Authors:Ameya Rege; Mikhail Itskov Pages: 585 - 593 Abstract: Cellulose aerogels are characterized by a cellular morphology. The mechanics of such materials is largely dictated by the behavior of their cell walls. Under tension, these aerogels undergo only small strains while their cell walls are subject to combined bending and tension loading. Accordingly, in the present paper, we describe the kinematics of these cell wall fibrils based on the Euler–Bernoulli beam theory. The microscopic damage criterion is based on the normal stress in the cell walls. Variation in the sizes of the microcells is accounted for by using the pore-size data from experiments. The so-resulting constitutive model includes few micromechanically motivated material parameters, shows very good agreement with our own experimental data of cellulose aerogels, and also accurately predicts material failure under tension. PubDate: 2018-02-01 DOI: 10.1007/s00707-017-1987-0 Issue No:Vol. 229, No. 2 (2018)

Authors:F. Casciati; S. Casciati; M. Vece Pages: 707 - 717 Abstract: Sensing devices are the main support for any experimental activity. The user expects that they are transparent, i.e., any measurement provides an assessment of a physical variable. Recent microelectronics developments caused significant modifications in the products offered by the market. Data fusion is the source of a recent jump in that technology, but the transparency of the result is no longer evident. In this paper, the authors consider the data fusion of displacement and acceleration measurements via a Kalman filter. The assemblage of two sensors is produced from scratch, and the critical aspects of the consequent data fusion are emphasized. PubDate: 2018-02-01 DOI: 10.1007/s00707-017-1994-1 Issue No:Vol. 229, No. 2 (2018)

Authors:Yanzheng Wang; Jan D. Achenbach Pages: 763 - 778 Abstract: Two models are proposed to obtain information on the material nonlinearity of an inclusion in a solid body. Material nonlinearity is usually generated by the development of material microscale damage. When the region of nonlinear material is large, incidence of ultrasound on the interface between the perfectly joined regions of linear and nonlinear material behavior produces very useful information. Using the continuity condition of stress and displacement at the interface, the harmonics in the nonlinear region, together with the compensatory waves, yield a reflected wave whose amplitude contains the defining constant of the material nonlinearity near the interface. The compensatory waves are introduced to ensure the continuity conditions at the interface. When the nonlinear region is an inclusion, the equivalent body force induced by the material nonlinearity generates a backscattered wave. The backscattered wave is determined in a simple manner by the use of the reciprocity theorem of elastodynamics. The backscattered wave obtained in this manner yields information on the nonlinear material properties and the size of the inclusion. In addition, a model based on the superposition of back-propagated compensatory waves from the two interfaces of the nonlinear region reveals the physical mechanism of wave scattering from the nonlinear inclusion. PubDate: 2018-02-01 DOI: 10.1007/s00707-017-1996-z Issue No:Vol. 229, No. 2 (2018)

Authors:Christian Bucher Pages: 901 - 910 Abstract: A purely kinematic approach to the formulation of plane stress/strain triangular elements with three nodes as well as tetrahedral elements with four nodes including rotational degrees of freedom is presented. The class of elements is shown to perform comparably well in several well-established test cases. Essentially, the displacement interpolation functions are cubic allowing for more flexibility in the displacement-based formulation. The in-plane triangle can be augmented by a plate bending element to form an efficient triangular shell element. PubDate: 2018-02-01 DOI: 10.1007/s00707-017-2045-7 Issue No:Vol. 229, No. 2 (2018)

Authors:S. I. Kundalwal; Vijay Choyal Abstract: Molecular dynamics simulations with Adaptive Intermolecular Reactive Empirical Bond Order force fields were conducted to determine the transversely isotropic elastic properties of carbon nanotubes (CNTs) containing vacancies. This is achieved by imposing axial extension, twist, in-plane biaxial tension, and in-plane shear to the defective CNTs. The effects of vacancy concentrations, their position, and the diameter of armchair CNTs were taken into consideration. Current results reveal that vacancy defects affect (i) the axial Young’s and shear moduli of smaller-diameter CNTs more than the larger ones and decrease by 8 and 16% for 1 and 2% vacancy concentrations, respectively; (ii) the plane strain bulk and the in-plane shear moduli of the larger-diameter CNTs more profoundly, reduced by 33 and 45% for 1 and 2% vacancy concentrations, respectively; and (iii) the plane strain bulk and in-plane shear moduli among all the elastic coefficients. It is also revealed that the position of vacancies along the length of CNTs is the main influencing factor which governs the change in the properties of CNTs, especially for vacancy concentration of 1%. The current fundamental study highlights the important role played by vacancy defected CNTs in determining their mechanical behaviors as reinforcements in multifunctional nanocomposites. PubDate: 2018-02-24 DOI: 10.1007/s00707-018-2123-5

Authors:Sheng Sang; Eric Sandgren; Ziping Wang Abstract: In this paper, we propose and study a single-phase elastic metamaterial with periodic chiral local resonator, which is composed of cylindrical central core surrounded by evenly distributed ligaments and embedded in the matrix in a square lattice. Based on the analytical and numerical analysis, we prove that the translational resonance of the unit cell can lead to negative effective mass density, and the rotational resonance of it can produce negative effective modulus. They can also work together to generate double-negative effective material properties. The wave attenuation of elastic waves in this elastic metamaterial is also demonstrated, which is owing to the negative effective mass density. In addition, the damping of the base material is also considered in the simulation. We finally examine the existence of negative band, and this leads to the physics of negative refraction, which is induced by simultaneous translational and rotational resonance of the unit cell. Our work can serve as the theoretical foundation for the design of single-phase elastic metamaterials. PubDate: 2018-02-23 DOI: 10.1007/s00707-018-2127-1

Authors:Alexander Svetashkov; Nikolay Kupriyanov; Kayrat Manabaev Abstract: The problem of structural design of polymeric and composite viscoelastic materials is currently of great interest. The development of new methods of calculation of the stress–strain state of viscoelastic solids is also a current mathematical problem, because when solving boundary value problems one needs to consider the full history of exposure to loads and temperature on the structure. The article seeks to build an iterative algorithm for calculating the stress–strain state of viscoelastic structures, enabling a complete separation of time and space variables, thereby making it possible to determine the stresses and displacements at any time without regard to the loading history. It presents a modified theoretical basis of the iterative algorithm and provides analytical solutions of variational problems based on which the measure of the rate of convergence of the iterative process is determined. It also presents the conditions for the separation of space and time variables. The formulation of the iterative algorithm, convergence rate estimates, numerical computation results, and comparisons with exact solutions are provided in the tension plate problem example. PubDate: 2018-02-23 DOI: 10.1007/s00707-018-2129-z

Authors:Xiannan Meng; Yongqi Wang Abstract: A depth-averaged two-velocity grain–fluid mixture model is proposed to describe flows of grain–fluid mixtures. Motivated by the experimental observations, the proposed model considers that the granular and the fluid phases are moving with different velocities, and the velocity difference between the granular phase and the fluid phase is coupled with the granular dilatancy that is described by a granular dilatancy law. The characteristics of flows allow to formulate a simpler depth-averaged PDE system. To scrutinize the proposed equations, an analysis for steady flows in rectangular channels is performed, which reproduces the cross-stream velocity profiles commonly observed in fields. Additionally, a uniform flow is investigated to illustrate the effects of the granular dilatancy on the velocities, flow depth, and volume fractions. PubDate: 2018-02-15 DOI: 10.1007/s00707-018-2111-9

Authors:Eman M. Hussein Abstract: This manuscript investigates the thermal stresses and temperatures in a porous plate hydrated with a liquid. The upper surface is taken to be impermeable, traction free and subjected to a thermal shock. The lower surface is laid on a rigid foundation. The effect of the porosity is analyzed through graphs. It is noticed that all functions for the two phases increase with the increasing porosity except for the stress and the displacement. The effect of time is analyzed through graphs. It is observed that the heat and elastic effects propagate with finite speeds. Comparison is made with a problem with the same configuration in the absence of fluid when the medium is not porous. It was found that the existence of the fluid decreases the temperature and the displacement, whereas opposite behavior is observed for the stress. PubDate: 2018-02-08 DOI: 10.1007/s00707-017-2106-y

Authors:Wei Tong Abstract: For better modeling plane-stress anisotropic plasticity of steel sheets, a direct calibration method is proposed and detailed for establishing a positive and convex sixth-order homogeneous polynomial yield function with up to sixteen independent material constants. The calibration method incorporates parameter identification, convexity testing, and if needed, an adjustment of an initially calibrated but non-convex yield function toward a convex one. Some advantages of the calibration method include (i) a systematic solution of only linear equations for the sixteen material constants of a steel sheet with various degrees of planar anisotropy, (ii) a practical numerical implementation of the necessary and sufficient conditions for convexity certification of the calibrated or adjusted yield function, and (iii) an incremental procedure using a parameterized version of the initially calibrated and non-convex yield function that can always lead to an approximate sixth-order yield function with guaranteed convexity. Results of applying the proposed calibration method to successfully obtain convex sixth-order yield functions are presented for three steel sheets with experimental measurement inputs from various types and numbers per type of uniaxial and biaxial tension tests. PubDate: 2018-02-08 DOI: 10.1007/s00707-018-2113-7

Authors:Andrea Burlon; Giuseppe Failla; Felice Arena Abstract: This paper deals with the coupled bending–torsional vibrations of beams carrying an arbitrary number of viscoelastic dampers and attached masses. Exact closed analytical expressions are derived for the frequency response under harmonically varying, arbitrarily placed polynomial loads, making use of coupled bending–torsion theory including warping effects and taking advantage of generalized functions to model response discontinuities at the application points of dampers/masses. In this context, the exact dynamic Green’s functions of the beam are also obtained. The frequency response solutions are the basis to derive the exact dynamic stiffness matrix and load vector of a two-node coupled bending–torsional beam finite element with warping effects, which may include any number of dampers/masses. Remarkably, the size of the dynamic stiffness matrix and load vector is \(8\times 8\) and \(8\times 1\) , respectively, regardless of the number of dampers/masses and loads along the beam finite element. PubDate: 2018-02-08 DOI: 10.1007/s00707-017-2078-y

Authors:G. Ruta; I. Elishakoff Abstract: In this paper, we study buckling of radially FGM circular plates. In a previous study, a fourth-order polynomial expressing the exact solution of a linear elastic problem was used as buckling mode shape. To generalise such investigation, in this contribution the buckling mode is postulated to take the shape of a fifth-order polynomial function of the radial coordinate. The flexural rigidity is consequently sought as a polynomial of suitable order, expressing the functional grading. New solutions in closed form are then obtained by a semi-inverse method. It is found that suitable choices of functional grading may increase the buckling load up to 246% with respect to the homogeneous and uniform cases. PubDate: 2018-02-08 DOI: 10.1007/s00707-017-2095-x

Authors:Hamed Asadi; Amin Rabiei Beheshti Abstract: The purpose of this study is to analyze the nonlinear dynamic responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams exposed to axial supersonic airflow in thermal environments. The dynamic model of the FG-CNTRC beam is developed with regard to the first-order shear deformation theory incorporating the von Kármán geometrical nonlinearity. The thermomechanical properties of the constituents are assumed to be temperature dependent. The third-order piston theory is adopted to estimate the nonlinear aerodynamic pressure induced by the supersonic airflow. Harmonic differential quadrature method is implemented to discretize the equations of motion in the spatial domain. A comprehensive parametric study is performed to expatiate on the effect of the distribution type and volume fraction of CNTs, boundary condition, slenderness ratio, and thermal environments on the aerothermoelastic responses of the FG-CNTRC beam. Simulation results indicate that the presence of the aerodynamic pressure not only increases the critical buckling temperature of the FG-CNTRC beam, but also changes the buckling mode shapes of the beam. Furthermore, the results show that aerothermoelastic characteristics of FG-CNTRC beams may be remarkably improved by the selection of a proper distribution of CNTs. Besides, it is found that FG-CNTRC beams with intermediate CNT volume fraction do not have an intermediate critical buckling temperature. PubDate: 2018-02-06 DOI: 10.1007/s00707-018-2121-7

Authors:Zhen Wu; Shiyin Liu; Huiwen Zhang; Xiaobo He; Junying Chen; Kai Yao Abstract: The steady-state diagnostic and prognostic simulation for the Xiao Dongkemadi glacier (XD) of the Tibetan Plateau was performed with the thermo-mechanically-coupled-with-Full-Stokes code Elmer (http://www.csc.fi/elmer/). In this paper, some changes of glacial thermodynamic parameters caused by ice thickness and atmospheric temperature variation were simulated in view of different thickness. The purpose of this study was to fill the gap in analyzing the ice dynamic characteristic of a polar continental glacier. The diagnostic simulation revealed the following conclusions: (1) when the thickness change was small, surface velocity, ice temperature, and deviation stress variation in the bedrock showed a tendency to change with thickness, and when the terrain was gentle, the thickness variation dominated the ice velocity. (2) The ice temperature of the bedrock was high in the whole profile and reached the pressure melting point in the terminus, and it was easy to slide at the bottom, which was consistent with the measured ground penetrating radar data near the terminus. (3) The static friction forces decrease with thickness, and they showed a complex nonlinear relationship, which revealed that the deviation stress in the bottom was influenced by thickness and ice temperature at the bedrock. The prognostic simulating from 2007 to 2047 presented: (1) The simulation forecasted a shrinkage of nearly 600 m in the terminus and the longitudinal section, and wound up diminished by nearly 25% by the end of 2047; (2) the change of thickness was small at the region between 5650 and 5700 m.a.s.l, which might be related to lower atmospheric temperature; (3) thickness dominated the deviation stress ( \(\sigma _{xx}\) and \(\sigma _{xz}\) ) in the bottom, and the impact of the terrain was little higher compared to deviation stress ( \(\sigma _{xx}\) ). In other words, the glacial thickness dominated the glacial force and movement to a great extent and the low temperature at high altitude reduced the XD’s sensitivity facing future climate warming. PubDate: 2018-02-05 DOI: 10.1007/s00707-018-2112-8

Authors:S. N. Korobeynikov; V. V. Alyokhin; A. V. Babichev Abstract: Molecular mechanics/molecular dynamics (MM/MD) methods are widely used in computer simulations of deformation (including buckling, vibration, and fracture) of low-dimensional carbon nanostructures (single-layer graphene sheets (SLGSs), single-walled nanotubes, fullerenes, etc). In MM/MD simulations, the interactions between carbon atoms in these nanostructures are modeled using force fields (e.g., AIREBO, DREIDING, MM3/MM4). The objective of the present study is to fit the DREIDING force field parameters (see Mayo et al. J Phys Chem 94:8897–8909, 1990) to most closely reproduce the mechanical parameters of graphene (Young’s modulus, Poisson’s ratio, bending rigidity modulus, and intrinsic strength) known from experimental studies and quantum mechanics simulations since the standard set of the DREIDING force field parameters (see Mayo et al. 1990) leads to unsatisfactory values of the mechanical parameters of graphene. The values of these parameters are fitted using primitive unit cells of graphene acted upon by forces that reproduce the homogeneous deformation of this material in tension/compression, bending, and fracture. (Different sets of primitive unit cells are used for different types of deformation, taking into account the anisotropic properties of graphene in states close to failure.) The MM method is used to determine the dependence of the mechanical moduli of graphene (Young’s modulus, Poisson’s ratio, and bending rigidity modulus) on the scale factor. Computer simulation has shown that for large linear dimensions of SLGSs, the mechanical parameters of these sheets are close to those of graphene. In addition, computer simulation has shown that accounting for in-layer van der Waals forces has a small effect on the value of the mechanical moduli of graphene. PubDate: 2018-02-03 DOI: 10.1007/s00707-018-2115-5

Authors:D. P. Zhang; Y. J. Lei; S. Adhikari Abstract: In this study, vibration characteristics of a piezoelectric nanobeam embedded in a viscoelastic medium are investigated based on nonlocal Euler–Bernoulli beam theory. In doing this, the governing equations of motion and boundary conditions for vibration analysis are first derived using Hamilton’s principle, where nonlocal effect, piezoelectric effect, flexoelectric effect, and viscoelastic medium are considered simultaneously. Subsequently, the transfer function method is employed to obtain the natural frequencies and corresponding mode shapes in closed form for the embedded piezoelectric nanobeam with arbitrary boundary conditions. The proposed mechanics model is validated by comparing the obtained results with those available in the literature, where good agreement is achieved. The effects of nonlocal parameter, boundary conditions, slenderness ratio, flexoelectric coefficient, and viscoelastic medium on vibration responses are also examined carefully for the embedded nanobeam. The results demonstrate the efficiency and robustness of the developed model for vibration analysis of a complicated multi-physics system comprising piezoelectric nanobeam with flexoelectric effect, viscoelastic medium, and electrical loadings. PubDate: 2018-02-03 DOI: 10.1007/s00707-018-2116-4

Authors:R. Q. Rodríguez; A. F. Galvis; P. Sollero; C. L. Tan; E. L. Albuquerque Abstract: This work presents the use of an explicit-form Green’s function for 3D general anisotropy in conjunction with the dual reciprocity boundary element method and the radial integration method to analyse elastodynamic problems using BEM. The latter two schemes are to treat the inertial loads in the time-domain formulation of the dynamic problem. The direct analysis with the Houbolt’s algorithm is used to perform the transient analysis. The efficient and accurate computation of the fundamental solutions has been a subject of great interest for 3D general anisotropic materials due to their mathematical complexity. A recently proposed scheme based on double Fourier series representation of these solutions is used to this end. Numerical examples are presented to demonstrate the feasibility and successful implementation of applying these schemes in synthesis to treat 3D elastodynamic problems of anisotropic materials. PubDate: 2018-02-02 DOI: 10.1007/s00707-018-2108-4

Authors:Georg Jehle; Alexander Fidlin Abstract: When the so-called eek effect emerges while shifting a vehicle shift gearbox, car drivers perceive audible noise and vibrations of drivetrain components. Some physical approaches have been provided in order to explain the effect as well as to search for countermeasures. In Jehle and Fidlin (ZAMM J Appl Math Mech 94(11):911–916 (2014), the interaction of sliding clutch disk and gears is addressed in a rigid body model. The clutch disk’s non-conservative follower forces in combination with geometric coupling in gears imply the action of non-symmetric restoring- and velocity-proportional forces. The desired motion of gearbox components can therefore undergo a mode-coupling flutter instability, out of which vibrations emerge with exponentially growing amplitudes. As the contacts in clutch and gears hold non-smooth transitions such as the possibility of sticking and opening, dynamic solutions are both limited and complex. In this contribution, first of all model details concerning the gear formulation are revised: rigid and viscoelastic normal contact are compared, which imply differences in the nature of the solution and method of stability analysis. Nevertheless the two approaches are shown to converge. Finally, the dynamics behind the loss of stability of the desired motion is investigated. PubDate: 2018-02-02 DOI: 10.1007/s00707-018-2110-x