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Archive of Applied Mechanics
Journal Prestige (SJR): 0.79  Citation Impact (citeScore): 2 Number of Followers: 6  Hybrid journal (It can contain Open Access articles)ISSN (Print) 0939-1533 - ISSN (Online) 1432-0681 Published by Springer-Verlag  [2658 journals]
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- Correction of post-necking stress–strain curve of copper using
surface strain method-
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Abstract: Correction of the stress–strain curve in the strained specimens after necking is one of the remarkable issues in mechanical engineering. The corrected curve strain–stress is needed to perform plastic or post-necking analysis in metals' large deformation issues. The stress becomes triaxle during the specimen's necking and includes tangential, radial, and circumferential stress components. The stress distribution is ununiformed in the necking area, and the actual stress is not obtained by dividing the force by the initial section surface. Instead, it is obtained by two different equations before and after necking. This research uses the surface strain method for a copper rod specimen on which several points are specified. The surface strain is obtained at any moment by measuring the distance between these points during the strain test using the image-processing technique. After computing the surface and radial strain, the correction factor is calculated using the relevant equations for determining the corrected actual stress values. The results are verified with the well-known results in the literature as presented by Davidenkov and Bridgham. Further, the finite element method is employed to perform numerical analysis. The commercial software ABAQUS is used to verify the results from image process analysis. The results show that determining the material model constants using the surface strain method does not require measurement of the necking radius at each moment during testing. Thus, this method outperforms the other ones in terms of simplicity, time, and accuracy. Additionally, the experimental and numerical are employed to present the corrected post-necking stress–strain curve.
PubDate: 2021-10-01
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- Surface effects on nano-contact based on surface energy density
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Abstract: In this paper, the two-dimensional nano-contact problem with the surface effect is systematically investigated based on Chen–Yao’s surface elastic theory. The Fourier integral transform method is adopted to derive the contact stress and displacement fields of a half-space subjected to a normal triangle distribution force. The theoretical result shows that the surface energy density of the indented bulk substrate, as only one additional parameter, serves as an important factor to influence the contact properties in contrast to the classical contact models. The numerical show that only when the ratio of the contact width to the volume surface energy density to the shear modulus is equal, the difference between the theoretical prediction of surface effect and the classical contact solution without surface effect will be significant. This result indicates that when the surface effect is considered and the surface effect parameter is positive, the semi-infinite substrate will harden, which should be helpful for better understanding the size-dependent mechanisms of surface energy density at nanoscale.
PubDate: 2021-10-01
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- A study on the mechanical response of magnesium using an anisotropic
elasticity twinning CP FEM-
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Abstract: Magnesium and its alloys are used in many applications due to their high strength-to-weight ratios. The poor formability which is caused by lack of available slip systems and the existence of twinning has been the major hindrance in expanding their usage to other new applications. In order to improve the formability of magnesium and its alloys, it is critical to understand the characteristics of the available slip and twin systems and the interactions among them. The slip activities occur due to dislocation motions, and twinning and dislocation motions interact with each other in order to reduce the overall plastic dissipation energy in deformation. Since the complex interaction hardening among slip and twin modes is not automatically realized by conventional standard CP (crystal plasticity) theories, additional measures must be included in the crystal plasticity constitutive theory to accurately represent the mechanical behavior of magnesium and its alloys. This paper takes into account interaction hardening among slip and twin modes by employing an interaction hardening model based on a physical property (saturation strength), which reduces trials and errors significantly in the stress–strain data fitting process. Taking into account elastic anisotropy, a twinning CP theory is proposed and an implicit time integration scheme for the proposed anisotropic elasticity twinning CP theory is derived in this study. The derived CP theory and the implicit time integration scheme are implemented into a large deformation FE code, and the single crystal channel-die compression tests and polycrystal uniaxial tension/compression tests of magnesium done in [1] are successfully reproduced by simulations. Using the anisotropic elasticity twinning CP FE code, the effects of strong elastic anisotropy on the convergence and stability of CP FE codes are investigated. Strong elastic anisotropy turns out to lower the stability and accuracy of CP FE codes, and the proposed implicit time integration scheme successfully overcomes these difficulties caused by strong elastic anisotropy.
PubDate: 2021-10-01
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- Influence of morphology on the effective hygro-elastic properties of
softwood (spruce) and hardwood (balsa)-
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Abstract: Wood materials are characterized by complex, hierarchical material structures spanning across various length scales. The present work aims at establishing a relation between the hygro-elastic properties at the mesoscopic cellular level and the effective material response at the macroscopic level, both for softwood (spruce) and hardwood (balsa). The particular aim is to explore the influence on the effective hygro-elastic properties under variations in the meso-scale morphology. The multi-scale framework applied for this purpose uses the method of asymptotic homogenization, which allows to accurately and efficiently obtain the effective response of heterogeneous materials characterized by complex meso-structural geometries. The meso-structural model considered for softwood is based on a periodic, two-dimensional statistically representative volume element that is generated by a spatial repetition of tracheid cells. The tracheid cells are modeled as hexagonal elements characterized by a certain geometrical irregularity. The hardwood meso-structure consists of a region composed of hexagonal cellular fibers with large vessels embedded, which is connected to a ray region that is constructed of ray cells. The hardwood fibers are modeled as hexagonal cellular elements, similar to softwood tracheids. The rays are represented by quadrilateral cells oriented along the radial direction, whereby different arrangements are considered, i.e., the ray cells are either regularly stacked or organized as a staggered configuration. The interface between the fiber and ray regions may also be characterized by a regular or a staggered arrangement. The meso-structural models for softwood and hardwood are discretized by means of plane-strain, finite element models, which describe the hygro-elastic response of the wood material in the radial–tangential plane. For softwood, the sensitivity of the effective elastic and hygro-expansive properties is explored as a function of the geometrical irregularity of the tracheids. For hardwood, the effective properties are studied under a variation of the ray cell arrangement, the type of interface between ray and fiber regions, and the vessel volume fraction. The modeling results agree well with results obtained from other numerical homogenization studies and show to be in reasonable agreement with experimental data taken from the literature.
PubDate: 2021-10-01
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- Nonlinear thermal analysis of multilayered composite and FGM plates with
temperature-dependent properties based on an asymptotic numerical method-
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Abstract: In this paper, a mathematical procedure is elaborated based on large deformation, finite element and perturbation methods for thermo-large amplitude analysis of anisotropic laminated and sandwich FGM plates with temperature-dependent properties. Nonlinear thermal dependence distribution following a power law is adapted. Various types of multilayered composite plates with position and temperature-dependent material properties are considered. Mathematical formulations and explicit relationships are presented in the frame of finite element methods. The structure is subjected to linear and uniform temperature variations. The temperature and the displacement are expanded in power series with unknown terms, and the numerical solution is obtained by the finite element method. The homotopy method is used for nonlinear thermal buckling, and a continuation procedure is elaborated for nonlinear thermal–displacement responses. The nonlinear thermal critical buckling load is first computed and the postbuckling equilibrium path of FGM and laminated plates under thermal loading is investigated. Temperature-dependent properties and geometry effects as well as boundary conditions on the nonlinear thermal buckling and postbuckling behaviors are analyzed.
PubDate: 2021-10-01
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- Analytical solution for torsion of cylindrical orthotropic annular
wedge-shaped bars reinforced by thin shells-
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Abstract: This paper deals with the Saint-Venant torsion of elastic, cylindrically orthotropic bar whose cross section is a sector of a circular ring shaped bar. The cylindrically orthotropic homogeneous elastic wedge-shaped bar strengthened by on its curved boundary surfaces by thin isotropic elastic shells. An analytical method is presented to obtain the Prandtl’s stress function, torsion function, torsional rigidity and shearing stresses. A numerical example illustrates the application of the developed analytical method.
PubDate: 2021-10-01
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- The reflection and transmission of a quasi-longitudinal displacement wave
at an imperfect interface between two nonlocal orthotropic micropolar
half-spaces-
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Abstract: This work is concerned with the reflection and transmission of quasi-longitudinal displacement wave incident at an imperfect interface between two nonlocal orthotropic micropolar half-spaces. The linear spring model is used to describe the imperfection of bonding behavior at the interface. Reflection, transmission coefficients and energy ratios of waves have been derived analytically for when a longitudinal displacement wave strikes for both imperfect and perfect interfaces. Finally, numerical examples are provided to show the effect of the imperfect interface, nonlocal parameter and incident angle on the reflection and transmission coefficients.
PubDate: 2021-10-01
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- Vibration response analysis of plate with microfloating raft arrays under
multi-point random excitation-
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Abstract: Inspired by the traditional floating raft vibration suppression system, in order to solve the problem of random vibration of the plate, through miniaturizing the floating raft system and using the microfloating raft arrays to replace the distributed dynamic vibration absorbers, a plate with microfloating raft arrays is constructed in this paper. The vibration response equation of the structure under multi-point random excitation is established by using modal superposition method. The auto-power spectral density (APSD) of displacement is obtained by using MATLAB, and the influence of system parameters on the vibration response is analyzed. Optimal combination of parameters is obtained by the generalized pattern search algorithm. Vibration reduction effect of this structure is analyzed. The results show that redistribution of microfloating raft element interval and an increase in the thickness, flexural rigidity and damping of the plate could increase the vibration suppression effect. It is also shown that an increase in mass ratio and stiffness ratio of the microfloating raft element could significantly reduce the vibration of the plate. When it achieves the optimal vibration suppression effect, the mass ratio, the stiffness ratio and the damping ratio are 0.3, 8.8562 and 4.7660, respectively. Compared with other plate structures, the plate with microfloating raft arrays of optimal parameter has the minimum APSD of displacement and minimum energy.
PubDate: 2021-10-01
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- Design of a robust control scheme for path tracking and beyond pull-in
stabilization of micro/nano-positioners in the presence of Casimir force
and external disturbances-
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Abstract: In this paper, attention was given to position control and path tracking of cantilever micro/nano-positioners subjected to Casimir force within and beyond the pull-in range. The material size dependency was incorporated in the model based on the modified couple stress theory. Using single-mode assumption, the system’s governing nonlinear partial differential equation (PDE) was transformed into a nonlinear state-space form. To verify the mathematical model, open-loop oscillations and the pull-in parameters were compared with the finite element simulation as well as experimental data. A robust non-singular terminal sliding mode controller with finite time convergence was designed to overcome the extending traveling rang problem in the presence of external disturbance. Finally, to compare the performance of the proposed controller, an optimal proportional integral derivative (PID) controller is designed and applied to the system. The achievements demonstrate that the designed controller can stabilize the system within and beyond the pull-in range without any fluctuation. Graphic abstract
PubDate: 2021-10-01
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- Longitudinal load distribution of a weakly connected prefabricated bridge
abutment-
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Abstract: A new type of prefabricated abutment with a weak connection is proposed. The longitudinal load (like banking force, earth pressure) distribution of this new type of prefabricated abutment was analyzed based on the hinge-joined slab method. A simplified method for calculating the stiffness parameters of the panels was introduced. The influence lines of the longitudinal load on the prefabricated abutment of an actual bridge were calculated by using the proposed theoretical method and finite element method. The comparison between theoretical calculation and simulation results shows that the theoretical calculation method proposed in this paper is correct. In order to investigate the influence of the different thicknesses of the cap beam and dimensions of prefabricated panels on the calculation error of the theoretical calculation method. The influence lines of the prefabricated abutments with different parameters were calculated theoretically and simulated. All calculation errors of the central values of influence lines were less than 20% when the thickness of the cap beam changes from 0.8 to 2.4 m, the errors were all less than 10% when the thickness of the cap beam was 1.2–1.575 m. This calculation further verified that the theoretical calculation method proposed in this paper is suitable for longitudinal load distribution of a weakly connected Prefabricated bridge abutment. It provides a reference for the design and theoretical calculation of prefabricated abutment.
PubDate: 2021-10-01
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- Study on shear buckling strength of curved corrugated steel webs for
bridges-
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Abstract: A theoretical formula for calculating the global shear buckling strength of curved corrugated steel webs (CSWs) under simply support conditions was derived. Their geometric parameters, namely the corrugation depth-to-web thickness ratio, web slenderness, and radius of curvature, which influence the elastic shear buckling strength, were also assessed. The computational error of the formula for the shear buckling of a curved CSW was verified to be within 2% using finite element analysis. Increasing the corrugation depth-to-web thickness ratio and decreasing web slenderness significantly reduced the elastic shear buckling strength. On the contrary, reducing the height of the web or increasing the web thickness had the opposite effect. Although the radius of curvature has little influence on the shear strength of a curved CSW, it significantly impacts the buckling mode. The results provide a theoretical reference for the design and application of curved CSW bridges.
PubDate: 2021-10-01
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- Comparison of discontinuous damage models of Mullins-type
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Abstract: The Mullins effect is a characteristic property of filled rubber materials whose accurate and efficient modelling is still a challenging task. Innumerable constitutive models for elastomers are described in the literature. Therefore, this contribution gives a review on some widely used approaches, presents a classification, proves their thermodynamic consistency, and discusses reasonable modifications. To reduce the wide range of models, the choice is restricted to those which reproduce the idealised, discontinuous Mullins effect. Apart from the theoretical considerations, two compounds were produced and tested under cyclic uniaxial and equibiaxial tension as well as pure shear. Based on this experimental data, a benchmark that compares the fitting quality of the discussed models is compiled and favourable approaches are identified. The results are a sound basis for establishing novel or improving existing rubber models.
PubDate: 2021-10-01
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- A mechanical method of tensile strength prediction for liquids with the
application of a new model for void nucleation-
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Abstract: A new model for void nucleation, employed in the mechanical method of tensile strength prediction for liquids, is presented in this paper based on classical nucleation theory and energy conservation analysis. The dependence of surface tension on void radius, which is presented in the method of Tolman’s correction, could influence the total energy for void nucleation, including the surface energy and the work of external tensile load. NAG (nucleation and growth) scheme is used in the present mechanical model to study the tensile process of the Al melt. The calculation results of material strength and void evolution of the melt under a high strain rate by using present mechanical method are studied and compared with those by MD (molecular dynamics) simulation.
PubDate: 2021-10-01
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- Numerical investigation of the MHD suction–injection model of viscous
fluid using a kernel-based method-
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Abstract: In this paper, a numerical investigation MHD squeezing flow between two parallel plates is presented. A method of stable approximation based on Gaussian Hilbert–Schmidt SVD (HS-SVD) is used. In the HS-SVD approach, by eliminating a significant portion of the ill-conditioning, an alternate basis for data-dependent subspace of “native” Hilbert space is obtained. The well-conditioning linear system is one of the critical advantages of using the alternate basis obtained from HS-SVD. There are three parameters A, S, and M, in the dimensionless equations and the effect of parameters on the flow field is investigated. The results show that by increasing Hartmann number (M) the axial velocity of the fluid flow decreases without a significant effect on the vertical velocity.
PubDate: 2021-10-01
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- A new numerical approach for determination of the Lemaitre’s ductile
damage parameter in bulk metal forming processes-
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Abstract: The damage of materials is the progressive or unexpected deterioration of mechanical strength because of loadings, thermal or chemical effects. The micromechanical damage process of ductile materials is generally studied by the continuum damage mechanics (CDM). One of the most well-known damage models is the Lemaitre’s ductile damage criterion. This model only requires one material-dependent parameter to represent damage evolution. In this investigation first, a novel numerical approach is proposed to determine the Lemaitre’s ductile damage parameter. Then, a user-defined material subroutine founded on the Lemaitre’s ductile damage model is developed. Following, numerical results are achieved for a standard round tensile test specimen. Finally, to validate the suggested method, experimental tests are carried out and compared with the numerical results. The comparison reveals a good agreement and excellent correlation between the numerical and practical results. Hence, it is concluded that the offered numerical approach can accurately determine the Lemaitre’s ductile damage parameter as well as the damage behavior of ductile metals.
PubDate: 2021-10-01
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- Large deformation analysis of two-dimensional visco-hyperelastic beams and
frames-
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Abstract: This contribution aims at developing a formulation for the large viscoelastic deformation of hyperelastic beams and frames under various loading and boundary conditions. To do so, the kinematics of deformation in two-dimensional space is formulated and basic kinematics and kinetic quantities are introduced. The quasi-linear viscoelasticity theory is employed to capture the time-dependent behavior of the underlying material. The corresponding time integration scheme and the consistent tangent moduli are then presented. Because of the highly nonlinear nature of governing equations at the large regime of deformations including time dependency, a nonlinear finite element formulation in the total Lagrangian framework is developed. Several numerical examples are provided to investigate the applicability of derived formulations. It is observed that the formulation can successfully capture the relaxation and creep phenomena in visco-hyperelastic beams and frames.
PubDate: 2021-10-01
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- Simulation of fully nonlinear water wave propagation over the flat bottom
and uneven bottom by meshless numerical wave tank-
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Abstract: A numerical wave tank (NWT) is developed by employing the local radial point interpolation collocation method, mixed Eulerian–Lagrangian approach, and the fourth-order Runge–Kutta method. The potential theory is used for a mathematical explanation of the wave-propagation problem. The Laplace equation in the Eulerian manner and the free surface conditions in the Lagrangian manner are used to simulate the fully nonlinear water waves. The incident waves are generated by imposing analytic forms of the potential on the upstream boundary. To avoid any reflection of the waves at the end of the tank, a damping zone is placed on the free surface before the downstream wall boundary. In order to demonstrate the efficiency and accuracy of the meshless NWT, the first-, second-, third-, and fifth-order Stokes waves are simulated and the numerical results are compared with the analytical solutions. In addition, the wave propagation of water waves in uneven bottom NWT is investigated. Fairly good agreements between the numerical results, the analytical solutions, and experimental data are observed.
PubDate: 2021-10-01
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- Crack identification in laminated composites based on modal responses
using metaheuristics, artificial neural networks and response surface
method: a comparative study-
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Abstract: Structures that are difficult to maintain and access need to have an efficient and robust process for continuous monitoring. Such monitoring through damage detection and identification studies is present in several engineering applications as it allows that corrective measures be applied in order to guarantee the structural safety of a given structure, machine or equipment. In particular, laminated composite materials, often used in aeronautical structures, have a complex failure mechanism where delamination or cracks in these materials are often not visible on the surface. Thus, the use of optimization methods for the characterization of damages in these materials becomes relevant. In this study, both the metaheuristic sunflower optimization, the artificial neural networks and the response surface method were used to solve an inverse crack identification problem. The crack was modeled as a thin elliptical hole in a rectangular laminated plate numerically modeled using the finite element method. As a result of the methods used, different approaches to the problem were obtained that present reliable shape, size and position identification of a crack sized between 3 and 30 mm. The results showed substantial and promising results in the uses of both metaheuristic techniques and artificial neural networks. However, neural networks have a certain competitive advantage over optimization techniques as long as the data that feeds the model present a certain level of quantity and quality. Results obtained were able to identify all damage parameters (location, extension and orientation), with errors less than 1%.
PubDate: 2021-10-01
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- First- and second-order sensitivity analysis of finite element models
using extended complex variables method-
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Abstract: This paper proposed a robust novel method that is called the extended complex variables method (ECVM) for the first- and second-order sensitivity analysis. In the most previous versions of complex variables method, only an imaginary step was used to analyze the sensitivity. However, ECVM is employed both the real and imaginary parts to improve the efficiency of it. The proposed method is applied for several problems with a closed-form solution, and the results are compared by past methods. It is illustrated that the first-order sensitivity analysis is not influenced by the change of the step size for both the traditional and extended complex variables methods. However, it is shown that, unlike the complex variable’s method, the efficiency of ECVM is high and it is independent of the step size for calculating the second-order sensitivity. The range of accurate results for second-order sensitivity analysis by ECVM is between two until four times more than CVM and FDM. Hence, this approach is suggested as an appropriate technique for calculating simultaneously the first- and second-order sensitivities with high accuracy as well as low computational cost.
PubDate: 2021-10-01
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- A novel computational method for dynamic analysis of flexible sandwich
plates undergoing large deformation-
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Abstract: To account for the nonlinear dynamic effects of flexible sandwich plates undergoing large deformation, a computational method for dynamic analysis of flexible sandwich plates is studied. According to the characteristics of sandwich plates, a simplified plate model is proposed based on the Kirchhoff plate theory, in which the shear stiffness of the core plate is neglected and the stiffness for the whole plate is derived. For the dynamic problem of flexible multibody systems, a thin plate element has been studied based on the absolute nodal coordinate formulation (ANCF). Meanwhile, a method based on invariant tensors is proposed for calculating elastic forces and their Jacobians, which can be calculated during preprocessing and applied for programmed calculation. Using examples, the proposed computational method is verified to be feasible and accurate. In addition, a benchmark example and a double-pendulum model are used to verify the applicability and feasibility of our analytical method for flexible sandwich plates in flexible multibody systems. Therefore, this method lays a foundation for the study of flexible dynamics problems regarding multibody systems with sandwich plates.
PubDate: 2021-10-01
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