Authors:Alessandro Baratta; Ileana Corbi; Ottavia Corbi Pages: 837 - 849 Abstract: In this paper, we introduce a phenomenological model approximating the behaviour of masonry structures, which is based on a low-tension elastic–brittle (EB) assumption with evolutionary tensile behaviour. The EB model is conceived by embedding a decaying tensile strength in the material behaviour, and it is able to achieve good agreement with the real behaviour of masonry. Since the model is quite sophisticated, non-holonomic, and the EB solution depends—amongst other things—on the loading path, it is worthwhile to investigate the relationships with more manageable and stable models rather than searching for unreliable solutions that depend on poorly predictable data. Namely, whereas it is quite clear and largely agreed upon that structural models widely applied in engineering (like perfectly plastic or no-tension models or other ones) are well-conditioned problems, the same does not apply to brittle structures. In this case, exact solutions are hard to be found and are scarcely attractive from the engineering point of view since they also depend on the load history and on unverifiable variables such as the local tensile strength. In view of these considerations, in this paper it is proved that stress fields in tensioned EB problems can be approached by highly stable solutions, on the upper and lower sides of the relevant complementary energy, and that the approximation gets closer as the limit tensile strength of the brittle material becomes lower. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1722-2 Issue No:Vol. 228, No. 3 (2017)

Authors:Deepak Kr. Pandit; Santimoy Kundu; Shishir Gupta Pages: 871 - 880 Abstract: The present paper investigates the theory of propagation of Voigt-type viscoelastic Love waves in a functionally graded material layer over an anisotropic porous half-space. The complex dispersion equation of Love waves has been expanded into real and imaginary parts. An assumption of the dissipation factor has been applied. Some particular cases have also been deduced, and it is noticed that the dispersion equation is in well agreement with the classical Love wave equation. In addition, to study the effect of initially stressed parameter, inhomogeneity parameter and porosity on phase velocity and dissipation function, some significant observations have been made by detailed numerical calculations and illustrated graphically. The results of this paper may present a deeper insight into the nature of the propagation behavior in elastic inhomogeneous functionally graded materials and can provide theoretical guidance for the design and optimization to the field of earthquake engineering. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1741-z Issue No:Vol. 228, No. 3 (2017)

Authors:Mahdi Adineh; Mehran Kadkhodayan Pages: 881 - 899 Abstract: A thermo-elastic analysis of a multi-directional functionally graded thick rectangular plate with different boundary conditions is carried out in this study. Some material properties are assumed to be temperature dependent and graded in all three spatial directions following a power law function. The differential quadrature method (DQM) is employed to obtain the temperature distribution throughout the 3D-FGM plate. The governing partial differential equations based on the three-dimensional thermo-elasticity theory are obtained, and the DQM is employed to discretize the resulting equations. Comparisons are made with the available results of 1D-FGM and 2D-FGM plates in the literature and an Abaqus model. Numerical results are obtained for different gradient indices, plate dimensions, and various thermal and mechanical boundary conditions. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1743-x Issue No:Vol. 228, No. 3 (2017)

Authors:J. H. Merkin Pages: 919 - 930 Abstract: The Falkner–Skan equation, defined by the parameter \(\beta \) , is considered subject to a free streamline (zero wall shear) boundary condition. Solutions are found only in \(\beta <0\) , the solution becoming singular as \(\beta \rightarrow 0\) . Several sets of solutions are seen in \(\beta <0\) , each emerging from the trivial solution \(f \equiv \eta \) at \(\beta =-\frac{1}{2} -k, \,k=0,1,2,\ldots \) . The first of these sets of solutions has \(f'(0)\) monotone with \(\beta \) , the solution terminating as \(\beta \rightarrow 0\) and becoming singular as \(\beta \rightarrow -1\) . The other sets of solutions each have a saddle-node bifurcation giving two solution branches, becoming singular and terminating as \(\beta \rightarrow -1\) . The asymptotic limits of \(\beta \rightarrow 0\) and \(\beta \rightarrow -1\) are discussed. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1751-x Issue No:Vol. 228, No. 3 (2017)

Authors:George Z. Voyiadjis; Peter I. Kattan Pages: 951 - 990 Abstract: An attempt is presented to provide for a global and holistic approach to the study of continuum damage mechanics. For this purpose, the authors classify material damage models into three categories. Furthermore, the concept of ready-made model templates for damage mechanics is proposed. In this regard, the authors provide details for fourteen basic damage mechanics templates. Each template comes with a schematic diagram along with a set of equations that govern the respective material damage template. The user can then use the chosen template and fill in the details to obtain the constitutive equations. The obtained material damage model is guaranteed to be systematic and consistent provided that proper use is made of the chosen template. Furthermore, three additional sections are added to provide details on how to generate advanced, special, and more complex damage mechanics templates that go beyond the rule of mixtures and for specific types of materials. The details of 14 complete and comprehensive damage mechanics templates for both metals and composite materials are presented in this work. Finally, using one chosen basic template, it is shown how to generate five additional and more complex templates. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1747-6 Issue No:Vol. 228, No. 3 (2017)

Authors:Luca Gambirasio; Egidio Rizzi; David J. Benson Pages: 991 - 1027 Abstract: Effective perforating gun firing constitutes a key process toward achieving safe and productive wells in hydrocarbon reservoir exploitation. Within this field, the present work pursues a novel modeling approach with two main aims: investigating the physical phenomena involved in the firing of a perforating gun in air at atmospheric pressure, by identifying all key factors stressing the gun carrier; assessing perforating gun performance dependence and optimization on the scallop geometry, in terms of the piercing capability of the carrier outcoming jets and of the gun carrier resistance. This is investigated through challenging 3D Eulerian FEM simulations, displaying coherence with key experimental evidences. The obtained results provide crucial information toward the understanding of the physical phenomena involved in gun firing and of the scallop geometry implications on gun performance. The present simulations set as an advanced tool for perforating gun design and optimization, in comparison with other methodologies like Lagrangian simulations or analytical modeling. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1750-y Issue No:Vol. 228, No. 3 (2017)

Authors:Mawafag F. Alhasadi; Salvatore Federico Pages: 1045 - 1069 Abstract: The pioneering work by John D. Eshelby in the 1950s and the 1960s on the theory of materials with defects has opened the doors to what today we call configurational mechanics or, in his honour, Eshelbian mechanics. Two of the main results that Eshelby obtained in this field are the use of the elastic energy-momentum tensor to calculate the net force on a defect and the study of materials with inclusions from the geometrical point of view. In Continuum Mechanics, the energy-momentum tensor is now commonly referred to as the Eshelby stress and is the physical quantity that captures the presence of singularities, such as point defects, inclusions, dislocations. In the study of materials with inclusions, Eshelby established a method for the calculation of the strain and stress fields, which entails a fourth-order tensor that relates the strain in the inclusion to the virtual strain (transformation strain or eigenstrain) defining the geometrical misfit between inclusion and matrix. Surprisingly, perhaps, the scientific communities in these two streams of research seem to have had little or no interaction, i.e. virtually all those researchers that have worked in terms of the Eshelby stress have never used the Eshelby fourth-order tensor, and vice versa. To the best of our knowledge, there exists no explicit mathematical relation between the two objects. Therefore, the objective of this paper is to study the relationship between the Eshelby stress and the Eshelby fourth-order tensor within an ellipsoidal inclusion, in the infinitesimal theory of elasticity. Of the three cases that shall be analysed, the first two are commonly referred to as “homogeneous inclusion” and “inhomogeneous inclusion” in the literature, while we refer to the latter as to “general inclusion”, since it describes both the other two as particular cases. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1734-y Issue No:Vol. 228, No. 3 (2017)

Authors:Hamdi Ezzin; Morched Ben Amor; Mohamed Hédi Ben Ghozlen Pages: 1071 - 1081 Abstract: The propagation of shear horizontal waves in laminated piezomagnetic/piezoelectric plates was investigated using the ordinary differential equation and stiffness matrix methods. Commonly used materials, namely barium titanate as piezoelectric ‘B’ and cobalt ferrite as piezomagnetic ‘F’, were retained for illustration. The dispersion curves of the first five modes were shown for different sequences F/F, B/B, and F/B. The effects of thickness ratio on phase and group velocities as well as the influence on the magneto-electromechanical coupling factor of the first mode were investigated. Large magneto-electromechanical coupling factors could be achieved by an appropriate adjustment of the thickness ratio. The present investigation is of practical interest for developing new layered composites made of smart piezoelectric and piezomagnetic devices for engineering applications. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1744-9 Issue No:Vol. 228, No. 3 (2017)

Authors:C. L. Li; Q. Han; Y. J. Liu; D. L. Xiao Pages: 1083 - 1095 Abstract: Elastic guided wave propagation in a rotating functionally graded material (FGM) annular plate is presented in this paper. The material properties are assumed to vary continuously along the radial direction. The elastodynamic equation of annular plates which take into account initial hoop, centrifugal and Coriolis effects is derived, and the wave finite element method is extended to model wave motion related to rotation with 3D-Chebyshev spectral elements. Firstly, wave properties in a straight bar are computed and compared to that of the Rayleigh–Ritz method. Then, wave propagation in the FGM annular plate with various material gradient indexes is considered and the results indicate that the index has large influence on wave characteristics. With contour profiles of transverse sections, propagating wave modes in the plate can be identified distinctly. Besides, the effects of rotation on wave propagation are discussed, which show that the extensional-like and shearing-like wave modes are very sensitive to the rotation at low frequencies but the flexural are not. In addition, the curve veering phenomenon existing in FGM annular plates is also found, which analyzes the influences of material gradient index and rotating speed and points out the variations in the relative critical frequencies. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1752-9 Issue No:Vol. 228, No. 3 (2017)

Authors:Amin Ghorbani Shenas; Parviz Malekzadeh; Sima Ziaee Pages: 1115 - 1133 Abstract: As a first endeavor, the thermal buckling of rotating pre-twisted functionally graded (FG) microbeams with temperature-dependent material properties is studied based on the modified strain gradient theory in conjunction with the first-order shear deformation theory of beams. The adjacent equilibrium criterion and Chebyshev–Ritz method are employed to derive the nonlinear algebraic eigenvalue equations governing the thermal buckling behavior of the microbeams, which are solved iteratively. The fast rate of convergence and accuracy of the method are numerically demonstrated. Then, the effects of the twist angle, rate of twist angle (as an important geometrical design parameter), material length scale parameter, material gradient index and angular velocity on the thermal load-bearing capacity of rotating pre-twisted FG microbeams under different boundary conditions are studied. It is shown that by increasing the hub radius, the angular velocity and the length scale parameter, the thermal buckling load increases, but an increase of the material gradient index reduces the critical thermal buckling load. In addition, the formulation can be easily degenerated to those of large-scale rotating pre-twisted FG beams. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1759-2 Issue No:Vol. 228, No. 3 (2017)

Authors:Xiufeng Xie; Junlin Li; Di Liu; Rong Guo Pages: 1153 - 1163 Abstract: The approximate transient response of a nonlinear vibro-impact system under Gaussian white noise excitation is investigated by the methods of stochastic averaging and the Mellin transform. The Zhuravlev nonsmooth transformation is utilized to convert the nonlinear vibro-impact system into an equivalent system without velocity jumps by introducing an impulsive damping term. The Itô stochastic differential equation with respect to the amplitude response and the related Fokker–Plank–Kolmogorov (FPK) equation governing the amplitude response probability density of the vibro-impact system are derived with the stochastic averaging method. The Mellin transform is introduced to solve the FPK equation. The differential relations of complex fractional moments are obtained. The probability density function for transient response of this system constructed by solving a set of differential equations yields complex fractional moments. Two illustrative examples are examined to evaluate the effectiveness of the proposed solution procedure. The effects of restitution factors are investigated on the transient probability density distribution of the vibro-impact systems. At the same time, the convergence and the error analyses for different restitution factors are illustrated. Influences of the truncate term on the convergence and the error are further illustrated. The results obtained from the proposed procedure agree well with the results from Monte Carlo simulations. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1761-8 Issue No:Vol. 228, No. 3 (2017)

Authors:Jie Cao; Xie-Fei Ding; Zheng-Nan Yin; Heng Xiao Pages: 1165 - 1175 Abstract: A direct approach is proposed to obtain new multi-axial elastic potentials for incompressible soft solids. Results are presented with novelties in three respects, namely (i) any given benchmark test data for three deformation modes may be exactly fitted, including uniaxial, equi-biaxial, and plane-strain extension; (ii) model parameters of direct physical meanings may be provided to represent both the strain-stiffening effect and failure behavior; and (iii) error estimation may be established for all possible deformation modes. Numerical examples are in good agreement with Treloar’s classic data for rubbers and with extensive data for gellan gels up to failure. PubDate: 2017-03-01 DOI: 10.1007/s00707-016-1753-8 Issue No:Vol. 228, No. 3 (2017)

Authors:B. M. Shankar; Jai Kumar; I. S. Shivakumara Abstract: The stability of natural convection in a fluid-saturated vertical anisotropic porous layer is investigated. The vertical rigid walls of the porous layer are maintained at different constant temperatures, and anisotropy in both permeability and thermal diffusivity is considered. The flow in the porous medium is described by the Lapwood–Brinkman model, and the stability of the basic flow is analysed numerically using Chebyshev collocation method. The presence of inertia is to inflict instability on the system and in the absence of which the system is always found to be stable. The mechanical and thermal anisotropies exhibit opposing contributions on the stability characteristics of the system. The mode of instability is interdependent on the values of Prandtl number and thermal anisotropy parameter, while it remains unaltered with the mechanical anisotropy parameter. The effect of increasing Prandtl and Darcy numbers shows a destabilizing effect on the system. Besides, simulations of secondary flow and energy spectrum have been analysed for various values of physical parameters at the critical state. PubDate: 2017-03-17 DOI: 10.1007/s00707-017-1831-6

Authors:Srivathsan Ravi; Andreas Zilian Abstract: This paper is devoted to monolithic modeling of piezoelectric energy harvesting devices. From a modeling perspective, piezoelectric energy harvesting is a strongly coupled phenomenon with two-way coupling between the electromechanical effect of the piezoelectric material and the harvesting circuit. Even in applications related to shunt damping, where the attached electrical circuit is passive, accurate modeling of the strong coupling is crucial for proper evaluation of the relevant parameters. The article proposes a monolithic mixed-hybrid finite element formulation for the predictive modeling and simulation of piezoelectric energy harvesting devices. The governing equations of the coupled electromechanical problem are converted into a single integral form with six independent unknown fields. Such a holistic approach provides consistent solution to the coupled field equations which involve structural dynamics, electromechanical effect of the piezoelectric patches and the dynamics of the attached harvesting circuit. This allows accurate computation of the eigenvalues and corresponding mode shapes of a harvester for any finite resistive load coupled to the harvester. The fully three-dimensional mixed-hybrid formulation is capable of analyzing structures with non-uniform geometry and varying material properties. The results of the finite element model are verified against the analytical results of a bimorph harvester with tip mass reported in the literature. PubDate: 2017-03-13 DOI: 10.1007/s00707-017-1830-7

Authors:I. Comez; M. A. Guler Abstract: In this study, the plane contact problem for a rigid cylindrical punch and a functionally graded bilayer is considered. The layers have different thicknesses and elastic constants. The normal and tangential forces are applied to the upper layer with a rigid cylindrical punch, and the lower layer is fully bonded to a rigid substrate. Poisson’s ratios are taken as constant, and elasticity moduli are assumed to vary exponentially through the thickness of the layers. With the use of Fourier integral transform, the plane contact problem is reduced to a singular integral equation in which the unknowns are the contact pressure and the contact width. The singular integral equation is solved numerically using Gauss–Jacobi integration formula. The effect of several geometrical and physical parameters such as the material inhomogeneity, the friction coefficient, the layers’ height, the mismatch in the material properties at the interface, and the contact width on the contact stress and in-plane stress are investigated in detail. PubDate: 2017-03-11 DOI: 10.1007/s00707-017-1827-2

Authors:Jing Pan; Lichun Bian Abstract: In the present study, a new method for investigating the effect of aggregation on carbon nanotube (CNT) composites has been developed, in which two aggregation parameters are introduced based on a combination of the self-consistent scheme and the Mori–Tanaka method. This paper mainly analyzes the effect of CNT agglomeration on the effective elastic modulus of CNT/polymer composites, and a micromechanical model is proposed for the analysis. The regions with concentrated CNTs are assumed to be spherical in shape and are considered as the inclusions. The dispersive CNTs in the pristine matrix can form a fictitious matrix. The effective elastic properties of inclusions and composites composed of inclusions and fictitious matrix are determined. It is found that the effective modulus of composite changes with the variation of two aggregation parameters. Moreover, the agglomeration of CNTs reduces the elastic stiffness of composites and the uniformly dispersed CNTs enhance the reinforcement effect. PubDate: 2017-03-03 DOI: 10.1007/s00707-017-1820-9

Authors:D. Aranda-Iglesias; G. Vadillo; J. A. Rodríguez-Martínez Abstract: In this paper, we have investigated the role played by the material compressibility in the oscillatory behaviour of hyperelastic spherical shells subjected to dynamic inflation. For that purpose, we carried out a comprehensive nondimensional numerical analysis using: (i) a finite differences MacCormack’s scheme implemented in MATLAB, and (ii) a finite element model developed in ABAQUS/Explicit (Abaqus Explicit v6.10 user’s manual, version 6.10 edn. ABAQUS Inc., Richmond, 2010). We have detected that numerical dispersion and diffusion impose limits to the capacity of the computations to describe the shock wave that emanates from the inner surface of the shell due to the application of the inflation pressure. Nevertheless, both numerical approaches capture the essential features that describe the oscillatory behaviour of the shell, including the maximum stretch of the oscillation. Using the key nondimensional groups that control the problem at hand, we have conducted a parametric study to assess the role played by nondimensional applied pressure, material compressibility, and nondimensional shell thickness in the oscillatory behaviour of the specimen. We have shown the interplay between the maximum amplitude of the oscillation and the applied pressure and obtained the critical pressure for which the oscillatory behaviour is lost, leading to an unbounded expansion of the spherical shell. Moreover, our calculations have revealed that the wave propagation within the specimen plays a key role in the dynamic response of the shell. The phase portraits used to represent the oscillatory behaviour of the spherical shell show a characteristic sawtooth form that is accentuated with the increase in material compressibility and shell thickness. PubDate: 2017-03-03 DOI: 10.1007/s00707-017-1821-8

Authors:Dimitrije Nikolić Abstract: Over the last few years, scholars have revisited the classical issue of identifying the limit equilibrium states of masonry arches. While the Couplet’s problem was rigorously solved by Serbian scholar Milutin Milankovitch more than a century ago, the minimum thickness of elliptical arches has been recently computed. However, albeit pointed masonry arches are very common in historic structures, particularly in Gothic architecture, their structural behaviour according to thrust line theory is not researched in sufficient detail. Therefore, the aim of this paper is to further develop the geometric formulation, i.e. macroscopic equilibrium analysis of a finite portion of an arch, used for semicircular and semielliptical arches, in order to compute the minimum thickness of pointed arches. Employing radial stereotomy, which concerns generic sections concurrent to the arch’s centre, the present paper derives a closed-form expression of the thrust line of pointed arches under self-weight. The paper concludes that, when the limit equilibrium state is attained, there are four admissible collapse modes with the precise order of the occurrence regarding eccentricity. Considering both incomplete and overcomplete arches, numerical calculations are conducted, resulting in the minimum thickness values of more than hundred arches having various eccentricity. In addition, the limit eccentricity corresponding to the arch having maximum use of its thickness is indicated and particularly treated. Finally, the correlation between eccentricity, embrace angle, and minimum thickness is graphically presented, enabling the clear distinction between the collapse modes. PubDate: 2017-03-03 DOI: 10.1007/s00707-017-1823-6

Authors:Cristian Marchioli Abstract: In large-eddy simulation (LES) of turbulent dispersed flows, modelling and numerical inaccuracies are incurred because LES provides only an approximation of the filtered velocity. Interpolation errors can also occur (on coarse-grained domains, for instance). These inaccuracies affect the estimation of the forces acting on particles, obtained when the filtered fluid velocity is supplied to the Lagrangian equation of particle motion, and accumulate in time. As a result, particle trajectories in LES fields progressively diverge from particle trajectories in DNS fields, which can be considered as the exact numerical reference: the flow fields seen by the particles become less and less correlated, and the forces acting on particles are evaluated at increasingly different locations. In this paper, we review models and strategies that have been proposed in the Eulerian–Lagrangian framework to correct the above-mentioned sources of inaccuracy on particle dynamics and to improve the prediction of particle dispersion in turbulent dispersed flows. PubDate: 2017-02-20 DOI: 10.1007/s00707-017-1803-x