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 Subjects -> MATHEMATICS (Total: 1022 journals)     - APPLIED MATHEMATICS (84 journals)    - GEOMETRY AND TOPOLOGY (21 journals)    - MATHEMATICS (757 journals)    - MATHEMATICS (GENERAL) (41 journals)    - NUMERICAL ANALYSIS (22 journals)    - PROBABILITIES AND MATH STATISTICS (97 journals) MATHEMATICS (757 journals)                  1 2 3 4 | Last

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 Archive of Applied MechanicsJournal Prestige (SJR): 0.79 Citation Impact (citeScore): 2Number of Followers: 6      Hybrid journal (It can contain Open Access articles) ISSN (Print) 0939-1533 - ISSN (Online) 1432-0681 Published by Springer-Verlag  [2351 journals]
• In-plane vibration of a circular ring with arbitrary concentrated elements
by an analytical method
• Abstract: This paper investigates the vibration characteristics of a circular ring with an arbitrary number of concentrated elements based on the Hamilton principle. The shear and inertia effects are introduced to the variational functional of system kinetic and potential energy by adopting the generalized shell theory. The concentrated elements are treated as the concentrated masses with elastic boundary condition. The system vibration displacements are analytically expanded in the form of Fourier series and substituted into the variational functional to obtain the equation of motion. Computed results are compared with those solutions obtained from the finite element program ANSYS to validate the accuracy of the present method. Effects of the asymmetrical concentrated elements on the convergence of circumferential wavenumbers are discussed. Moreover, the coupling characteristics of different circumferential wavenumbers caused by the asymmetrical or symmetrical concentrated elements and their influences on the vibration response characteristics of the system under simple harmonic excitations are studied.
PubDate: 2019-06-17

• Motion spaces of machine–process combinations
• Abstract: Machines and mechanisms realize processes, from the shaping process of a milling machine to the motion process of an automotive system. The dynamics of a machine generated by a properly chosen set of constraints in combination with an appropriate drive system is designed to meet the prescribed requirements of the process, which is done by projecting the machine equations of motion on the process dynamics. We get a set of nonlinear relations, which represent the machine motion in terms of the required process motion. A well-known example is the projection of arbitrarily many robot degrees of freedom on one given path degree of freedom resulting in a set for evaluating possible motion spaces, now supplemented also by constraint force spaces, helpful for design and optimization. For multidimensional processes, things become more complex but feasible. This paper presents a corresponding approach applying multibody system theory in combination with transformations from the machine side to the process side and vice versa. Practical aspects are discussed and examples given.
PubDate: 2019-06-11

• Dynamics and motion control of a capsule robot with an opposing spring
• Abstract: Non-classical locomotion systems have the perspective for a wide application in the vast fields of bio-medical and maintenance technology. Capsule bots are small, simple, and reliable realizations with a great potential for practical application. In this paper, the motion of a capsule-type mobile robot along a straight line on a rough horizontal plane is studied applying analytical and experimental methods. The robot consists of a housing and an internal body attached to the housing by a spring. The motion of the system is generated by a force that acts between the housing and the internal body and changes periodically in a pulse-width mode. The average velocity of the motion of the robot is studied as a function of the excitation parameters. The results from the model-based and experimental investigations agree with each other. It can be concluded that the presented robot design can be a basis for the creation of mobile robotic systems with locomotion properties that can be controlled by the parameters of a periodic actuation force.
PubDate: 2019-06-11

• Bending of beams with bisymmetrical cross sections under non-uniformly
distributed load: analytical and numerical-FEM studies
• Abstract: The paper is devoted to simply supported beams subjected to non-uniformly distributed loads. Shapes of bisymmetrical cross sections of the beams are expressed by special functions. The analytical model of the beams is formulated with consideration of the shear effect. A nonlinear hypothesis of deformation of a planar cross section of beams is assumed. The bending moment and the shear transverse force are formulated. Moreover, numerical-FEM models of the beams are developed. Deflections are calculated with the use of two methods for an exemplary beam family. The results of the studies are presented in tables.
PubDate: 2019-06-05

• Correction to: Mean stress effect in multiaxial fatigue limit criteria
• Abstract: The calculation of the parameter was written without last operations (addition of 1, squaring the product, subtraction of 1).
PubDate: 2019-06-04

• An approach to predict human–structure interaction in the case of
staircases
• Abstract: This paper presents a general approach for modelling human–structure interaction in the case of vertical vibrations that is based on a model of the system and on a solution procedure that is able to account for the most complex dynamic conditions, such as people ascending/descending light staircases. The approach combines the effects of changes in pedestrians’ positions along the structure and changes in pedestrians’ postures during movement. Furthermore, the model used describes the coupled system composed by the structure and the people on the structure, splitting the actions of pedestrians into two components: passive and active forces. This approach and two further enhancements of the model were used to evaluate the dynamic interactions between pedestrians and a staircase, and the results were validated via an extensive experimental campaign carried out using a staircase in the Bovisa Campus of Politecnico di Milano as a test case structure.
PubDate: 2019-06-01

• Advanced modeling of ferroic materials
• PubDate: 2019-06-01

• 3D magnetostrictive Preisach model for the analysis of magneto-electric
composites
• Abstract: In the present contribution, we compare numerical simulations of magneto-electric composites with experimental measurements. The coupling between electric polarization and magnetization of such materials can improve the operation of sensors and actuators and can enable new technical devices. These composites consist of a ferroelectric and a magnetostrictive phase and generate the ME coupling as a strain-induced product property. However, the responses of the individual phases are highly nonlinear. It is important to predict the behaviors of both phases in an appropriate manner to ensure a realistic prediction of the magneto-electric coefficient. Therefore, we simulate the nonlinear ferroelectric hysteresis curves based on the ferroelectric and ferroelastic switching behavior of the spontaneous polarization directions on the submicroscopic level. Therefore, a switching criterion considering the change in the free energy is evaluated. For the simulation of the magnetostrictive behavior, we derive in this contribution a three-dimensional Preisach model. For this, the classical scalar Preisach model acts on a rotational time-dependent magnetization vector. After a homogenization approach within the finite-element ( $$\hbox {FE}^2$$ )-method, the effective macroscopic hysteresis curves are obtained. Furthermore, the magneto-electric coefficient is obtained from the homogenization and compared with experimental measurements in terms of magnitude and nonlinear behavior.
PubDate: 2019-06-01

• A two-scale homogenization analysis of porous magneto-electric two-phase
composites
• Abstract: A computational homogenization analysis for the simulation of porous magneto-electric composite materials is presented. These materials combine two or more ferroic states with each other enabling a coupling between magnetization and electric polarization. This magneto-electric coupling finds application in sensor technology or data storage devices. Since most single-phase multiferroics show coupling at very low temperatures beyond technically relevant applications, two-phase composites, consisting of a ferroelectric and a ferromagnetic phases, are manufactured. They generate a strain-induced magneto-electric coupling at room temperature. The performance and reliability of these materials is influenced by defects or pores, which can arise during the manufacturing process. We analyze the impact of pores on the magnitude of the magneto-electric coupling coefficient. In order to determine the effective properties of the composite, a two-scale finite element ( $$\hbox {FE}^2$$ ) homogenization approach is performed. It combines the macroscopic and microscopic scale by direct incorporation of the microscopic morphology. We derive the basic equations for the localization and the homogenization of the individual field variables and give an algorithmic expression for the effective tangent moduli. We discuss the influence of pores on the magneto-electric coupling in two-phase composites by analyzing numerical examples.
PubDate: 2019-06-01

• On the emergence of out-of-plane ferroelectricity in ultrathin films
• Abstract: The presence of a spontaneous and switchable polarization is the defining property of a ferroelectric material. Such materials are indispensable in a countless number of industrial and scientific applications. Furthermore, the enhancement of ferroelectric property at reduced dimensions is crucial for continuous advancement in nanoelectronic applications. In this work, we investigate the onset of out-of-plane ferroelectricity in open-circuited stress-free BaTiO $$_3$$ ultrathin films by performing molecular dynamics simulations using the core–shell model potential. In doing so, we try to obtain electric polarization hysteresis loops using an appropriate range of external electric loading. It is found that out-of-plane ferroelectricity is suppressed in ultrathin films with thickness 10 or less than 10 unit cells, indicating that there exists a critical thickness for the emergence of out-of-plane ferroelectricity in ultrathin films. It is also found that the ultrathin films exhibit asymmetrical hysteresis loops slightly above the critical thickness.
PubDate: 2019-06-01

• FEM analysis of a multiferroic nanocomposite: comparison of experimental
data and numerical simulation
• Abstract: In this contribution, we analyze the properties of two-phase magneto-electric (ME) composites. Such ME composite materials have raised scientific attention in the last decades due to many possible applications in a wide range of technical devices. Since the effective magneto-electric properties significantly depend on the microscopic morphology, we investigate in more detail the changes in the in-plane polarization due to an applied magnetic field. It was shown in previous works that it is possible to grow vertically aligned nanopillars of magnetostrictive cobalt ferrite in a piezoelectric barium titanate matrix by pulsed laser deposition. Based on x-ray linear dichroism, the displacements of titanate ions in the matrix material can be measured due to an applied magnetic field near the boundary of the interface between the matrix and the nanopillars. Here, we focus on (1–3) fiber-induced composites, based on previous experiments, where cobalt ferrite nanopillars are embedded in a barium titanate matrix. In the numerical simulations, we adjusted the boundary value problem to match the experimental setup and compare the results with previously made assumptions of the in-plane polarizations. A further focus is taken on the deformation behavior of the nanopillar over its whole height. Such considerations validate the assumption of the distortion of the nanopillars under an external magnetic field. Furthermore, we analyze the resulting magneto-electric coupling coefficient.
PubDate: 2019-06-01

• Simulation of magnetised microstructure evolution based on a
micromagnetics-inspired FE framework: application to magnetic shape memory
behaviour
• 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: 2019-06-01

• Analysis of an optimization problem for a piezoelectric energy harvester
• Abstract: The problem of optimal energy harvesting for a piezoelectric element driven by mechanical vibrations is stated in terms of an ODE system with hysteresis under the time derivative coupling a mechanical oscillator with an electric circuit with or without inductance. In the piezoelectric constitutive law, both the self-similar piezoelectric butterfly character of the hysteresis curves and feedback effects are taken into account in a thermodynamically consistent way. The physical parameters of the harvester are chosen to be the control variable, and the goal is to maximize the harvested energy for a given mechanical load and a given time interval. If hysteresis is modeled by the Preisach operator, the system is shown to be well-posed with continuous data dependence. For the special case of the play operator, we derive first-order necessary optimality conditions and an explicit form of the gradient of the total harvested energy functional in terms of solutions to the adjoint system.
PubDate: 2019-06-01

• Constitutive modeling of polycrystalline multiconstituent and multiphase
ferroic materials based on a condensed approach
• Abstract: The constitutive behavior of polycrystalline ferroelectric or ferromagnetic materials is essentially determined by ferroelectric domain and ferromagnetic Bloch or Neel wall motions, respectively, on the one hand and grain interactions on the other. In physically motivated models, domain switching and the rotation of elementary magnets, respectively, are directly considered coping with the first issue. In phenomenological macroscale approaches, both domain processes and grain interactions are merged in one constitutive model. The implementation of constitutive equations into a finite element code provides intrinsic interactions due to the coupling of physical quantities on the node- and element-level. The condensed approach is based on microphysical considerations of domains and accounts for grain interaction on the level of generalized residual stresses due to mismatches of individual grains and the associated effective medium. The approach is first applied to the prediction of magnetoelectric coupling in a multiferroic ferroelectric–ferromagnetic compound, where its basic idea is translated to model interactions of the constituents without going back to any discretization scheme. Second, a tetragonal–rhombohedral ferroelectric composition is considered with associated interactions in multiphase grains.
PubDate: 2019-06-01

• Investigations on enhanced Fischer–Burmeister NCP functions: application
to a rate-dependent model for ferroelectrics
• Abstract: This contribution deals with investigations on enhanced Fischer–Burmeister nonlinear complementarity problem (NCP) functions applied to a rate-dependent laminate-based material model for ferroelectrics. The framework is based on the modelling and parametrisation of the material’s microstructure via laminates together with the respective volume fractions. These volume fractions are treated as internal-state variables and are subject to several inequality constraints which can be treated in terms of Karush–Kuhn–Tucker conditions. The Fischer–Burmeister NCP function provides a sophisticated scheme to incorporate Karush–Kuhn–Tucker-type conditions into calculations of internal-state variables. However, these functions are prone to numerical instabilities in their original form. Therefore, some enhanced formulations of the Fischer–Burmeister ansatz are discussed and compared to each other in this contribution.
PubDate: 2019-06-01

• Coupled phase field simulations of ferroelectric and ferromagnetic layers
in multiferroic heterostructures
• 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: 2019-06-01

• Shape optimization of material inclusions in dielectric elastomer
composites
• Abstract: In recent years, dielectric elastomers became a new alternative in the field of actuation technology. Because of the softness of these materials, they can be deformed in a finite strain regime under the application of electric fields. Due to the low relative permittivity, the electromechanical coupling is weak which makes large electric fields in the range of 20–30 MV/m necessary for large actuation purposes. To overcome this handicap, composite materials consisting of an elastomer matrix with ceramic inclusion have been proposed in the last years. The present work aims at an analysis of the compressive deformation of the composite by a numerical comparison of three inclusion geometries. The results show optimization possibilities regarding the shape of the inclusion which allow for larger dielectric elastomer deformations at lower applied electric fields.
PubDate: 2019-06-01

• Periodic boundary conditions for the simulation of 3D domain patterns in
tetragonal ferroelectric material
• Abstract: Periodic domain patterns in tetragonal ferroelectrics are explored using a phase field model calibrated for barium titanate. In this context, we discuss the standard periodic boundary condition and introduce the concept of reverse periodic boundary conditions. Both concepts allow the assembly of cubic cells in accordance with mechanical and electrical conditions. However, application of the reverse periodic boundary condition is due to an increased size of the RVE and enforces more complex structures compared to the standard condition. This may be of particular interest for other multiphysics simulations. Additionally, we formulate mechanical side conditions with minimal spherical (hydrostatic) stress, or conditions with controlled average strain. It is found that in sufficiently small periodic cells, only a uniform single domain, or the simplest stripe domains constitute equilibrium states. However, once the periodic cells are of order 20 domain wall widths in size, more complex, 3-dimensional patterns emerge. Some of these patterns are known from prior studies, but we also identify other domain patterns with long, ribbon-like domains threaded through them and some vortex-like structures.
PubDate: 2019-06-01

• Micromechanical simulation of ferroelectric domain processes at crack tips
• Abstract: The electromechanical loading situation at cracks in ferroelectric ceramics is essentially affected by domain switching. Under high electrical and/or mechanical external fields, the state of polarization and remanent strains is substantially changed at the crack tip. These irreversible dissipative processes influence the fracture toughness of the cracked ferroelectric material. In the present paper, the micromechanical domain switching processes at the crack tip are studied by numerical simulation and compared with the in situ experimental results obtained by Jones et al. (Acta Mater 55(16):5538–5548, 2007) using X-ray diffraction analyses in synchrotron. Main attention is payed to the spatial distribution of preferred domain orientation in a mechanically loaded compact tension specimen made of a soft tetragonal lead zirconate titanate ceramics. It is found that the mechanically induced favored domain orientation distribution depends on position within the plane of the CT specimen and correlates with projected deviatoric stresses and strains. Some issues concerning shortcomings in the experimental and simulation results are raised and discussed. The outcome of this type of simulations forms the basis for more realistic fracture mechanical evaluations in future.
PubDate: 2019-06-01

• A phase-field model for transversely isotropic ferroelectrics
• Abstract: We propose an electro-mechanically coupled phase-field model for ferroelectric materials that show cubic–tetragonal phase transition. The cubic phase is idealized by an isotropic formulation, and the tetragonal phase is idealized by a transversely isotropic formulation. We consider a classical phase-field model with Ginzburg–Landau-type evolution of the order parameter. The order parameter drives the transition of all involved moduli tensors such as elastic, dielectric and piezoelectric moduli, which in turn maintain their typical features and stability as a result of a selected phase-transition function. The model is described in coordinate-invariant form and implemented into a finite element framework with implicit time integration of the evolution equation. Representative numerical examples in two and three dimensions demonstrate the main features of the constitutive model and the numerical stability of the formulation.
PubDate: 2019-05-13

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