Authors:Baisheng Wu; Weijia Liu; Xiaoyang Wu Pages: 1919 - 1927 Abstract: A bandwidth method based on power ratio is proposed to evaluate the system damping by using frequency response functions. For single-degree freedom systems, exact formula for calculating damping ratio from displacement frequency response function is established. Additionally, an approximate formula to estimate the damping ratio from acceleration frequency response function is also derived. Both are represented in terms of the power ratio and the bandwidths relative to the corresponding peak frequencies. In contrast to the well-known half-power method, the proposed method can be used for relatively large damping ratios by selecting a corresponding high power ratio. The accuracy of the proposed formulas in damping estimation is investigated for a four-degree of freedom system by numerical experiments. The results show that by increasing the power ratio, the estimation errors in damping ratios for the four-degree of freedom system can be significantly reduced. PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1434-2 Issue No:Vol. 88, No. 11 (2018)

Authors:Florence Dinzart; Antoine Jeancolas; Napo Bonfoh; Hafid Sabar; Marius Mihaluta Pages: 1929 - 1944 Abstract: In this work, a new multi-coated inclusion model to determine the effective thermal conductivity of reinforced composite materials is developed. The methodology is based on Green’s functions technique and integral equation which gives the local thermal fields through concentration equations in each phase of the composite-inclusion. The solution is presented within the general framework of anisotropic thermal behavior of the phases and ellipsoidal inclusions. The effective behavior of multi-coated inclusion-reinforced material is determined within a ‘ \((N+1)\) -phase’ Generalized Self-Consistent Scheme. To assess the present model’s reliability, some comparisons with other micromechanical models and exact solutions are presented for different inclusions’ morphologies. The model is applied to two-phase materials, and the results are compared to bounds established for ellipsoidal shape. Some results for three-phase materials are given regarding the influence of the thermal contrast between phases and the shape of inclusions. PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1418-2 Issue No:Vol. 88, No. 11 (2018)

Authors:P. F. Pelz; M. M. G. Kuhr Pages: 1945 - 1951 Abstract: The interface of two normal colliding media is always unstable. This is true even for both media showing the same density. The common precondition for a Rayleigh–Taylor instability “the lighter medium pushes the heavier” is generalised for the case that two media experience different accelerations in a short period after colliding. The arithmetic average of the accelerations determines the evolution of the wavy interface shape. The theory is applicable for various technologies of impact welding, such as explosion and magnetic pulse welding. PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1420-8 Issue No:Vol. 88, No. 11 (2018)

Authors:Yinggang Miao; Bing Du; Muhammad Zakir Sheikh Pages: 1953 - 1964 Abstract: Metallic materials are mostly rate dependent in mechanical behavior, but their elastic modulus under high strain rate is hard to measure accurately. In this paper, two methodologies are proposed based on stress wave theory in hope of accurate measurement for metallic materials, for example Ti6Al4V alloy. One is based on the one-dimension stress wave propagation in a long Ti6Al4V bar, and the elastic modulus under a high strain rate is obtained from the calculated stress wave speed. The other technique is to utilize the integrated Hopkinson pressure bar made of Ti6Al4V material. The obtained elastic moduli from these methods are compared and analyzed, and the results are consistent with each other. The numerical simulations with cylindrical and dogbone-shaped specimens are conducted to show the influence of bar indentation on measurement accuracy. An alternative method is introduced based on the vertical split Hopkinson pressure bar, which can extend the integrated Hopkinson pressure bar method for most metallic materials with small bulk. The verification experiments are also conducted. Finally, the limiting strain rate is estimated for potential measurement problems. PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1422-6 Issue No:Vol. 88, No. 11 (2018)

Authors:Antonios I. Arvanitakis Pages: 1965 - 1973 Abstract: Internal variables in continuous media with a microstructure of multiple phases spatially distributed within its volume are discussed in this paper. However, in our analysis phase transition boundaries are represented implicitly under the use of the level-set formulation. Each level-set function representing an interface corresponds to an internal variable of state. Employing the general thermodynamic theory of internal variables within the framework of canonical thermomechanics, we derive the evolution equations for the level-set functions describing the motion of the interfaces inside a material. Finally, the concept of two internal variables and both dissipative and non-dissipative cases is discussed. PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1424-4 Issue No:Vol. 88, No. 11 (2018)

Authors:Lei Zhou; Jaan-Willem Simon; Stefanie Reese Pages: 1975 - 2001 Abstract: The finite element analysis of complex structures involves a high computational effort, since the equation system to be solved includes a large number of degrees of freedom. This holds particularly in nonlinear finite element analysis. In order to reduce the numerical effort, the total system is subdivided into substructures which are analyzed separately from each other. The computing time can be further reduced, if the number of degrees of freedom of the substructures and thereby the dimension of the global equation system are decreased. In the present paper, this is achieved by projection-based model order reduction applied at the level of the substructures. The corresponding modes include internal and boundary nodes. The precomputation is carried out either directly with respect to the global system or only on one representative substructure. For the coupling, a new surface-to-surface tied contact formulation based on the penalty method is presented which couples the reduced and unreduced substructures. This is also possible for non-matching meshes. Several nonlinear numerical examples are performed which show the feasibility of the new approach. PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1427-1 Issue No:Vol. 88, No. 11 (2018)

Authors:Tuan-Kiet Nguyen; Dinh-Huan Phan; Tan-Tung Phan; Anh-Vu Phan Pages: 2003 - 2016 Abstract: The use of the symmetric Galerkin boundary element method (SGBEM) for studying the quasi-static interaction between multiple growing micro-cracks is presented in this work. The micro-cracks can conveniently be modeled in infinite domains, and this type of analysis can be handled by the SGBEM in a straightforward manner. In fact, it reduces the size of the analysis due to the absence of a physical boundary. A quasi-static multi-crack growth model based upon the maximum hoop stress criterion (MHSC), and the SGBEM was developed in this work. An improved quarter-point crack-tip element and adjusted maximum crack increments were employed to enhance the accuracy and effectiveness of the crack growth prediction. The improved quarter-point element has been known for producing accurate stress intensity factors required by the MHSC, while the technique used to adjust the maximum crack increment at each iteration of crack growth simulations allows to achieve converged (accurate) crack extension paths even if a relatively large maximum crack increment is selected at the onset. Several numerical examples were presented to show the effectiveness of the proposed multi-crack growth model. PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1430-6 Issue No:Vol. 88, No. 11 (2018)

Authors:Vahid Monfared Pages: 2017 - 2030 Abstract: In this research work, hydrostatic stress behavior of creeping composite is predicted using Legendre polynomials (special functions), governing and basic equations, micromechanics model and golden functions. Prediction of the creep hydrostatic stress behavior is experimentally complicated and intricate and sometimes is impossible. Significant applications of the present model are in the fields of plasticity and elasticity analyses, nanocomposites, turbine blades and disks design. The present analytical method can prevent from difficulties arising from the experimental and finite element methods. Also, the regions under the creep rupture and debonding are predicted by finite element method. Finally, because of using the analytic, controller and golden functions, good and reasonable agreements are found among FEM, experimental method and present analytical method results. PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1432-4 Issue No:Vol. 88, No. 11 (2018)

Authors:Dongquan Wu; Hongyang Jing; Lianyong Xu; Lei Zhao; Yongdian Han Pages: 2031 - 2050 Abstract: The numerical simulation and a new theoretical approach were conducted to investigate the creep crack initiation (CCI) time and the effect of constraints induced by the specimen thickness of P92 steel. The theoretical enhanced \(C^{*}-Q^{*}\) approach, which considered the load-independent constraint parameter \(Q^{*}\) , was proposed to predict the CCI time around a sharp crack tip. Moreover, finite element analysis was used to verify the load independence of parameter \(Q^{*}\) as the value of \({C}^{*}\) varied. The larger thickness of the compact tension (CT) specimen contributed to a larger constraint parameter \(Q^{*}\) , and the highly constrained CT specimens with larger thicknesses observably showed lower CCI times. The variation of hydrostatic stresses, triaxiality and multiaxial strain factor considering the constraint was discussed. The suitability of the analytical approach was verified to predict CCI, and the comparison between analytical and simulated results demonstrated that the \(C^{*}-Q^{*}\) two-parameter prediction approach under stress intensity factor and Riedel–Rice (K-RR) control (initially by K, then by transient creep stress or Riedel–Rice conditions) and Hutchinson–Rice–Rosengren and Riedel–Rice (HRR-RR) control (initially by plastic HRR control, then by RR conditions) could conservatively and effectively characterize the CCI times. The K-RR solutions were more accurate when initial stress intensity factor \({K}<6\,\hbox {MPam}^{1/2}\) , and the HRR-RR solutions were more appropriate when \({K}>6\,\hbox {MPam}^{1/2}\) . PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1433-3 Issue No:Vol. 88, No. 11 (2018)

Authors:Murat Kandaz; Hüsnü Dal Pages: 2051 - 2070 Abstract: Microbeams are common structures encountered in micro- and nano-electromechanical systems. Their mechanical response cannot be modelled by local theories of continuum mechanics due to size effect, which becomes more pronounced as the structural length scale approaches the microstructural length scale. The size effect can be circumvented by higher-order continuum theories. In this study, Euler–Bernoulli microbeams are analysed with modified strain gradient theory (MSGT) and modified couple stress theory (MCST). The weak forms for the numerical implementation are obtained by using variational methods. Then, the set of algebraic equations for the finite element method are derived. As a novel aspect, the performance of MSGT and MCST is compared and the length scale parameters of these theories are identified for gold microbeams from the existing experimental results in the literature. With the help of the identified parameters, the cut-off point for the applicability of the classical beam theories for gold microbeams is assessed. The study suggests use of higher-order theories for the state-of-the-art gold microbeam structures having thickness \(t<30\,\upmu {\hbox {m}}\) . PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1436-0 Issue No:Vol. 88, No. 11 (2018)

Authors:Shuohua Zhang; Ruijun Zhang; Qin He; Dongsheng Cong Pages: 2071 - 2080 Abstract: Guide rails are important part of the elevator guide system, which is significant to its dynamic characteristics that influence the vibration of the elevator system. In this study, the researchers set up a guide rail, guide shoe and car coupling system model which is based on the interaction relationship between guide rail, guide shoe and car. The influence of the three parameters such as the length, weight per unit length and the bending stiffness on the dynamic characteristics of the guide rail is analyzed by applying above model, using the step-by-step integration integral method under the discrete variables. The results showed that weight per unit length affects the quiver of the guide rail. The bending stiffness of the guide rail mainly affects the vibration displacement, the length, which has a significant influence on the vibration displacement and the quiver of the guide rail. The results reveal the inherent law between the structural parameters and the dynamic characteristics, which will provide theoretical guidance for the manufacture and selection of the guide rail and the design of the elevator. PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1437-z Issue No:Vol. 88, No. 11 (2018)

Authors:Rolf Mahnken; Peter Lenz; Christian Dammann Pages: 2081 - 2099 Abstract: This work presents the derivation of the effective shear modulus for a heterogeneous material composed of multilayered composite spheres embedded in a linear elastic matrix. It is based on the composite spheres model known from the literature. In contrast to Herve and Zaoui (Int J Eng Sci 31:1–10, 1993), the effective shear modulus is obtained by equating the results of two models: In the first model, a heterogeneous sphere is embedded in an equivalent homogeneous material, whereas in the second model, the heterogeneous sphere is replaced by an equivalent homogeneous sphere. In the context of both, a shear stress approach and a shear deformation approach, this results in an overdetermined system of equations which is solved with the least squares method. In a numerical study, our results are compared to effective moduli and bounds from the literature. Furthermore, a convincing agreement with experimental data for glass microspheres embedded in a polyester matrix is demonstrated. PubDate: 2018-11-01 DOI: 10.1007/s00419-018-1431-5 Issue No:Vol. 88, No. 11 (2018)

Authors:H. Borja da Rocha; L. Truskinovsky Abstract: We study thermally activated unzipping, which is modeled as a debonding process. The system is modeled as a parallel bundle of elastically interacting breakable units loaded through a series spring. Using equilibrium statistical mechanics, we compute the reversible response of this mechanical system under quasi-static driving. Depending on the stiffness of the series spring, the system exhibits either ductile behavior, characterized by noncooperative debonding, or brittle behavior, with a highly correlated detachment of the whole bundle. We show that the ductile to brittle transition is of the second order and that it can also be controlled by temperature. PubDate: 2018-11-07 DOI: 10.1007/s00419-018-1485-4

Authors:Teik-Cheng Lim Abstract: This paper evaluates the longitudinal wave speed through a plate in which its two opposing sides are elastically restrained in the width direction, taking into consideration the material auxeticity and strain as well as changes to the density and cross-sectional area. Apart from the known role of Young’s modulus and density, the present results reveal that the wave speed can be enhanced by increasing the width elastic restraint. In the case of high elastic restraint, the speed of both tensile and compressive waves can be minimized by selecting plate materials with Poisson’s ratio of low magnitude. In the case of low elastic restraint, the speed of tensile and compressive waves can be greatly reduced by selecting plate materials with large positive and large negative Poisson’s ratio, respectively. For the special case of negligible strain, the longitudinal wave speed reduces to the elementary wave speed in prismatic rods and in plates of infinite width when the width elastic restraint stiffness approaches zero and infinity, respectively. The obtained results not only avail more parameters for adjusting the longitudinal waves in plates, but also identify the differing methods of effectively controlling the wave speed between tensile and compressive waves when the strain magnitude is non-negligible. PubDate: 2018-10-31 DOI: 10.1007/s00419-018-1484-5

Authors:Karsten Buckmann; Björn Kiefer; Thorsten Bartel; Andreas Menzel Abstract: Microstructure evolution in magnetic materials is typically a non-local effect, in the sense that the behaviour at a material point depends on the magnetostatic energy stored within the demagnetisation field in the entire domain. To account for this, we propose a finite element framework in which the internal state variables parameterising the magnetic and crystallographic microstructure are treated as global fields, optimising a global potential. Contrary to conventional micromagnetics, however, the microscale is not spatially resolved and exchange energy terms are neglected in this approach. The influence of microstructure evolution is rather incorporated in an effective manner, which allows the computation of meso- and macroscale problems. This approach necessitates the development and implementation of novel mixed finite element formulations. It further requires the enforcement of inequality constraints at the global level. To handle the latter, we employ Fischer–Burmeister complementarity functions and introduce the associated Lagrange multipliers as additional nodal degrees-of-freedom. As a particular application of this general methodology, a recently established energy-relaxation-based model for magnetic shape memory behaviour is implemented and tested. Special cases—including ellipsoidal specimen geometries—are used to verify the magnetisation and field-induced strain responses obtained from finite element simulations by comparison to calculations based on the demagnetisation factor concept. PubDate: 2018-10-31 DOI: 10.1007/s00419-018-1482-7

Authors:Di-sheng Ou; Xiong-xin Zhou; Mao-hua Lin; C. T. Tsai Abstract: For engineering structures, the limits of internal stresses, nodal displacements and fundamental frequencies must be simultaneously considered. This had been paid attention in the theory of structural optimization. Actually, most examples of only considering static constraints or only considering dynamic constraints were presented for simultaneously considering static and dynamic constraints. A few examples of considering both static and dynamic constraints were presented, but the advantage could not be presented. It is the reason that the singularity of structural optimization for considering dynamic constraints has not been discussed. To discover the singularity, an optimization model to simultaneously consider static and dynamic constraints is used for the truss size optimization. And according to the extremum conditions of the optimization problem, Ratio-Extremum method is proposed to solve the optimization problems of considering both static and dynamic constraints and only considering dynamic constraints, in which a new searching direction of design variables is to be discussed. Particularly, the step-size factors can be determined by formulas to iteratively solve Lagrangian multipliers and design variables. Numerical examples of 15-bar planar and 72-bar spatial trusses are used to show the singular solutions. On the convergent points, the optimization weights of only considering dynamic constraints are about 66.17% and 71.14% more than the weights of considering both static and dynamic constraints, respectively. The convergent solutions of only considering dynamic constraints are not the best results. However, additional static constraints can be helpful to obtain better results for considering dynamic constraints. PubDate: 2018-10-30 DOI: 10.1007/s00419-018-1483-6

Authors:Wolfgang Dornisch; David Schrade; Bai-Xiang Xu; Marc-André Keip; Ralf Müller Abstract: The combination of materials with either pronounced ferroelectric or ferromagnetic effect characterizes multiferroic heterostructures, whereby the different materials can be arranged in layers, columns or inclusions. The magnetization can be controlled by the application of electrical fields through a purely mechanical coupling at the interfaces between the different materials. Thus, a magneto-electric coupling effect is obtained. Within a continuum mechanics formulation, a phase field is used to describe the polarization and the magnetization in the ferroelectric and ferromagnetic layers, respectively. The coupling between polarization/magnetization and strains within the layers, in combination with the mechanical coupling at the sharp layer interfaces, yields the magneto-electric coupling within the heterostructure. The continuum formulations for both layers are discretized in order to make the differential equations amenable to a numerical solution with the finite element method. A state-of-the-art approach is used for the ferroelectric layer. The material behavior of the ferromagnetic layer is described by a continuum formulation from the literature, which is discretized using a newly proposed approach for the consistent interpolation of the magnetization vector. Four numerical examples are presented which show the applicability of the newly proposed approach for the ferromagnetic layer as well as the possibility to simulate magneto-electric coupling in multiferroic heterostructures. PubDate: 2018-10-30 DOI: 10.1007/s00419-018-1480-9

Authors:John T. Katsikadelis Abstract: In this investigation, an answer is given to the question of whether Newton’s law of motion is of integer or non-integer, i.e., fractional, order differential form. The answer is given by seeking Newton’s law of motion in the form of a fractional differential operator. Then, applying an identification procedure using separately virtual Galileo’s experimental data on the inclined plane and Kepler’s laws of planetary motion, the fractional differential operator is established yielding the equation of motion. Both identifications yield the law of motion in the form of a fractional differential equation, which is converted into a second-order differential equation, verifying thus that for a body with constant mass Newton’s law of motion is indeed of integer differential form. PubDate: 2018-10-30 DOI: 10.1007/s00419-018-1486-3

Authors:A. H. Karimi; M. Shadmani Abstract: In this paper, nonlinear vibration of an Euler–Bernoulli beam excited by a harmonic random axial force is studied. The equation of motion contains a term with time-varying coefficient which is solved by modified Lindstedt–Poincaré method. Then the effect of the random axial force on the response is investigated using the obtained approximate solution. Two cases are considered in random analysis, namely random amplitude and random phase of the axial force. For both cases, the ensemble average, mean square value and the autocorrelation function are obtained. The results have indicated that for each case the mean and the mean square value are a function of time which means that the lateral displacement of the beam is a nonstationary process. A numerical study is also conducted based on the iteration of numerical solution in order to verify the derived analytical formulae. It is shown that a good agreement is seen between the analytical and numerical solution statistical properties. PubDate: 2018-10-29 DOI: 10.1007/s00419-018-1474-7

Authors:Andrej Likeb; Nenad Gubeljak; Yury Matvienko Abstract: For safe transport and reliable supply of petrochemical substances, it is crucial to ensure the structural integrity of the equipment, pipelines in particular. Regarding the large diameters and high mass per distance, pipelines for natural gas are designed as thin-walled cylindrical structures. To ensure the structural integrity of the unknown material means to measure and therefore empirically test the material fracture properties of the laboratory specimen for giving an assessment of the accepted defect size. Compared to standards and regulations, such as the ASTM E-1820, BS 7448 standards and the GKSS procedure, the production of standard specimens for measuring the fracture toughness is commonly very difficult or even impossible for applications. On the basis of the Slovenian–Russian bilateral project, we investigate and propose a solution for this issue with a new kind of specimen, called the pipe-ring specimen. The specimens were made from a segment of the observed thin-walled pipeline from the construction filed or stored in a warehouse. The measurement procedure is similar as for the standard SENB specimens and extensometer because of the geometry of the specimen, which is cut from the pipe and contains only a machine-made notch. The next step is to test specimens axially on the three-point bending load test on the hydraulic machine. Because the ring as the specimen is not standardized, it is necessary to show and prove how, and if it is possible to use ring specimens as an alternative option to the standard specimens for testing and determining fracture properties of testing material for thin-walled pipelines. In the frame of the three main experimental, analytical and numerical approaches, this publication shows the numerical approach of defining the stress intensity factor (SIF) for crack opening mode I with and without prior fatigue pre-cracking. Besides the limit load, the SIF presents one of two main parameters for developing the failure assessment diagram and estimating the possible accepted defects in a material relating to its’ structural integrity. PubDate: 2018-10-25 DOI: 10.1007/s00419-018-1481-8