Dissimilar Bodies Research Articles

Transient tractive rolling contact between elastically dissimilar and multi-layered bodies

This paper discusses the tractive rolling contact between dissimilar and multi-layered bodies. Drawn from the Kalker’s theory on the three dimensional rolling contact, the rolling contact in presence of tangential forces and a spinning moment is formulated. In the present paper, the focus is put on the tangential component of the problem. Then, the variational formulation of the contact problem is solved using a Conjugate Gradient Method (CGM) coupled with Fast Fourier Transform (FFT) algorithms for acceleration. The proposed solver allows to solve the tractive rolling contact problem in both transient and steady-state regimes. The multi-layered aspect of the bodies in contact is taken into account through the influence coefficients used for the calculation of the elastic displacements and stresses. Further, a validation of the model is performed by comparison with models from the literature. The transition from the Cattaneo–Mindlin shift to the steady-state regime is analysed, with Kalker’s solution in the validation section for elastically similar bodies, and further in a parametric study for elastically dissimilar bodies. Moreover, the parametric study allows to highlight the effects of various combinations of the tangential loading input on the stick and the slip zones within the contact zone. Finally, the three dimensional stresses are analysed in a multi-layered body.

A Frenchman in Tokyo

The article examines Endō Shūsaku’s Wonderful Fool (1959) through the lens of disability studies to argue that the novel’s protagonist Gaston Bonaparte—a Frenchman and failed seminary candidate prone to misadventures in Tokyo—subverts cultural structures of ableism in postwar Japanese society. Described as a horse-faced man with a monstrous physicality, Gaston embodies a disabled Christ figure whose presentation integrates numerous transcultural characteristics. The article situates the novel during postwar Japan, in relation to the beginning of disability movements in 1960s Tokyo, to suggest Endō’s implicit criticism of ableism—a perpetuating, defining cultural feature of postwar Japanese society giving rise to exclusionary treatments of physically and culturally dissimilar bodies. Endō’s novel not only promotes a Christian-oriented inclusivity as a solution to postwar Japan’s social brokenness but also a theology of disability—namely, a recognition that embracing Christ and Christian virtues entails an interdependence with all disabled and foreign bodies. Wonderful Fool uses a disabled folkloric-Christological figure—a paradoxical, transnational union between the East and West—through whom Endō envisions a cultural shift toward disability acceptance and Christian evangelization in Japan.

User-oriented Natural Human-Robot Control with Thin-Plate Splines and LRCN

We propose a real-time vision-based teleoperation approach for robotic arms that employs a single depth-based camera, exempting the user from the need for any wearable devices. By employing a natural user interface, this novel approach leverages the conventional fine-tuning control, turning it into a direct body pose capture process. The proposed approach is comprised of two main parts. The first is a nonlinear customizable pose mapping based on Thin-Plate Splines (TPS), to directly transfer human body motion to robotic arm motion in a nonlinear fashion, thus allowing matching dissimilar bodies with different workspace shapes and kinematic constraints. The second is a Deep Neural Network hand-state classifier based on Long-term Recurrent Convolutional Networks (LRCN) that exploits the temporal coherence of the acquired depth data. We validate, evaluate and compare our approach through both classical cross-validation experiments of the proposed hand state classifier; and user studies over a set of practical experiments involving variants of pick-and-place and manufacturing tasks. Results revealed that LRCN networks outperform single image Convolutional Neural Networks; and that users' learning curves were steep, thus allowing the successful completion of the proposed tasks. When compared to a previous approach, the TPS approach revealed no increase in task complexity and similar times of completion, while providing more precise operation in regions closer to workspace boundaries.

The New Purposes of Destroyment Mechanics of Dissimilar Bodies

Recently, with the rapid development of fracture mechanics, the range of tasks that it allows to solve is also expanding. The article provides a brief overview of problems with singular stress fields starting from a simple fissure and up to V-shaped elements made of dissimilar materials. It shows that the fissure is a special case of an entire class of problems. The destruction of pipelines, as well as all other structures, occurs through the birth and development of fissures. It means that it is more important to study problems with singular stress fields in the oil and gas industry. The article provides a solution to a general problem from which all known solutions follow in particular cases. But if in the case of a fissure the dimension of all stress intensity coefficients is the same and constant, then in general the dimensions of the KIN are determined by the values of a parameter that depends on the elastic properties of materials, as well as on the crack opening angle. This property of KIN, causes difficulties with calculating of strength. Therefore there is a problem - how to determine the strength conditions of structural elements with such singular points. This problem requires further research in this area.

Nonequilibrium effects in the Casimir force between two similar metallic plates kept at different temperatures

We study the Casimir pressure between two similar plates of finite thickness kept at different temperatures in the case when the dielectric permittivity of the plates depends on temperature. It is suggested to consider the dielectric permittivity at two different temperatures as the permittivities of two dissimilar bodies, thus allowing to apply the theory of Casimir forces out of thermal equilibrium developed earlier in the literature. Following this approach, we show that, in addition to the equilibrium contribution to the nonequilibrium Casimir pressure, a proper nonequilibrium contribution arises for temperature-dependent dielectric permittivities. Furthermore, the equilibrium contribution in this case does not equal the mean of the equilibrium Casimir pressures at the temperatures of the plates. As an application, the total nonequilibrium Casimir pressure between two gold plates and between two titanium plates is calculated as a function of the plate thickness and their separation, using the Drude and the plasma model. For plate separations ranging from 0.5 to 2 micrometers, the relative difference between the theoretical predictions for these two models reaches 39%. The proper nonequilibrium term may be as large as 4% of the magnitude of the total nonequilibrium pressure.

Computing the composite coefficient of restitution for inelastic impact of dissimilar bodies

This paper develops an analytical method for computing the composite coefficient of restitution (COR) for a collision between dissimilar bodies composed of strain-hardening materials. This method can be used for lumped parameter modeling of collisions in which yielding occurs during impact in either one or both colliding bodies. The effect of the strain-hardening coefficient and relative impact velocity on a composite COR of either similar or dissimilar bodies is investigated. It is shown that the effect of the strain-hardening coefficient is significant when yield stresses of the colliding bodies are close to one another. Furthermore, for a collision between dissimilar bodies, the composite COR depends mostly on the hardening modulus of the body with the more compliant contact region. Also, the composite COR decreases as relative impact velocity increases. Finally, a lumped parameter nonlinear spring model is used to predict the normal force-displacement behavior of the two dissimilar bodies in a collinear collision. This lumped parameter model can be extended to more complex granular flow simulations involving a large number of particles. The resulting analytical expression can be useful for rigid body dynamic analysis codes as well as in design analysis.

Asymptotic Stress Fields for Complete Contact Between Dissimilar Materials

We investigate the influence of material dissimilarity on the traction fields at the corners of a contact between an elastic right-angle wedge and an elastic half-plane. The local asymptotic fields are characterized in terms of the properties of the leading eigenvalue for cases of slip and stick as a function of the Dundurs bimaterial parameters α and β, and the coefficient of friction f. Permissible values of α and β are partitioned into two possible ranges, one where behavior is qualitatively similar to the case where the indenting wedge is rigid [α = 1] and the other where behavior is similar to the case where the materials are the same [α = β = 0]. The results give insight into the high local stresses at the edge of a contact between elastically dissimilar bodies and can also be used to evaluate the effectiveness of mesh refinement in corresponding finite element models.

Analysis of edge slipping in a complete and adhesive contact of elastically dissimilar bodies subject to normal indentation

A slipping at the edge of a complete contact problem is studied. An asymptotic method is first used for the stress evaluation in the vi- cinity of the contact edge. The characteristics of the induced eigenvalue problem are solved. The influence of the contacting material's dissimilarity on the eigensolutions is particularly investigated. Generalized stress intensity factors are defined with developing a method to select the mode separation angles. Assistance of a finite element analysis is explained, which is necessary to deduce the asymptotic solution of a semi-infinite body to a finite problem. Normalization of the stress equation with respect to the recently exploited parameters of length and stress dimensions (do and Go, respectively) is also introduced. The condition of edge slipping is suggested by comparing the coefficient of friction with the ratio of eigenvectors of the shear and normal components. It was found that a leading edge slip will be formed in the vicinity of the contact edge. A trailing edge slip may take place inside the contact region. The size of the leading edge slip region is also evaluated. This dramatically decreases if the coefficient of friction increases as reasonably expected.

Fretting Contact of Two Dissimilar Elastic Bodies with Functionally Graded Coatings

A two-dimensional fretting contact problem involving normal and tangential loading of two dissimilar elastic bodies with functionally graded coatings is analyzed. The bodies are first brought into contact by a monotonically increasing normal load and then a cycled tangential load is applied with the normal load held constant. Friction with a finite coefficient is assumed between the contact surfaces. The linear multi-layered model is used to model functionally graded coating with arbitrarily varying shear modulus and constant Poisson's ratio under plane strain deformation. With the use of the transfer matrix method and Fourier integral transform technique, the problem is reduced to a set of Cauchy singular integral equations which are solved numerically. An iterative method is developed to determine the stick/slip region and contact tractions. The numerical results show that the functionally graded coating on the harder body can lower the fretting contact stresses and thus improve the resistance to the fretting contact damage, and that in comparison with a homogeneous coating, a functionally graded coating can eliminate the interfacial stress concentration induced by material property mismatch.

Skill Transfer from Human to Robot by Direct Teaching and Task Sharing -A Case Study with Origami Folding Task-

Manipulation skill, which is a sort of implicit knowledge, is very ***di cult to be transfered even among humans. Skill transfer from human to robot is even more di cult because humans and robots have dissimilar bodies. The authors already proposed a novel method to transfer manipulation skill from a human to a robot by direct teaching. A Hidden Markov Model (HMM) was employed to model the statistical characteristics of the teaching data demonstrated by a human. A nominal trajectory and sensory feedback control laws were extracted from the statistical characteristics of the trained HMM. In this paper, a new method to extract sensory feedback control laws by direct teaching is proposed. The proposed method fully takes the statistical information of the teaching data from the canonical correlations between force (sensing) and velocity (action). Then, sensory feedback control laws, whose weighting factors have temporal continuity and directional dependency, are constructed without introducing any threshold values which had to be determined by trial and error in the previous method. Like the previous study by the authors, the proposed method is applied to an origami-folding task and experimental results show that the success rate and the folding quality of ‘Valley-fold’ are improved. It is shown that task sharing by direct teaching is a key to successfully transferring manipulation skills between human and robot who have dissimilar bodies.

Collision of dissimilar blunt elastic bodies: a plane problem

The paper deals with a direct central impact of two infinite cylindrical bodies having differently shaped cross sections and made of different materials. A nonstationary plane problem of elasticity is solved. The contact boundary is moving and determined during the solution. A mixed boundary-value problem is formulated. Its solution has the form of Fourier series. Satisfying mixed boundary conditions gives an infinite system of Volterra equations of the second kind for the unknown coefficients of the series. The basic characteristics of the impact process and their dependence on the physical and mechanical properties of the bodies are determined numerically

Hertzian fracture at finite friction: A parametric study

Friction has a profound influence on Hertzian fracture initiation when dissimilar materials are involved. Experimental studies show that the presence of friction results in higher fracture loads and fracture radii as compared to the frictionless case. It has also been shown recently that the experimental observations concerning Hertzian fracture initiation at unloading may be explained by the effect friction has on a surface tensile stress distribution. Presently a contact cycle between two dissimilar elastic bodies at finite Coulomb friction has been investigated numerically for a wide range of material parameters and contact geometries. Emphasis has been given to the surface tensile stress distribution which is assumed to be a governing parameter for Hertzian fracture initiation. In particular it was found that during loading the contact region divides into invariant stick and inward slip regions and the presence of outward frictional shear tractions reduces the maximum surface tensile stress and shifts it away from the contact contour as compared to the frictionless case. At unloading, the distributions of stick-slip zones were found to be severely history- and geometry-dependent and shear tractions reversed their direction over part of the contact area. Consequently, tensile stresses were found to grow at unloading. Results concerning the influence of the friction coefficient, Dundur's parameter and the specimen's Poisson's ratio on the absolute maximum surface tensile stress obtained at a frictional contact cycle are reported along with the magnitudes of the relative increase of maximum tensile stresses at unloading. Based on a critical stress fracture criterion it is discussed how the predicted increases will influence the critical loads required for crack initiation.

Dislocation tri-material solution in the analysis of bridged crack in anisotropic bimaterial half-space

The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half-space is analyzed for a general case of elastic anisotropic bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (Ψ-integral) is demonstrated as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM. Also the application of the configurational force mechanics is discussed within the context of the investigated problem.

Analysis of Edge Bridged Crack in Bimaterial Anisotropic Half-Space

The problem of an edge-bridged crack terminating perpendicular to a bimaterial interface in a half- space is analyzed for a general case of elastic anisotropy bimaterials and specialized for the case of orthotropic bimaterials. The edge crack lies in the surface layer of thickness h bonded to semi-infinite substrate. It is assumed that long fibres bridge the crack. Bridging model follows from the assumption of “large” slip lengths adjacent to the crack faces and neglect of initial stresses. The crack is modelled by means of continuous distribution of dislocations, which is assumed to be singular at the crack tip. With respect to the bridged crack problems in finite dissimilar bodies, the reciprocal theorem (ψ - integral) is discussed as to compute, in the present context, the generalized stress intensity factor through the remote stress and displacement field for a particular specimen geometry and boundary conditions using FEM.

Thermoelastic Stability of Layer Bonded to Half Plane

Sandwich and bimetallic plating significantly enhance many engineering applications within the civil engineering, marine engineering, and naval architecture fields due to its high strength-to-weight ratio. However, the design of sandwich plates requires an assessment of how they react to environments in which elevated temperatures are probable. A simple model, consisting of a layer bonded to a half plane, is used to predict the thermoelastic stability of such sandwich and bimetallic plating. It is found that the conduction of heat between the two dissimilar elastic bodies can cause thermoelastic instabilities within the system. The characteristic equation governing the thermoelastic stability of the layer bonded to a half plane exhibits instabilities dependent on the material properties of the layer and half plane. These instabilities are categorized, based on the ratio of the material properties, into three types.

Numerical analysis of fretting contacts of dissimilar isotropic and anisotropic materials

A numerical method is presented to obtain the contact tractions when two dissimilar isotropic or anisotropic bodies are in partial slip contact. The solution to the governing coupled singular integral equations (SIEs) is obtained by incorporating the appropriate singular behaviour for the contact pressure and the shear traction. The edges of the contact zone and the stick zone are determined by iteration such that the constant multipliers of the singular functions vanish. For anisotropic materials the out-of-plane shear traction is assumed to be very small and hence neglected. The solution method has been successfully verified by comparing its results to solutions available in the literature and to the results obtained by the finite element method (FEM). By modifying the slip function to take into account the remote stress on the half-space, the SIE method can be used to analyse fretting contact problems. The resulting technique efficiently accounts for the effect of load history on the contact tractions and the contact and stick zone sizes. The pronounced effect that load history has on the stick zone size is illustrated.

Thermoelastic Stability of Two Bonded Half Planes

This paper investigates the thermoelastic stability of two bonded half planes consisting of different materials, using a perturbation method. It is found that the conduction of heat across an interface between two dissimilar elastic bodies can cause thermoelastic instabilities within the system. This type of instability has been shown to occur for the case where two frictionless half planes are in contact. The characteristic equation governing the thermoelasticity stability of the two bonded half planes takes the same form as that of the two frictionless half planes, thereby having, qualitatively, the same stability boundaries. The significance of this investigation relates to civil and marine engineering applications in which sandwich or bimetallic plate construction may be applicable.

Dynamic SIF of interface crack between two dissimilar viscoelastic bodies under impact loading

In this paper, the transient dynamic stress intensity factor (SIF) is determined for an interface crack between two dissimilar half-infinite isotropic viscoelastic bodies under impact loading. An anti-plane step loading is assumed to act suddenly on the surface of interface crack of finite length. The stress field incurred near the crack tip is analyzed. The integral transformation method and singular integral equation approach are used to get the solution. By virtue of the integral transformation method, the viscoelastic mixed boundary problem is reduced to a set of dual integral equations of crack open displacement function in the transformation domain. The dual integral equations can be further transformed into the first kind of Cauchy-type singular integral equation (SIE) by introduction of crack dislocation density function. A piecewise continuous function approach is adopted to get the numerical solution of SIE. Finally, numerical inverse integral transformation is performed and the dynamic SIF in transformation domain is recovered to that in time domain. The dynamic SIF during a small time-interval is evaluated, and the effects of the viscoelastic material parameters on dynamic SIF are analyzed.

Spherical indentation of elastic–plastic solids

The finite–element method is used to perform an accurate numerical study of the normal indentation of an elastic–plastic half–space by a rigid sphere. The effects of elasticity and strain–hardening rate of the half–space are explored, and the role of friction is assessed by analysing the limiting cases of frictionless contact and sticking friction. Indentation maps are constructed with axes of contact radius a (normalized by the indenter radius R and the yield strain of the half–space. Competing regimes of deformation mode are determined and are plotted on the indentation map: (i) elastic Hertzian contact; (ii) elastic–plastic deformation; (iii) plastic similarity regime; (iv) finite–deformation elastic contact; and (v) finite–deformation plastic contact. The locations of the boundaries between deformation regimes change only slightly with the degree of strain–hardening rate and of interfacial friction. It is found that the domain of validity of the rigid–strain–hardening similarity solution is rather restricted: it is relevant only for solids with a yield strain of less than 2 x 10 −4 and a / R

Contact Problems of Two Dissimilar Anisotropic Elastic Bodies

In this paper, a two-dimensional contact problem of two dissimilar anisotropic elastic bodies is studied. The shapes of the boundaries of these two elastic bodies have been assumed to be approximately straight, but the contact region is not necessary to be small and the contact surface can be nonsmooth. Base upon these assumptions, three different boundary conditions are considered and solved. They are: the contact in the presence of friction, the contact in the absence of friction, and the contact in complete adhesion. By applying the Stroh’s formalism for anisotropic elasticity and the method of analytical continuation for complex function manipulation, general solutions satisfying these different boundary conditions are obtained in analytical forms. When one of the elastic bodies is rigid and the boundary shape of the other elastic body is considered to be fiat, the reduced solutions can be proved to be identical to those presented in the literature for the problems of rigid punches indenting into (or sliding along) the anisotropic elastic halfplane. For the purpose of illustration, examples are also given when the shapes of the boundaries of the elastic bodies are approximated by the parabolic curves.