Showing papers in "Archive of Applied Mechanics in 2006"
TL;DR: In this paper, the authors discuss some of the recent advances in the field of stochastic structural mechanics and also solicit ideas on possible future developments in structural analysis and design, as well as provide a survey of the current state-of-the-art.
Abstract: Uncertainties are a central element in structural analysis and design. But even today they are frequently dealt with in an intuitive or qualitative way only. However, as already suggested 80 years ago, these uncertainties may be quantified by statistical and stochastic procedures. This contribution attempts to shed light on some of the recent advances in the now established field of stochastic structural mechanics and also solicit ideas on possible future developments.
123 citations
TL;DR: In this article, a finite element method is proposed that can capture arbitrary discontinuities in a two-phase medium by exploiting the partition-of-unity property of finite element shape functions.
Abstract: A finite element method is proposed that can capture arbitrary discontinuities in a two-phase medium. The discontinuity is described in an exact manner by exploiting the partition-of-unity property of finite element shape functions. The fluid flow away from the discontinuity is modelled in a standard fashion using Darcy’s relation, while at the discontinuity a discrete analogon of Darcy’s relation is proposed. The results of this finite element model are independent of the original discretisation, as is demonstrated by an example of shear banding in a biaxial, plane-strain specimen.
119 citations
TL;DR: In this paper, a review of the state of the art of FEM to compute the coupled electromechanical boundary value problem of cracks in 2D and 3D piezoelectric structures under static and dynamic loading is presented.
Abstract: Piezoelectric materials have widespread applications in modern technical areas such as mechatronics, smart structures or microsystem technology, where they serve as sensors or actuators. For the assessment of strength and reliability of piezoelectric structures under combined electrical and mechanical loading, the existence of cracklike defects plays an important role. Meanwhile, piezoelectric fracture mechanics has been established quite well, but its application to realistic crack configurations and loading situations in piezoelectric structures requires the use of numerical techniques as finite element methods (FEM) or boundary element methods (BEM). The aim of this paper is to review the state of the art of FEM to compute the coupled electromechanical boundary value problem of cracks in 2D and 3D piezoelectric structures under static and dynamic loading. In order to calculate the relevant fracture parameters very precisely and efficiently, the numerical treatment must account for the singularity of the mechanical and electrical fields at crack tips. The following specialized techniques are presented in detail (1) special singular crack tip elements, (2) determination of intensity factors K
I
–K
IV
from near tip fields, (3) modified crack closure integral, (4) computation of the electromechanical J-integral, and (5) exploitation of interaction integrals. Special emphasis is devoted to a realistic modeling of the dielectric medium inside the crack, leading to specific electric crack face boundary conditions. The accuracy, efficiency, and applicability of these techniques are examined by various example problems and discussed with respect to their advantages and drawbacks for practical applications.
108 citations
TL;DR: In this paper, the propagation of plane waves in a fiber-reinforced, anisotropic, generalized thermoelastic media is discussed, and the governing equations in x-y plane are solved to obtain a cubic equation in phase velocity.
Abstract: The propagation of plane waves in a fibre-reinforced, anisotropic, generalized thermoelastic media is discussed. The governing equations in x–y plane are solved to obtain a cubic equation in phase velocity. Three coupled waves, namely quasi-P, quasi-SV and quasi-thermal waves are shown to exist. The propagation of Rayleigh waves in stress free thermally insulated and transversely isotropic fibre-reinforced thermoelastic solid half-space is also investigated. The frequency equation is obtained for these waves. The velocities of the plane waves are shown graphically with the angle of propagation. The numerical results are also compared to those without thermal disturbances and anisotropy parameters.
84 citations
TL;DR: In this article, the bending effects of the imperfections of lattice materials were predicted and compared with the experiment results, showing that carbon reinforced lattice material is still much stiffer and stronger than foams and honeycombs.
Abstract: To acquire materials of higher specific stiffness and strength, stretching dominated lattice materials reinforced by carbon fibers were designed and manufactured. The mechanical behaviors were predicted and experimented. The imperfections of lattice materials, such as the waviness of the struts, non-circular cross-sections and cantilever ribs, greatly influenced their performance. The bending effects of the imperfections were predicted and compared with the experiment results. Although influenced by the imperfections, carbon reinforced lattice materials are still much stiffer and stronger than foams and honeycombs.
78 citations
TL;DR: In this paper, the authors focus on the case of deformable media which admit the existence of thermodynamically reversible phenomena by means of a diffusive internal variable of state, or alternately an additional degree of freedom, in any case presenting some weak nonlocality (gradient effects).
Abstract: Working in parallel on the energy equation in a special form and the associated canonical equation of momentum, we focus attention on the case of deformable media which are basically finitely elastic, but which also admit the existence of thermodynamicallyirreversible phenomena by means of a diffusive internal variable of state, or alternately an additional degree of freedom, in anycase presenting some weak nonlocality (gradient effects). Two descriptions follow thereof, one that can be called standard according to rational thermomechanics (there exists a generalized internal force or thermodynamically conjugated force for a variable and its gradient separately, and the entropy flux has its classical definition) or the so-called field-theoretic viewpoint in which only one generalized force (based on a variational derivative of the energy) is used. In the latter one, the entropy flux deviates form its classical definition but, simultaneously, by virtue of the space–time consistency, the Eshelby stress tensor has to be altered. Simple examples with diffusion of an internal variable illustrate these formulations that may be valuable in the description of some bio- and geomaterials.
78 citations
TL;DR: In this article, a stochastic stability (DH-stability) concept is introduced to quantify the lower bound on the size of representative volume elements (RVEs) for random heterogeneous materials.
Abstract: This paper details a procedure to determine lower bounds on the size of representative volume elements (RVEs) by which the size of the RVE can be quantified objectively for random heterogeneous materials. Here, attention is focused on granular materials with various distributions of inclusion size and volume fraction of inclusions. An extensive analysis of the RVE size dependence on the various parameters is performed. Both deterministic and stochastic parameters are analysed. Also, the effects of loading mode and the parameter of interest are studied. As the RVE size is a function of the material, some material properties such as Young's modulus and Poisson's ratio are analysed as factors that influence the RVE size. The lower bound of RVE size is found as a function of the stochastically distributed volume fraction of inclusions; thus the stochastic stability of the obtained results is assessed. To this end a newly defined concept of stochastic stability (DH-stability) is introduced by which stochastic effects can be included in the stability considerations. DH-stability can be seen as an extension of classical Lyapunov stability. As is shown, DH-stability provides an objective tool to establish the lower bound nature of RVEs for fluctuations in stochastic parameters.
71 citations
TL;DR: A theoretical approach based on the Dahl friction model that describes the friction reduction observed in the presence of the tangential vibrations at an arbitrary angle is presented in this article. But, the authors do not consider the effect of tangential compliance of the contacts.
Abstract: A reduction of friction by vibrations has been observed in various experiments This effect can be applied to actively control frictional forces by modulating vibrations Moreover, common methods of controlling friction rely on lubricants and suitable material combinations The superimposition of vibrations can further reduce the friction force This study presents a theoretical approach based on the Dahl friction model that describes the friction reduction observed in the presence of the tangential vibrations at an arbitrary angle Analysis results indicated that the tangential compliance should be considered in modeling the effect of vibrations in reducing friction At any vibration angle, the tangential compliance of the contacts reduces the friction reduction effect The vibrations parallel to the macroscopic velocity are most effective for friction reduction
69 citations
TL;DR: In this paper, the problem of thermoelastic interactions in an elastic infinite medium with cylindrical cavity at an elevated temperature field arising out of a ramp-type heating and loading bounding surface of the cavity, and the surface is assumed initially quiescent.
Abstract: This paper presents the problem of thermoelastic interactions in an elastic infinite medium with cylindrical cavity at an elevated temperature field arising out of a ramp-type heating and loading bounding surface of the cavity, and the surface is assumed initially quiescent. The governing equations are taken in a unified system from which the field equations for coupled thermoelasticity as well as for generalized thermoelasticity can be easily obtained as particular cases. Due attention has been paid to the finite time of rise of temperature, stress, displacement, and strain. The problem has been solved analytically using a direct approach. The derived analytical expressions have been computed for a specific situation. Numerical results for the temperature distribution, thermal stress, displacement, and strain are represented graphically. A comparison is made with the results predicted by the three theories.
58 citations
TL;DR: In this paper, the asymptotic stress field for a narrow notch with a rounded notch root is deduced from an Airy's stress function, and based on this stress field a fracture criterion is developed.
Abstract: Narrow notches often cause damage that can lead to the destruction of components. The stress field in the vicinity of such crack-like notches in two-dimensional (2D) structures is similar to the stress field around equivalent cracks. Therefore similar investigations are necessary to predict the fracture load for components with cracks or narrow notches. Thus, the asymptotical stress field for a narrow notch with a rounded notch root is deduced from an Airy’s stress function. Based on this stress field a fracture criterion is developed. Comparing the theoretical fracture limit curves derived from the fracture criterion with experimental results it can be shown that for brittle material the local stress state at the fracture initiation point is the same for mode I, mixed-mode and mode II loading.
54 citations
TL;DR: The inverse dynamic analysis based on measurements of the human gait for subjects with different kinds of disorders is presented and a method to estimate the energy expenditure for human motions is proposed.
Abstract: For the design and improvement of orthotic and prosthetic devices the biomechanical effort is an important criterion to obtain a more comfortable and natural gait of humans with gait disorders. In the first part of the paper the inverse dynamic analysis based on measurements of the human gait for subjects with different kinds of disorders is presented. The second part is devoted to a method to estimate the energy expenditure for human motions. This approach allows the computation of metabolical cost for human locomotion using Hill-type muscle models.
TL;DR: In this article, the authors investigated the characteristics of the unity-magnitude (UM) shaping coefficients as a function of system parameters and proposed an analysis procedure to obtain UM input shaper impulse time sequences, which is compared to the zero vibration (ZV) shaper in both response and robustness to modeling error.
Abstract: Command profiles are required to move a dynamical system from rest to rest without residual vibration in a minimum time. The unity-magnitude (UM) input shaper is one of the faster input shaping techniques. However, analytical solution of the impulse time locations is impossible due to the dependent residual vibration constraint equations. Many researchers solve these by using curve fitting. In this paper, the characteristics of the UM shaping coefficients as a function of system parameters are investigated. An analysis procedure to obtain UM input shaper impulse time sequences is presented. Finally, the proposed technique is compared to the zero vibration (ZV) shaper in both response and robustness to modeling error.
TL;DR: In this paper, the authors investigated a piezoelectric layer with a rigid indenter on its surface and gave an exact solution for the failure behavior near the indenter front.
Abstract: This paper investigates a piezoelectric layer with a rigid indenter on its surface. Exact solution is given for a piezoelectric medium whose thickness is considerably larger than the diameter of the indenter. Different electrical boundary conditions that employ conducting or insulating indenters are presented. Effect of the permittivity of air (which surrounds the piezoelectric medium) is considered and is found to be negligible. Expressions for the singular mechanical and electric fields near the indenter front are established. Those expressions are useful for investigating the possible failure behavior of piezoelectric material near the indenter front. In addition, a numerical solution technique for an indentured piezoelectric layer of finite thickness is also given.
TL;DR: In this article, a new method based on the principle of minimum potential energy is presented, aiming to overcome some weakness of the present discrete element method (DEM), and the authors put forward the DEM with a tight theory base and a fit technique for treating continuum dynamic problems.
Abstract: A new method based on the principle of minimum potential energy is presented, aiming to overcome some weakness of the present discrete element method (DEM). Our primary research is to put forward the DEM with a tight theory base and a fit technique for treating continuum dynamic problems. By using this method, we can not only extend the existing seven-disc model, but also establish a new nine-disc model in a general way. Moreover, the equivalences of two kinds of models have been verified. In addition, three numerical examples of stress wave propagation problems are given in order to validate accuracy and efficiency of the present DEM models and their algorithms. Finally, the dynamic stress concentration problem of a square plate with a circular hole is analyzed.
TL;DR: In this article, the postbuckling response of perfect and geometrically imperfect elastic columns resting on an elastic Winkler type foundation is thoroughly discussed, and the critical state of perfect columns is a stable symmetric bifurcation point and consequently there is no sensitivity to initial geometrical imperfections.
Abstract: The postbuckling response of perfect and geometrically imperfect elastic columns resting on an elastic Winkler type foundation is thoroughly discussed. This is established by employing an approximate analytic technique leading to very reliable results in the vicinity of the critical state. It was found that the critical state of perfect columns is a stable symmetric bifurcation point and consequently there is no sensitivity to initial geometrical imperfections. Moreover, a simple but readily analyzed mechanical model is proposed to simulate the salient features of buckling mechanism of the column on elastic foundation with those of the model. The simplicity, reliability and efficiency of the proposed analysis as well as the successful modeling of the buckling mechanism of the column by that of a single mode mechanical model are illustrated with the aid of numerical examples.
TL;DR: In this article, the authors examined the possibility of resistance reduction due to a rippled surface topography in Stokes flow and analyzed the influence of wall riblets perpendicular to the flow direction on the mean transport velocity in gravity-driven creeping film flows.
Abstract: It is widely accepted that for bodies in turbulent flows a reduction of skin friction can be reached if the surface of the body is provided with small ridges aligned in the local flow direction. This surprising and counterintuitive phenomenon is called the shark-skin effect, motivated from the dermal surface morphology of sharks. In the present article we examine the possibility of resistance reduction due to a rippled surface topography in Stokes flow. We especially analyse the influence of wall riblets perpendicular to the flow direction on the mean transport velocity in gravity-driven creeping film flows following the idea that eddies generated in the valleys of the riblets act like fluid roller bearings and hence may reduce drag. Using a theoretical treatment of the Stokes equations with complex function theory, parameter studies with varying flow rate, bottom amplitude and bottom shape are presented. For the given bottom shapes the maximum enhancement of transport velocity is found by optimising the film thickness.
TL;DR: In this paper, a new design optimization system is developed which employs an iterative optimization technique and numerical simulation of a sheet-metal-forming process, which is based on the interaction of high- and low-fidelity simulation models in order to reduce overall computing time.
Abstract: This paper deals with an optimization methodology for the design of the sheet-metal-forming process. In this study, a new design optimization system is developed which employs an iterative optimization technique and numerical simulation of a sheet-metal-forming process. The main feature of this new optimization method is that it is based on the interaction of high- and low-fidelity simulation models in order to reduce overall computing time. In the iterative optimization procedure, only the corrected low-fidelity model is used. The high-fidelity model, which requires much longer computing time, is used only for the correction of the low-fidelity analysis and validation of the final solution. To demonstrate the developed optimization method on a practical application, it is applied to the optimum blank design for deep-drawing process of a rectangular box. In deep-drawing, the flange of the drawn product is usually trimmed off to obtain the desired product geometry, and the trimmed material is wasted. Therefore, the formulation of the optimization problem is to determine the optimum initial blank geometry which minimizes the amount of the trimmed material, that is, the waste of material. It is confirmed that the blank design was optimized successfully in remarkably short computing time by the developed optimization method.
TL;DR: In this article, the authors report the use of three-dimensional creep continuum damage mechanics techniques to study the creep failure of a medium-bore low-alloy ferritic-steel cylinder-cylinder branched pressure vessel welded connection, tested at a constant pressure of 4 MPa, at a uniform temperature of 590°C.
Abstract: The paper reports the use of three-dimensional creep continuum damage mechanics techniques to study the creep failure of a medium-bore low-alloy ferritic-steel cylinder–cylinder branched pressure vessel welded connection, tested at a constant pressure of 4 MPa, at a uniform temperature of 590°C. The development of computational techniques is reported to analyse this problem with a four-material model of the welded connection which includes: parent, type IV, heat-affected zone (HAZ) and weld materials. The results of analyses are presented for two sets of creep damage constitutive equations. For both equation sets, lifetimes are conservatively, yet accurately predicted; however, the results of metallographic examinations of a tested vessel are not accurately predicted. To overcome this deficiency further analyses of the vessel are recommended which include: a coarse-grained HAZ (CGHAZ), adjacent to the weld material; and, more-refined finite element modelling.
TL;DR: In this article, the dynamic responses of an ice-covered fluid to impulsive disturbances are analyzed for two-and three-dimensional cases, where the initially quiescent fluid is assumed to be inviscid, incompressible and homogenous.
Abstract: The dynamic responses of an ice-covered fluid to impulsive disturbances are analytically investigated for two- and three-dimensional cases. The initially quiescent fluid of infinite depth is assumed to be inviscid, incompressible and homogenous. The thin ice-cover is modelled as a homogenous elastic plate with negligible inertia. Four types of impulsive concentrated disturbances are considered, namely an instantaneous mass source immersed in the fluid, an instantaneously dynamic load on the plate, an initial impulse on the surface of the fluid, and an initial displacement of the ice plate. The linearized initial-boundary-value problem is formulated within the framework of potential flow. The solutions in integral form for the vertical deflexions at the ice-water interface are obtained by means of a joint Laplace-Fourier transform. The asymptotic representations of the wave motions for large time with a fixed distance-to-time ratio are derived by making use of the method of stationary phase. It is found that there exists a minimal group velocity and the wave system observed depends on the moving speed of the observer. For an observer moving with the speed larger than the minimal group velocity, there exist two trains of waves, namely the long gravity waves and the short flexural waves, the latter riding on the former. Moreover, the deflexions of the ice-plate for an observer moving with a speed near the minimal group velocity are expressed in terms of the Airy functions. The effects of the presence of an ice-cover on the resultant wave amplitudes, the wavelengths and periods are discussed in detail. The explicit expressions for the free-surface gravity waves can readily be recovered by the present results as the thickness of ice-plate tends to zero.
TL;DR: In this article, the authors analyzed the antiplane electromechanical fields associated with a circular piezoelectric semiconductor of 6 mm symmetry embedded in a matrix of a different PES.
Abstract: We analyze anti-plane electromechanical fields associated with a circular piezoelectric semiconductor of 6 mm symmetry embedded in a matrix of a different piezoelectric semiconductor. An exact solution is obtained. The solution shows the presence of field concentration near the interface. It is also found that the strain and electric fields inside the inclusion are not uniform.
TL;DR: In this paper, a quasi-linearization finite differences (QLDF) scheme was developed for large-deflection analysis of prismatic and non-prismatic slender cantilever beams subjected to various types of continuous and discontinuous external variable distributed and concentrated loads in horizontal and vertical global directions.
Abstract: An efficient scheme, called quasi-linearization finite differences, is developed for large-deflection analysis of prismatic and non-prismatic slender cantilever beams subjected to various types of continuous and discontinuous external variable distributed and concentrated loads in horizontal and vertical global directions. Simultaneous equations of highly nonlinear and linear terms are obtained when casting the derived exact highly nonlinear governing differential equation using central finite differences on the nodes along the beam. A quasi-linearization scheme is used to solve these equations based on successive corrections of the nonlinear terms in the simultaneous equations. The nonlinear terms in the simultaneous equations are assumed constant during each correction (iteration). Several representative numerical examples of prismatic and non-prismatic slender cantilever beams with different loading conditions are analyzed to illustrate the merits of the adopted numerical scheme as well as its validity, accuracy and efficiency. The results of the present scheme are checked using large-displacement finite element analysis by the MSC/NASTRAN program. A comparison between the present secheme, MSC/NASTRAN and available results from the literature reveals excellent agreement. The advantage of the new scheme is that the load can be applied in one step with few iterations (3–6 iterations).
TL;DR: In this paper, the effect of the notch radius on the starting point of the R-curve, the so-called crack-tip toughness KI0, was investigated.
Abstract: In experimental R-curve investigations crack development usually starts from notches. The validity of R-curves depends on the size of the notch root radius. This influence is completely ignored in most cases. In this theoretical study it is shown how the notch radius affects the formally computed crack resistance curve. First, the influence of the notch radius on the starting point of the R-curve, the so-called crack-tip toughness KI0, will be addressed. Then, the effect of the notch on the shielding stress intensity factor will be discussed, and, finally, the influence on T-stress and the consequences on local path stability will be shown.
TL;DR: In this article, the nonlinear equations of motion of planar bending vibration of an inextensible viscoelastic carbon nanotube (CNT)-reinforced cantilevered beam are derived.
Abstract: The nonlinear equations of motion of planar bending vibration of an inextensible viscoelastic carbon nanotube (CNT)-reinforced cantilevered beam are derived. The viscoelastic model in this analysis is taken to be the Kelvin–Voigt model. The Hamilton principle is employed to derive the nonlinear equations of motion of the cantilever beam vibrations. The nonlinear part of the equations of motion consists of cubic nonlinearity in inertia, damping, and stiffness terms. In order to study the response of the system, the method of multiple scales is applied to the nonlinear equations of motion. The solution of the equations of motion is derived for the case of primary resonance, considering that the beam is vibrating due to a direct excitation. Using the properties of a CNT-reinforced composite beam prototype, the results for the vibrations of the system are theoretically and experimentally obtained and compared.
TL;DR: In this paper, a non-linear boundary and initial value problem is solved by the finite element system SPC-PMHP, which was developed in the frame of the special research program SFB393 for parallel computers.
Abstract: This work comprises the development, implementation and application of methods for the parameter identification of damage mechanical constitutive laws. Ductile damage is described on a continuum mechanical basis by extension of the von Mises yield condition with the Gurson–Tvergaard–Needleman as well as with the Rousselier model. The classical Rousselier model is complemented by accelerated void growth and void nucleation. The non-linear boundary and initial value problem is solved by the finite element system SPC–PMHP, which was developed in the frame of the special research program SFB393 for parallel computers. The material parameters are identified by locally measured displacement fields and measured force–displacement curves. For the material parameter identification a non-linear optimization algorithm is used, which renders the objective function to a minimum by means of a gradient based method. A useful strategy to identify the material parameters was found by careful numerical studies. Finally, using the object grating method the local displacement fields as well as the force–displacement curves are measured at notched flat bar tension specimens made of StE 690 and the parameters of the material are identified.
TL;DR: In this article, the effects of gear hammering in diesel engines are investigated using a multibody model, a fully nonlinear finite-element model and a modally reduced model in combination with a local force law.
Abstract: Gear hammering in diesel engines is a well-known phenomenon in geared drives, exhibiting not only noise but also influencing the performance and durability of diesel engines. Gear hammering is characterised by flanks in contact that lift off and cause impacts when the contact reestablishes, which induces high, sharp dynamic loads. The knowledge of these contact forces is very important for the design of gears. Since contact forces in meshing gears are extremely difficult and expensive to measure, the simulation of these forces plays an important role. Nowadays, these contact simulations are usually carried out within overall models of entire engines using commercial multibody programs that provide submodels for gear contacts, usually based on rigid-body models. However, to reduce inertia effects, gears in geartrains are often designed with very thin bodies, whose elastic compliance influences the contact behaviour to a large extent. For a closer insight into the dynamic behaviour, and especially the influence of thin gear bodies during impact, a typical gear pairing is selected and impacts between one tooth pair are investigated for different boundary and initial conditions with three different models. Besides a multibody model, similar to those used in commercial multibody programs, a fully nonlinear finite-element model and a modally reduced model in combination with a local force law is used. The results of the different approaches are benchmarked in terms of accuracy and numerical effort.
TL;DR: In this paper, a closed form solution of electric fields and elastic fields for the crack with the strip saturation zone is obtained by using the complex function theory, and the generalized Dugdale zone model is also employed in order to investigate the effect of the saturation zone shape on the stress intensity factor.
Abstract: A crack with an electric displacement saturation zone in an electrostrictive material under purely electric loading is analyzed. A strip saturation model is here employed to investigate the effect of the electrical polarization saturation on electric fields and elastic fields. A closed form solution of electric fields and elastic fields for the crack with the strip saturation zone is obtained by using the complex function theory. It is found that the KI-dominant region is very small compared to the strip saturation zone. The generalized Dugdale zone model is also employed in order to investigate the effect of the saturation zone shape on the stress intensity factor. Using the body force analogy, the stress intensity factor for the asymptotic problem of a crack with an elliptical saturation zone is evaluated numerically.
TL;DR: In this article, a constitutive model of viscoplasticity with an equilibrium hysteresis in the small-strain regime is developed for thin-walled tubes of polyoxymethylene (POM).
Abstract: In this article tension, compression and torsion tests are presented using thin-walled tubes of polyoxymethylene (POM). These isothermal experiments show non-linear rate dependence, a tension–compression asymmetry and a pronounced relaxation behaviour. On the basis of the experiments carried out, a constitutive model of viscoplasticity with an equilibrium hysteresis in the small-strain regime is developed. Test calculations using finite elements based on the DAE approach show the capabilities of the thermomechanically consistent model. In particular, a very efficient stress algorithm can be derived which has no iteration on the element level. Moreover, it will be shown that time-adaptive finite elements could be of high importance if rate-dependent constitutive models are applied.
TL;DR: In this paper, the authors studied the mathematical structure of viscoplastic solutions to the problem of flow between two coaxial rotating cylinders and the asymptotic behavior of the velocity field in the vicinity of the maximum friction surface for a class of constitutive laws.
Abstract: Viscoplastic models including a saturation stress are considered. The existence of the saturation stress significantly changes the mathematical structure of solutions near maximum friction surfaces (surfaces where the friction stress is equal to the local shear yield stress). The main features of solutions based on such theories are: (a) sliding must occur at the maximum friction surfaces under certain conditions, (b) the velocity field may be singular in the vicinity of maximum friction surfaces. The objective of the present paper is to study these features of solutions. The mathematical structure obtained is considered to be advantageous for a class of materials and may lead to a convergence of viscoplastic solutions to the corresponding rigid perfectly plastic solutions. It seems that the latter is of importance for the construction of a unified theory that could describe the material behavior in the range from rate-independent plasticity to viscoplasticity. In the present paper, the study of the main features of the model is based on the exact closed-form solution to the problem of flow between two coaxial rotating cylinders. In the case of sliding, in addition to the aforementioned features, the asymptotic behavior of the velocity field in the vicinity of the maximum friction surface is found for a class of constitutive laws.
TL;DR: In this article, a new expression for the radiation force function for spheres in a stationary (or standing) and quasi-stationary wave is obtained based on the far-field acoustic scattering field.
Abstract: A new expression for the radiation force function – which is the radiation force per unit energy density and unit cross-sectional surface area – for spheres in a stationary (or standing) and quasi-stationary wave is obtained based on the far-field acoustic scattering field. The radiation force function formulation has been simplified mathematically and improved into a more general form. Numerical results are presented for rigid and elastic spheres, air bubbles in water as well as liquid drops in air to illustrate the theory. It is demonstrated that expressions for the radiation force functions obtained from the far-field derivation approach are equivalent to those obtained from the near-field-based derivation.
TL;DR: In this article, a spherical wave propagating in the radial and latitude directions and oscillating in longitude direction in the case of fiber-reinforced linearly elastic material is studied.
Abstract: We study a spherical wave propagating in the radial and latitude directions and oscillating in the longitude direction in the case of fibre-reinforced linearly elastic material. A function system solving Euler's equation of motion in this case and depending on certain Bessel and associated Legendre functions is derived.