling of several enzymatic mechanisms, focusing on its asymptotic analysis, which needs the use of advanced mathematical tools, such as center manifold theory, normal forms, and bifurcation theory. Moreover, we present some perspectives, linking the models here presented with similar models, arising from different research fields. PubDate: 2015-09-01

Abstract: We investigate the dynamic stability of a pipe that conveys fluid, clamped or pinned at one end and with an intermediate support, thus exhibiting an overhang. The model of the pipe incorporates both Euler–Bernoulli and Bresse–Timoshenko schemes as well as transverse inertia. Material and external damping mechanisms are taken into account, while the conveyed fluid is supposed to be in fully turbulent flow. The pipe can rest on a linear elastic Winkler soil. The influence of all the physical quantities and of the overhang length on the critical velocity of the fluid front is investigated. Some numerical results are presented and discussed. PubDate: 2015-09-01

Abstract: In case of the secondary bone fracture healing, four characteristic steps are often distinguished. The
first stage, hematoma and clot formation, which is an object of our study, is important because it prepares
the environment for the following stages. In this work, a new mathematical model describing basic effects
present short after the injury is proposed. The main idea is based on the assumption that blood leaking from
the ruptured blood vessels propagates into a poroelastic saturated tissue close to the fracture and mixes with
the interstitial liquid present in pores. After certain time period from the first contact with surrounding tissue,
the solidification of blood in the fluid mixture starts. This results in clot formation. By assuming the time
necessary to initiate solidification and critical saturation of blood in the mixture, the shape and the structure of
blood clot could be determined. In numerical example, proposed mathematical formulas were used to study
the size of the gap between fractured parts and its effect in blood clot formation. PubDate: 2015-09-01

Abstract: A 1-dimensional second gradient damage continuum theory is presented within the framework of the variational approach. The action is intended to depend not only with respect to the first gradient of the displacement field and to a scalar damage field, but also to the field of the second gradient of the displacement. Constitutive prescriptions of the stiffness (the constitutive function in front of the squared first gradient term in the action functional) and of the microstructural material length (i.e., the square of the constitutive function in front of the squared second gradient term in the action functional) are prescribed in terms of the scalar damage parameter. On the one hand, as in many other works, the stiffness is prescribed to decrease as far as the damage increases. On the other hand, the microstructural material length is prescribed, in contrast to a certain part of the literature, to increase as far as the damage increases. This last assumption is due to the interpretation that a damage state induces a microstructure in the continuum and that such a microstructure is more important as far as the damage increases. At a given value of the damage parameter, the behavior is referred to second gradient linear elastic material. However, the damage evolution makes the model not only nonlinear but also inelastic. The second principle of thermodynamics can be considered by assuming that the scalar damage parameter does not decrease its value in the process of deformation, and this implies a dissipation for the elastic strain energy. It is finally remarked that damage initiation, in this second gradient continuum damage model, can be induced not only from a prescribed initial lack of stiffness, but also from an external concentrated double force or from suitable boundary conditions, and these last options have advantages that are discussed in the paper. For example, in this last case, it is possible to initiate the damage in the neighborhood of the boundaries, that is, the case in most of the empirical situations. Simple numerical simulations are also presented in order to show the exposed concepts. PubDate: 2015-09-01

Abstract: A locally phase-shifted Sine–Gordon model well accounts for the phenomenology of unconventional Josephson junctions. The phase dynamics shows resonant modes similar to Fiske modes that appear both in the presence and in the absence of the external magnetic field in standard junctions. In the latter case, they are also in competition with zero field propagation of Sine–Gordon solitons, i.e., fluxons, which give rise to the so-called zero field steps in the current–voltage (I–V) of the junction. We numerically study the I–V characteristics and the resonances magnetic field patterns for some different faceting configurations, in various dissipative regimes, as a function of temperature. The simulated dynamics of the phase is analyzed for lower-order resonances. We give evidence of a nontrivial dynamics due to the interaction of propagating fluxons with localized semifluxons. Numerical results are compared with experimental outcomes obtained on high-quality high-Tc grain boundary YBCO junctions. PubDate: 2015-09-01

Abstract: Thermomechanics and granular micromechanics approaches are combined to derive constitutive equations for modeling rate-dependent granular materials with damage and plasticity. The derivation is motivated by the recognition that the effect of micro-scale mechanisms upon the macro-scale behavior is known to be significant for granular materials. A general thermomechanical framework applicable to rate-dependent granular materials with damage and plasticity is developed. Based upon this framework, an expression for macro-scale Cauchy stress tensor is obtained in terms of the micro-scale grain interaction forces and the relationship between micro- and macro-scale kinematics. In addition, a Clausius–Duhem type inequality applicable to inter-granular interaction is derived, which is used to establish micro-scale constitutive relations for particular type of inter-granular interactions. The expression for Cauchy stress tensor and the micro-scale constitutive relations is then combined under a mean field kinematic assumption to obtain evolution-type macro-scale constitutive equations. The advantage of the granular micromechanics approach is that the damage and plasticity are defined using simple 1d functions at micro-scale, and complicated plastic potentials, damage functions and rules for their evolution are not required. The resultant model is applied to investigate primary, secondary and tertiary creep, creep-recovery as well as rate-dependent response under uniaxial compressive loading. Model applicability is also demonstrated for asymmetric tensile-compressive response under creep-recovery loading. The model is used to evaluate the evolution of elastic energy, and viscous, plastic and damage dissipation at the macro- and micro-scale with respect to creep time and loading level. The results show the development of loading-induced anisotropy due to damage and plasticity in these materials. PubDate: 2015-09-01

Abstract: We discuss free oscillations of some elastic structures consisting of an elastic substrate and an ordered array of aligned nano-sized objects. Considering various shapes of nano-objects such as beams, tubes, and spheres, we investigate the spectrum of eigenfrequencies of these structures in comparison with the spectra of one nano-object and of the substrate. As a result, we find the correspondence between the spectrum of whole structure and the spectrum of one nano-object, which gives the possibility to determine few first eigenfrequencies of nano-sized objects. PubDate: 2015-09-01

Abstract: The frequency response curves of a non-uniform beam undergoing nonlinear oscillations are determined analytically by the multiple time scale method, which provides approximate, but accurate results. The axial inertia in neglected, and so the equations of motion are statically condensed on the transversal displacement only. The nonlinearity due to the stretching of the axis of the beam is considered. The effects of variable cross-section, of variable material properties and of the distributed axial loading are taken into account in the formulation. They have been illustrated by means of two examples and are also compared with existing results. The main result of this work is that the effects of any type of non-uniformity can be detected by simple formulas. PubDate: 2015-09-01

Abstract: In this paper, the relaxed micromorphic model proposed in Ghiba et al. (Math Mech Solids, 2013), Neff et al. (Contin Mech Thermodyn, 2013) has been used to study wave propagation in unbounded continua with microstructure. By studying dispersion relations for the considered relaxed medium, we are able to disclose precise frequency ranges (band-gaps) for which propagation of waves cannot occur. These dispersion relations are strongly nonlinear so giving rise to a macroscopic dispersive behavior of the considered medium. We prove that the presence of band-gaps is related to a unique elastic coefficient, the so-called Cosserat couple modulus μ
c
, which is also responsible for the loss of symmetry of the Cauchy force stress tensor. This parameter can be seen as the trigger of a bifurcation phenomenon since the fact of slightly changing its value around a given threshold drastically changes the observed response of the material with respect to wave propagation. We finally show that band-gaps cannot be accounted for by classical micromorphic models as well as by Cosserat and second gradient ones. The potential fields of application of the proposed relaxed model are manifold, above all for what concerns the conception of new engineering materials to be used for vibration control and stealth technology. PubDate: 2015-09-01

Abstract: Bifurcation analysis of a structure constituted by two towers, linked by a viscous device at the tip and subjected to turbulent wind, is carried out. The towers have geometrical and mechanical parameters so that the steady part of the wind, whose contribution is evaluated in the framework of the steady theory, induces a 1:1 resonant double-Hopf bifurcation. The turbulent part of the wind, assumed as composed by two frequencies that are equal and double to the main frequency of the unlinked towers, respectively, induces parametric and external harmonic forces. These forces interact with the self-excitation due to the steady part of the wind, bringing imperfection in the bifurcation scenario. Transitions from resonant to non-resonant cases are analyzed in terms of behavior charts, and post-critical dynamics is studied in the space of bifurcation parameters. PubDate: 2015-09-01

Abstract: In this work, the effects of inherent variability of the geometric properties of dimer granular chains on their capacity to passively attenuate propagating pulses are investigated. Numerical studies are performed for both the nominal model and the system with uncertainty. The deterministic system is governed by a single parameter (the ratio of the radii of “heavy” and “light” beads of the dimer) and is fully rescalable with energy. The effects of uncertainty, i.e., of the spatial variability of the radii of the light (odd) beads of the granular chain, on the transmitted force at its boundary are investigated. Reliability analysis through Monte Carlo simulations and sensitivity analysis of the dimer with uncertain properties are carried out, and a deeper insight for improved bead configurations is provided. It is shown that the optimal level of force attenuation achieved with a deterministically predicted optimal parameter can be further increased when certain spatial variations in the parameter, based on specific wave number content, are introduced. PubDate: 2015-09-01

Abstract: This paper presents a new approach for the cross-sectional analysis within the framework of the Generalised Beam Theory (GBT), and it is applicable to open, closed or partially closed cross-sections. This approach falls within a category of cross-sectional analysis available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses. The novelty of the proposed approach relies on the use of an unrestrained planar frame for the evaluation of the conventional and extension modes, therefore allowing the identification of both sets of modes from the solution of a planar eigenvalue problem, whose eigenmodes correspond to the sought conventional and extension modes. In the available dynamic GBT approach, the conventional modes are obtained from a planar dynamic analysis enforcing inextensibility to the members of the frame, and the extension modes are then evaluated from the conventional modes enforcing particular constraint conditions. Numerical examples are presented considering open unbranched, open branched and partially closed cross-sections to highlight the ease of use of the proposed approach and to discuss the contribution of the different modes to the structural response. The accuracy of the numerical results is validated against those calculated with a shell element model developed in Abaqus. PubDate: 2015-09-01

Abstract: In the paper, it is considered an exact spatial Kirchhoff rod structural model. The configuration space for this model that has dimension 4 is obtained considering an ad hoc split of the rotation operator that implicitly enforces the constraints on the directors. The tangent stiffness operator, essential for the nonlinear numerical simulations, has been studied. It has been obtained as second covariant gradient of the internal energy functional for the considered structural model that preserves symmetry for any configuration, either equilibrated or not. The result has been reached evaluating the Levi-Civita connection for the tangent space of the configuration manifold. The results obtained extend to the case of Kirchoff -Love rods those presented by Simo (Comput Methods Appl Mech Eng 49:55–70, 1985) for Timoshenko rods. Given the different structure of the tangent spaces in this case, it has been necessary to introduce a specific metric that accounts for the rotation of the intrinsic triad due to the change of the position of the centroid axis of the rod. PubDate: 2015-09-01

Abstract: Dynamics of a Timoshenko beam under an influence of mechanical and thermal loadings is analysed in this paper. Nonlinear geometrical terms and a nonuniform heat distribution are taken into account in the considered model. The mathematical model is represented by a set of partial differential equations (PDEs) which takes into account thermal and mechanical loadings. The problem is simplified to two PDEs and then reduced to ordinary differential equations (ODEs) by means of the Galerkin method taking into account three modes of a linear Timoshenko beam. Correctness of the analytical model is verified by a finite element method. Then, the nonlinear model is studied numerically by a continuation method or by a direct numerical integration of ODEs. An effect of the temperature distribution on the resonance near the first natural frequency and on stability of the solutions is presented. The increase of mechanical loading results in hardening of the resonance curve. Thermal loading may stabilise the beam dynamics when the temperature is decreased. The elevated temperature may transit dynamics from regular to chaotic oscillations. PubDate: 2015-09-01

Abstract: Parameters identification of nonstationary systems is a very challenging topic that has only recently received critical attention from the research community. Aim of the paper is the structural health monitoring of bridge-like structures excited by a massive moving load, whose characteristics, such as the mass and speed, are unknown, in the presence of a localized damage along the structure. A novel method for the simultaneous identification of both the load characteristics and damage parameters from vibration measurements is proposed: the data processing relies on the ensemble empirical mode decomposition and the normalized Hilbert transform. Neither a priori information about the response of the undamaged structure nor the free decay of the damaged system is required, only a single-point measurement is needed. The empirical instantaneous frequency is firstly employed to estimate the load characteristics; secondly, the effect of the moving mass is filtered from the instantaneous frequency, and then, the damage position is identified. The performance of the technique are studied varying the load characteristics, damage locations, and crack depths. The effect of ambient noise is also taken into account. Numerical experiments show the identification is rather accurate, results are not very sensitive to the crack location and depth, while they are sensibly affected by the speed of the moving load. PubDate: 2015-09-01