Authors:W. A. Jiang; K. Liu; G. L. Zhao; M. Chen Pages: 4771 - 4778 Abstract: This paper is concerned with adiabatic invariants, applied to Noether symmetrical perturbation of disturbed non-material volumes. The disturbed equation of non-material volumes is proposed, the identity of Noether symmetry for the disturbed system is described, and the corresponding Noether exact invariant is derived. The perturbation to the Noether symmetry and adiabatic invariant for non-material volumes is employed by introducing the concept of adiabatic invariant. The Noether identity of symmetrical perturbation for the disturbed non-material volumes is reported, and Noether adiabatic invariant is obtained. Two examples are given to illustrate the application of the method, and the corresponding exact invariant and adiabatic invariant are obtained under the Noether symmetrical transformations. PubDate: 2018-12-01 DOI: 10.1007/s00707-018-2257-5 Issue No:Vol. 229, No. 12 (2018)

Authors:T. Fąs; K. Kazimierska-Drobny; M. Kaczmarek Pages: 4779 - 4790 Abstract: A model of the indentation of a circular elastic membrane (neo-Hookean material) on an incompressible liquid layer and an effective numerical solution method are presented. For the interface between the indenter and the membrane, stick or slip contact conditions are considered. The solution procedure identifies the liquid pressure and, for slip contact, the radius in the reference configuration displaced to the edge of the indenter. Assuming a range of material and test performance parameters regarding deep tonometry of soft subcutaneous tissue, the predictions for the distributions of stretches, line tensions and profiles of the indented membrane are analyzed. Among the key results of this work are the dependencies of the total indentation force and the liquid pressure on the Young’s modulus of the membrane’s material that appeared to be approximately linear for a range of Young’s modulus values. The profiles of the membrane for different indentation depths are close to parabolic and can be used to relate the longitudinal line tension at the edge of the indenter to the total indentation force. PubDate: 2018-12-01 DOI: 10.1007/s00707-018-2248-6 Issue No:Vol. 229, No. 12 (2018)

Authors:Chun-Ron Chiang Pages: 4831 - 4844 Abstract: Explicit expressions for Eshelby’s tensor of an elliptic inclusion in orthotropic materials are derived in this paper. The main approach is based on the general solution for elliptic-hole problems in orthotropic materials. The derivation based on a direct integration of elastic Green’s function along the elliptic contour is also used to illustrate a certain useful connection between these two approaches; this connection has not been fully recognized and published before. The theoretical results are checked with those obtained via the Fourier transform method and those found by direct numerical integration. PubDate: 2018-12-01 DOI: 10.1007/s00707-018-2254-8 Issue No:Vol. 229, No. 12 (2018)

Authors:Junhua Xiao; Yaoling Xu; Fucheng Zhang Pages: 4915 - 4925 Abstract: A theoretical study is performed on the fracture characteristics for the problem of two symmetrical edge cracks emanating from a circular hole with surface effect under far-field antiplane shear loading. Based on the theory of Gurtin–Murdoch surface model, a rigorous analytical solution of the stress intensity factor and the strain energy release rate at a crack tip is presented by using the complex potential function and a conformal mapping technique. When the cracked hole becomes nano-sized, the stress intensity factor and the strain energy release rate show significant size dependence. The interaction effects between cracks and hole on the stress intensity factor and the strain energy release rate are discussed in providing numerical examples. PubDate: 2018-12-01 DOI: 10.1007/s00707-018-2297-x Issue No:Vol. 229, No. 12 (2018)

Authors:Jérôme Colin Pages: 4945 - 4952 Abstract: The interaction between edge dislocations and a cylindrical circular cavity embedded in an infinite-size solid submitted to a biaxial stress has been studied from a theoretical point of view. In the case where a first dislocation has reached the cavity, a (meta)stable equilibrium position has been found for the second dislocation gliding from infinity in the same plane as the one of the first dislocation. The critical value of the stress for which the second dislocation also reaches the cavity has been determined. An equivalent study has then been performed for the following gliding dislocations. The possibility of formation from the cavity of another dislocation still in the same gliding plane but in the diametrically opposite part of the solid has finally been analyzed. PubDate: 2018-12-01 DOI: 10.1007/s00707-018-2300-6 Issue No:Vol. 229, No. 12 (2018)

Authors:M. Ciavarella; Y. J. Ahn Pages: 4953 - 4961 Abstract: The crack analogue model was developed to interpret various experimental observations of damage and cracking in fretting fatigue. This method assumes infinite friction at the interface and defines the oscillatory stress-intensity factor at the contact edge when the tangential load cyclically varies while the normal force is constant. However, practical engineering systems are subject to periodic loading in both the normal and shear directions, so that the contact area is not constant any more. Recently, Ciavarella and Berto suggested a crude extension to the crack analogue model in order to include the case of varying normal load, which is still not immediate to use since the singularities move in space and have no equivalent to fatigue from a crack. In this paper, we shall investigate the validity of the proposed model. For this, we shall establish an exact solution for a full stick contact problem with harmonic loading in normal and tangential directions. Here, this solution shows that there is a moving singularity at the edge of the contact area as unloading proceeds. The magnitude of the moving singularity depends on the tangential force difference between unloading and loading curve at constant normal force and the instantaneous value of the contact semi-width. Also, this solution shows that there is a logarithmic singularity which does not move. PubDate: 2018-12-01 DOI: 10.1007/s00707-018-2278-0 Issue No:Vol. 229, No. 12 (2018)

Authors:Hui Fan; Limei Xu Pages: 5121 - 5132 Abstract: A Love wave is derived for a new physical configuration in which a surface layer described by the couple stress theory covers a classical elasticity half-space. The dispersion equation is derived analytically when the thickness of the surface layer approaches zero. The correctness of the dispersion equation is confirmed via the second derivation path, namely the surface elasticity. The membrane with microstructure is described by the surface elasticity which significantly simplifies the derivation. New propagation features deduced from the dispersion curves are discussed. PubDate: 2018-12-01 DOI: 10.1007/s00707-018-2293-1 Issue No:Vol. 229, No. 12 (2018)

Abstract: The aim of the acousto-elastic theory was to measure ultrasonic velocity changes which characterize the mechanical nonlinearity of a prestressed material. In this context, our purpose is to tabulate the invariant third-order elastic coefficients including the piezoelectric, electrostrictive, and dielectric corrections. The investigation is limited to trigonal and hexagonal crystalline structures, which represent the most often encountered symmetry classes for the piezoelectric materials. In fact, the enumeration includes the high-order tensors involved in the analysis of nonlinear behaviors associated with various electromechanical coupling forms. The obtained results are extensions to previous calculations in this area which bring some corrections to certain published combinations related to the invariance rules. The numerical procedure built using the software MATLAB is based on coordinate system transformations performed on the eigenbasis of their corresponding symmetry axes three- and sixfold. In this purpose, we found some contradictions between our results and a former paper published in Journal of Applied Physics. To the authors’ knowledge, rechecking of the relationships between the invariant third-order constants and comparison with this last reference has not been discussed yet. The relationships between the invariant third-order coefficients presented in this work provide a number of attractive properties for use in mechanical and physical applications. PubDate: 2018-12-15

Abstract: In this paper, a design of active elastic metamaterial that possesses negative density and tunable bulk modulus is presented for the negative refraction of in-plane elastic waves at deep subwavelength scale. The metamaterial is fabricated in an aluminum plate, and the resonant structure in a unit cell of the metamaterial composes of a coated steel that functions as a translational resonator and a radially polarized piezoelectric transducer shunted with negative capacitance. Based on effective continuum theory, the effective mass density and bulk modulus are numerically determined. The passive and active elements work together to generate broad band double-negative material properties. Simulation results verified and demonstrated the negative refraction of elastic waves at the interface between proposed elastic metamaterials and natural solids. The proposed elastic metamaterial may thus be used as a flat lens with broad working frequency regime for in-plane elastic wave focusing. PubDate: 2018-12-14

Abstract: The chemical reactions taking place in lithium-ion batteries can trap lithium and alter the distribution of lithium and the deformation of the electrode during electrochemical charging and discharging. In this work, we incorporate the strain generated by chemical reactions in the transient analysis of diffusion-induced stress and numerically solve the one-dimensional problem under galvanostatic and potentiostatic operations, respectively. The numerical results show that both the diffusion and local chemical reaction contribute to the expansion of the electrode. Under the potentiostatic operation, lithiation introduces a stress spike at the fixed end at the onset of the lithiation. The chemical reactions play a significant role in controlling the temporal evolution of lithium and the deformation of electrode, which needs to be taken into account in the analysis of structural durability of lithium-ion batteries. PubDate: 2018-12-14

Abstract: A semi-infinite round cylindrical cavity filled with an ideal compressible fluid is considered. It contains a spherical body located close to its end. The body performs periodic motion with a specified frequency and amplitude. The problem of determining the acoustic field of velocities (pressure) in the fluid is solved depending on the character of excitation and geometrical parameters of the system. The study uses the method of separation of variables, translational addition theorems for spherical wave functions and relationships representing spherical wave functions in terms of cylindrical ones and vice versa. Such an approach satisfies all boundary conditions and yields an exact boundary problem solution. The computations are reduced to an infinite system of algebraic equations, the solution of which with the truncation method is asserted to converge. Determining the pressure and velocity fields has shown that the system being considered has several excitation frequencies, at which the acoustic characteristics exceed the excitation amplitude by several orders. These “resonance” frequencies differ from such frequencies inherent an infinite cylindrical waveguide with a spherical body in both cases. In this case, even when the radius of a spherical radiator is small and abnormal phenomena in an infinite vessel are weak they can manifest themselves substantially in a semi-infinite vessel. PubDate: 2018-12-14

Abstract: The problem of large deformations of a composite nonlinear elastic hollow cylinder subjected to internal and external pressures and loaded at the ends by axial force and torque is considered. The composite cylinder is a tube with internal and external coatings in the form of prestressed hollow circular cylinders. The exact solution of the problem, which is valid for any models of isotropic incompressible elastic materials, is found. PubDate: 2018-12-13

Abstract: A theoretical study of sound transmission in rigid duct through clamped triple plates separated by two impervious air cavities is formulated. The vibrating motion of the plates and the sound pressure field are expanded in terms of an infinite series of the modal functions. The accuracy of the theoretical predictions is first checked against experimental and numerical results, with good agreement achieved. The model predictions are then used to explore the influence of key parameters on the sound isolation capability of the triple-plate configuration, including the thickness of the plates and that of the air cavities. Furthermore, the sound transmission loss (STL) of the triple-plate model is compared with that of a double plate. Results showed that replacing the double plates with three plates while keeping the air cavity gaps between the plates the same degrades the STL in the low-frequency range. However, using the triple plates is more suitable to enhance the sound insulation performance when enough space is available. PubDate: 2018-12-13

Abstract: A new anisotropic hyperelastic model has been developed to model the deformation response of a knitted-fabric-reinforced rubber composite. The composite has a sandwich structure with a fiber net layer embedded in two rubber layers. Due to the architecture of the knitted fabric, the composite demonstrates an anisotropic hyperelastic response, which is modeled through a strain energy density function that incorporates the effects of deformed rubbers and stretched fibers. The rubber is considered as a neo-Hookean material, while the knitted fabrics are modeled as cords with negligible stiffness in bending. The effect of reinforcement comes from the conservation of the total length of the fiber cords. In addition, a slack variable is proposed to account for the effect of processing-induced fabric pre-stretch or fabric slack on the resulting composite response. This novel approach enables the determination of the constitutive behavior of the composite in closed form based on the constituent rubber and fiber properties and fabric architectures. The proposed analytical model is validated through a full 3D finite element (FE) model, in which the rubber and fiber reinforcement are modeled explicitly. Since the proposed model captures the key parameters that dictate the deformation response of knitted-fabric-reinforced composites, it can be employed as an efficient modeling tool to guide the design of rubbers and fabric architectures with targeted composite performance. PubDate: 2018-12-13

Abstract: Dissimilar orthotropic stiffness coefficient variations are a characteristic feature of unidirectionally reinforced fiber composites with a variable fiber volume fraction, but have not been commonly considered in the literature. The objective of this work is to account for them and obtain a three-dimensional elasticity solution with specific reference to simply supported rectangular plates. The analysis involves the solution of variable coefficient governing equations using the power series approach. For a graphite–epoxy plate with a sandwich-like configuration, results useful as a benchmark for future comparisons are tabulated for a specific power law variation of the volume fraction. It is shown that the thickness-wise variations of displacements and stresses are significantly nonlinear, and such variations are not captured correctly by the classical plate theory. Further, on the basis of the elasticity solution, the relative benefit of using a sandwich-like configuration versus a homogeneous plate is shown to depend on the span-to-thickness ratio and to decrease significantly as the plate becomes thick. PubDate: 2018-12-13

Abstract: In this paper, the consistent rotation-based formulation (CRBF) is used to develop new three-dimensional beam elements starting with the absolute nodal coordinate formulation (ANCF) kinematic description. While the proposed elements employ orientation parameters as nodal coordinates, independent rotation interpolation is avoided, leading to unique displacement and rotation fields. Furthermore, the proposed spatial ANCF/CRBF-based beam elements adhere to the noncommutative nature of the rotation parameters, allow for arbitrarily large three-dimensional rotation, and eliminate the need for using co-rotational or incremental solution procedures. Because the proposed elements have a general geometric description consistent with computational geometry methods, accurate definitions of the shear and bending deformations can be developed and evaluated, and curved structures and complex geometries can be systematically modeled. Three new spatial ANCF/CRBF beam elements, which use absolute positions and rotation parameters as nodal coordinates, are proposed. The time derivatives of the ANCF transverse position vector gradients at the nodes are expressed in terms of the time derivatives of rotation parameters using a nonlinear velocity transformation matrix. The velocity transformation leads to lower-dimensional elements that ensure the continuity of stresses and rotations at the element nodal points. The numerical results obtained from the proposed ANCF/CRBF elements are compared with the more general ANCF beam elements and with elements implemented in a commercial FE software. PubDate: 2018-12-13

Authors:Simon Schnabl; Igor Planinc Abstract: This paper presents a new mathematical model for analytical investigation of global buckling behavior of slender concrete-filled steel tubular (CFST) columns with circumferential gaps and partial debonding between the concrete core and the steel tube. The analytical buckling load of circular and slender CFST columns with circumferential gaps and partial debonding is derived for the first time. The critical buckling load decreases as the magnitude and length of the circumferential gap increases. Nevertheless, it is shown that if the length of the circumferential gap is smaller than the length of the CFST column, this effect is less than 4%. On the other hand, for a fully delaminated CFST column, this effect can be up to approximately 40%. Similarly, the first buckling shape modes proved to be notably affected by the circumferential gap only if its length is greater than 75% of the CFST column length. The results can be used as a benchmark solution for the buckling problem of slender circular CFST columns with circumferential gaps and partial debonding between the materials. PubDate: 2018-12-12 DOI: 10.1007/s00707-018-2322-0

Authors:Y. P. Zhang; N. Challamel; C. M. Wang; H. Zhang Abstract: This paper is concerned with the bending behaviour of small-scale simply supported plates as predicted by using the Eringen nonlocal plate model (ENM), the Hencky bar-net model (HBM) and the continualised nonlocal plate model (CNM). HBM comprises rigid beam segments connected by rotational and torsional springs. CNM is a nonlocal model derived by using a continualisation approach that does away with the unknown scale coefficient \(e_{0}\) in ENM. The exact bending solutions for simply supported rectangular nano-plates are derived by using ENM, HBM and CNM. By making the segment length \(\ell \) of HBM equal to the scale length of continualised and Eringen’s nonlocal plate model and noting the phenomenological similarities between ENM, HBM and CNM, the Eringen’s length scale value \(e_0 \) is found to be dependent on the aspect ratio of the simply supported plate and independent of the applied transverse loading. For a very small scale length \(\ell \) , \(e_0\) of ENM converges to values ranging from \(1/\sqrt{8}\) to \(1/\sqrt{6}\) for square plate to longish rectangular plate when calibrated by either HBM or CNM. PubDate: 2018-12-12 DOI: 10.1007/s00707-018-2326-9

Authors:Sergey V. Ershkov; Dmytro Leshchenko Abstract: In this paper, we proceed to develop a new approach which was formulated first in Ershkov (Acta Mech 228(7):2719–2723, 2017) for solving Poisson equations: a new type of the solving procedure for Euler–Poisson equations (rigid body rotation over the fixed point) is suggested in the current research. Meanwhile, the Euler–Poisson system of equations has been successfully explored for the existence of analytical solutions. As the main result, a new ansatz is suggested for solving Euler–Poisson equations: the Euler–Poisson equations are reduced to a system of three nonlinear ordinary differential equations of first order in regard to three functions \(\Omega _{i}\) ( \(i = 1, 2, 3\) ); the proper elegant approximate solution has been obtained as a set of quasi-periodic cycles via re-inversing the proper elliptical integral. So the system of Euler–Poisson equations is proved to have analytical solutions (in quadratures) only in classical simplifying cases: (1) Lagrange’s case, or (2) Kovalevskaya’s case or (3) Euler’s case or other well-known but particular cases. PubDate: 2018-12-11 DOI: 10.1007/s00707-018-2328-7

Authors:Hamed Farokhi; Mergen H. Ghayesh Abstract: The formulations for the modified couple stress theory (MCST) are consistently derived in general orthogonal curvilinear coordinate systems. In particular, the expressions for the rotation vector, higher-order strain, and stress tensors, i.e., the rotation gradient tensor and the deviatoric part of the symmetric couple stress tensor, and the classical strain and stress tensors are derived for an arbitrary orthogonal curvilinear coordinate system. Additionally, using the theory of surfaces, the formulations for the MCST are derived for general doubly curved coordinates, which are more convenient to use for shells of arbitrary curvature. The expressions for special cases, i.e., cylindrical and spherical shells, are obtained. The MCST expressions derived in this study are comprehensive and generally and can be used for consistent utilisation of the MCST in any orthogonal curvilinear coordinate system. PubDate: 2018-12-07 DOI: 10.1007/s00707-018-2331-z