Contact Boundary Research Articles

Seiberg–Witten Floer Homotopy Contact Invariant

We introduce a Floer homotopy version of the contact invariant introduced by Kronheimer–Mrowka–Ozsváth–Szabó. Moreover, we prove a gluing formula relating our invariant with the first author’s Bauer–Furuta type invariant, which refines Kronheimer–Mrowka’s invariant for 4-manifolds with contact boundary. As an application, we give a constraint for a certain class of symplectic fillings using equivariant KO-cohomology.

Explicit-Implicit Schemes for Calculating the Dynamics of Layered Media with Nonlinear Conditions at Contact Boundaries

In this paper we consider the problem of dynamic loading of a deformable solid medium con- taining slip planes with nonlinear slip conditions on them. An explicit-implicit scheme was constructed for the numerical solution of the constitutive system of equations, which exactly reduces to correcting the stress tensor values after performing the elastic step. An implicit approximation of the constitutive relations containing a small parameter in the denominator of the nonlinear free term was used with the second order of the approximation. The correction procedure is applicable for those cases when the viscosity parameter of interlayers providing the sliding mode of the contact boundaries is not small. The solution of the problem of the seismic waves propagation in an inhomogeneous fractured geological massif in a two-dimensional case was obtained numerically

Making cobordisms symplectic

We establish an existence h h -principle for symplectic cobordisms of dimension 2 n > 4 2n>4 with concave overtwisted contact boundary.

Numerical analysis of shear interaction of an underground structure with soil

A soil layer behaviour under the shear interaction of an underground structure with soil is studied. Structural failure is considered under conditions of strained soil, and complete cohesion is assumed at the underground structure-soil contact boundary. The Finite Difference Method is used to numerically investigate the process of the structure-soil shear interaction under consideration. The main attention is paid to the adequacy of the conditions of soil-structure interaction, and to the strain state of the near-contact soil layer around the underground structure. The results are plotted and analysed. From the results obtained, the existence of a near-contact soil layer is shown; the use of the condition of complete cohesion is justified considering the structural failure of soil under conditions of complex interaction; the possibility to determine the thickness of the near-contact soil layer and of the layers with the respective degrees of structural failure is shown.

NONLINEAR PROBLEM OF FRACTURE MECHANICS OF AN INTERFACE CRACK SUBJECTED TO SHEAR WAVE

Solution for the problem for an interface crack under the action of a harmonic shear wave in normal direction is presented. The contact of the crack faces is put into consideration. The problem is solved by the boundary integral equations method, the vector components in the boundary integral equations are presented by Fourier series. The unilateral Signorini boundary conditions are involved to prevent the interpenetration of the crack faces and the emergence of tensile forces in the contact zone. Amonton-Coulomb Friction Law included allows to put into consideration relative resting of the crack opposite faces or their relative motion when one crack face is slipping or sliding across another face. The contact boundary restrictions are implemented using the iterative correction algorithm. The mathematical model adequacy is checked by comparing with classical model solution for statics problems that takes into account the crack faces contact. Numerical researches of friction influence on the displacement and contact forces distribution, size of contact zone are carried out. Influence of the faces contact and value of the friction coefficient on the distribution of stress intensity coefficients of normal rupture and transverse shear, which are the parameters of the biomaterial fracture, are presented and analyzed. It is shown that the nature of change in the distribution of the stress intensity coefficients for the conditions of tensile and shear waves is fundamentally different. It is concluded that it is possible to extend the approach proposed to the problems of three-dimensional fracture mechanics for composites with interfacial cracks at arbitrary dynamic loading.

A damage model for granite subjected to quasi‐static contact loading

AbstractAn anisotropic damage model is employed in order to simulate the fracture pattern of Bohus granite under quasi‐static (Q‐S) spherical indentation loading. The chosen damage description is added to the previously employed Drucker–Prager (DP) plasticity model with variable dilation angle. The resulting constitutive model is implemented to simulate the behavior of Bohus granite under indentation up to the load capacity of the material. The initial fragmentation, corresponding to the first small load‐drop in the force–penetration curve, is likely due to the high radial tensile stress state at or close to the contact boundary. Both predicted fracture pattern and force–penetration results from the numerical simulation are compared to experimental data and a good agreement is found. The variability in tensile strength of the material is included in the chosen damage model by taking advantage of Weibull statistics. In this work, it is suggested that indentation test results by themselves may be used to calibrate the statistical distribution of tensile strength at small size scales such as in indentation applications.

Some Issues on Crystal Plasticity Models Formulation: Motion Decomposition and Constitutive Law Variants

In this paper, kinematic relations and constitutive laws in crystal plasticity are analyzed in the context of geometric nonlinearity description and fulfillment of thermodynamic requirements in the case of elastic deformation. We consider the most popular relations: in finite form, written in terms of the unloaded configuration, and in rate form, written in terms of the current configuration. The presence of a corotational derivative in the relations formulated in terms of the current configuration testifies to the fact that the model is based on the decomposition of motion into the deformation motion and the rigid motion of a moving coordinate system, and precisely the stress rate with respect to this coordinate system is associated with the strain rate. We also examine the relations of the mesolevel model with an explicit separation of a moving coordinate system and the elastic distortion of crystallites relative to it in the deformation gradient. These relations are compared with the above formulations, which makes it possible to determine how close they are. The results of the performed analytical calculations show the equivalence or similarity (in the sense of the response determined under the same influences) of the formulation and are supported by the results of numerical calculation. It is shown that the formulation based on the decomposition of motion with an explicit separation of the moving coordinate system motion provides a theoretical framework for the transition to a similar formulation in rate form written in terms of the current configuration. The formulation of this kind is preferable for the numerical solution of boundary value problems (in a case when the current configuration and, consequently, contact boundaries, are not known a priori) used to model the technological treatment processes.

Surface Phenomena at the Interface between Silicon Carbide and Iron Alloy.

The paper discusses a potential composite produced using the casting method, where the matrix is gray cast iron with flake graphite. The reinforcement is provided by granular carborundum (β-SiC). The article presents model studies aimed at identifying the phenomena at the contact boundary resulting from the interaction of the liquid matrix with solid reinforcement particles. The scope of the research included, primarily, the metallographic analysis of the microstructure of the resulting composite, carried out by using light (LOM) and scanning electron (SEM) microscopy with energy dispersive X-ray spectroscopy (EDS) analysis. The occurrence of metallic phases in the boundary zone was indicated, the contents and morphology of which can be optimized in order to achieve favorable functional properties, mainly the tribological properties of the composite. In addition, the results obtained confirm the possibility of producing similar composites based on selected iron alloys.

Simple models for simulating shear key arrangement in nonlinear seismic analysis of arch dams

Shear keys are commonly designed on contraction joints to limit joint slipping and improve the overall seismic behavior of arch dams. However, shear keys are usually over-simplified in the current nonlinear seismic analysis. This paper proposes a geometric simplification method for simulating shear key arrangement. Actual shear keys on a contraction joint are simplified into the combination of large oblique-type shear keys along the cantilever direction and horizontal direction. Key geometric features and progressive failure of shear keys can be naturally considered using the contact boundary model and the plastic-damage model. Nonlinear seismic analysis of the Xulong arch dam is implemented with different shear key models for verification and comparison. The proposed method is firstly verified by analyzing seismic responses of the dam with geometrically-simplified shear keys and fine shear keys, respectively. Furthermore, seismic responses of the dam with geometrically-simplified shear keys, free-slipping plane joints (ignoring shear keys but considering surface friction), and non-slipping plane joints (modeling perfect shear keys) are compared to investigate the effects of shear key modeling methods. Ignoring shear keys and modeling perfect shear keys underestimate and overestimate the seismic capacity of the dam, respectively. The nonlinear dynamic behavior of shear keys can be more reasonably represented with the proposed method without much increasing modeling efforts.

A software package for modeling the propagation of dynamic wave disturbances in heterogeneous multi-scale media

The paper considers a software package designed to simulate the propagation of dynamic wave disturbances in heterogeneous media. One of the main features of the considered software package is numerical algorithms with an explicit selection of inhomogeneities. Within the framework of the work, such inhomogeneities as pores, fractures and interfaces between media (contact boundaries) are considered. The considered algorithms make it possible to perform calculations in different scale settings in micro and macro sizes. The mathematical model is based on the equations of the linear theory of elasticity. For the calculation, block structural meshes are used. The software package is parallelized using MPI and OpenMP technologies. Separate parts of the algorithm are parallelized using graphics accelerators such as GPGPU. The paper describes the features of the algorithms under consideration and provides examples of calculations that demonstrate the capabilities of the algorithm.

ABOUT THE ANALYTICAL SOLUTION OF THE EQUATION OF IMPACT FORCE OF TWO ELASTIC BODIES

A nonlinear differential equation of the force of direct central impact of elastic bodies of revolution, which have a singular point on the boundary contact surface, where its curvature is infinite, is compiled. To determine the coefficients of the equation and the order of its power nonlinearity, the well-known solution of the axisymmetric contact problem of the theory of elasticity, constructed by I. Ya. Shtaermann, is used. In the formulation of the dynamic problem, the classical assumptions of the theory of quasi-static impact proposed by H. Hertz were also used. The constituted equation of impact force is reduced to the Bernoulli equation and its closed analytical solution is constructed, which is expressed in terms of the Ateb-sine. Analytical time dependences of the impact force and the convergence of the centers of mass of elastic bodies are obtained. Compact formulas have been derived for calculating the maxima of these quantities, as well as the durations of the process of compression and impact of bodies. Compact approximations of Ateb-sine by elementary functions are proposed. Thanks to these approximations, it was possible to obtain a fairly simple analytical sweep in time of a fast-flowing mechanical process. Traditionally, in other works such a scan was obtained by numerical solution of the corresponding integral equations that determine the force of an impact. Examples of calculations are given in which the influence of various factors on the main characteristics of a body impact with a small initial velocity is investigated. The limitation on the collision rate is due to the elastic formulation of the problem, where the possibility of plastic deformations is excluded. As a result of this formulation, the need to determine the rate of recovery rate has disappeared, for it is equal to one. Comparison of numerical results is carried out, to which the obtained analytical solutions and the numerical integration of the impact force equation on a computer lead. Small divergences of the results confirmed the accuracy of the derived calculation formulas. Numerical results relate to the impact of a steel body on a fixed rubber half-space, the analogue of which is observed in practice when falling pieces of mineral raw materials on the rolls of a vibration classifier lined with rubber.

The strength of the communication elements of pneumatic tires as composite material

The mechanical properties at the boundary of the distribution of the rubber matrix and metal and fabric fibrous materials as a separate area in the mechanism of crack inhibition and its effect on the durability of pneumatic tires during the accumulation of damage during operation are considered. Experimental studies on the stratification of the elements of the composition of the tire material in samples made from different parts of the car tire. The strength at the contact boundary "rubber matrix-fibers of metal cord" and between the fibers of the cord, which allows to assess the total strength of the tire material as a composition of reinforcing elements and the matrix in the accumulation of damage created during operation, artificial the nature and behavior of the rupture of the samples during the tests, the morphology of fracture on the surface of the interaction of the reinforcing fibers of the wire with the rubber matrix was evaluated.

A finite volume penalty based segment-to-segment method for frictional contact problems

This paper presents a new contact boundary condition for finite volume simulations of frictional contact problems involving geometrical and material non-linearities. Deformation of bodies in contact is described by the updated Lagrangian form of the momentum equation which is discretised in space using the cell-centred finite volume method. The proposed contact boundary condition is based on the finite volume implementation of the penalty based segment-to-segment contact force calculation method in which normal contact pressure, governed by a penalty law, is integrated across the discretised contact surface, enforcing contact constraints in an integral manner. Such an approach, as opposed to the pointwise contact force calculation algorithm, allows for more accurate and more robust treatment of the contact area edge, simultaneous calculation of contact forces on both contact surfaces as well as smoother contact force during large sliding. The proposed numerical method is tested on challenging mechanical contact problems showing very good agreement with the available benchmark results.

Finite element analysis of indentation contact of double piezoelectric spheres

As a result of the limited research works on the contact between piezoelectric materials, this research seeks to delve into this area, by using the finite element method. A two-dimensional finite element model of nanoindentation response of piezoelectric materials is established via this method. The axisymmetric contact behavior of the two transversely isotropic piezoelectric spheres under the condition of friction-free sliding is analyzed, and the relationship between indentation displacement, electric potential and contact force is obtained, which are linear and quadratic respectively. The results show that the variation trend of the stress field and electric field at the contact boundary presents a non-monotonic relationship with an increase in the distance from the indenter to the center of the loading axis. In addition, the results of finite element numerical simulation are in good agreement with the numerical verification results. For semi-infinite materials, the model can be used for accurate contact analysis, which guides verifying the extraction technology of contact characteristics of finite piezoelectric materials. The results obtained in this paper are helpful to understand the microscopic contact mechanics of piezoelectric materials.

Fracture prediction in spin forming of anisotropic metal sheets

Fracture often occurs in the spin forming process of thin-walled metal sheets, due to the limited fracture strain and local large plastic deformation of the sheets during the process. However, the accurate fracture prediction is a huge challenge due to the combinations of material anisotropy, complex deformation history and contact boundary conditions in the process. Though there are scattered uncoupled ductile fracture criteria proposed with various deformation mechanisms, reasons for their different fracture prediction abilities remain unclear. Thus in this study, eight popular uncoupled ductile fracture criteria i.e., Freudenthal, C-L, R-T, Brozzo, Oh, Oyane, MMC4 and DF2016, are embedded into an anisotropic constitutive model through VUMAT interface in the ABAQUS simulation software and then realized their fracture prediction in the spin forming process of an anisotropic metal sheet. The results show that the damage accumulation in the spin forming process occurs in a wide range of stress triaxiality, and the most damage accumulation occurs in the stress triaxiality range of 0–1/2. Furthermore, the eight fracture criteria have different prediction abilities in the process and a new deformation history related equivalent fracture strain is proposed to explain these differences. In addition, there exists the abnormal phenomenon that some simple damage models, as Oyane, Oh, etc. provide the more accurate fracture prediction ability than the complex and advanced MMC4 and DF2016 models in the process, and reasons for this phenomenon are explained.

Effects of TiO2 Nanoparticle Addition on Microstructure and Selected Properties of Ag-xTiO2 Composites.

The paper presents the results of a study of the microstructure and selected properties of silver-based composites reinforced with TiO2 nanoparticles, produced by the powder metallurgy method. Pure silver powders were mixed with TiO2 reinforcement (5 and 10 wt%) and 5 mm steel balls (100Cr6) for 270 min in a Turbula T2F mixer to produce a homogeneous mixture. The composites were made in a rigid die with a single-action compaction press under a pressure of 400 MPa and 500 MPa and then sintered under nitrogen atmosphere at 900 °C. Additionally, to improve the density and mechanical properties of the obtained sinters, double pressing and double sintering operations were conducted. As a result, compacts with a density of 90–94% were obtained. The microstructure of the sintered compacts consists of uniform grains, and the TiO2 reinforcement phase particles are located on the grain boundaries. There were no discontinuities at the Ag–TiO2 contact boundary, which was confirmed by SEM and TEM analysis. The use of a higher pressure had a positive effect on the hardness and flexural strength of the tested materials. It was found that the composites with 5 wt% TiO2 pressed under 500 MPa are characterized by the highest level of mechanical properties. The hardness of these composites is 57 HB, while the flexural strength is 163 MPa.

Investigation of the Influence of Ultrasound Action on Diffusion Processes in an Explosion-Welded Bimetal System Cu-Al during Heat Treatment

The influence of ultrasound on the main regularities of the formation and growth of the diffusion zone at the interlayer boundary of an explosion-welded layered composite material of Al-Cu systems is investigated. It is proved that the effect of ultrasound contributes to the reduction of the latent period of the nucleation of intermetallic phases at the interlayer boundary, lowers the temperature of the beginning of the eutectic transformation (by about 10 ° C), but at the same time does not affect the phase composition of the diffusion zone as a result of homogeneous reactions at the boundary of contact of solids. It has been established that the thickness of the diffusion zone, with the duration of the supplied acoustic vibrations, ensures the absence of cracks in the diffusion zone, leading to delamination of the material, increases by 30-40% at a fixed temperature of intense diffusion.

Comparative finite element analysis of bracket deformation in tie wings and slot region during simulated torque

Torque in orthodontics is the activation of the archwire for the third-order movement of teeth. During this force transfer mechanism from the twisted archwire, the bracket is prone to deformation. This study aimed to compare the deformation in tie wings and the slot region of the bracket during torque using finite element analysis. Three-dimensionally modeled 0.017×0.025-in and 0.019×0.025-in stainless steel (SS) and titanium molybdenum alloy archwires were assembled in 0.018-in and 0.022-in solid modeled SS edgewise brackets, respectively. The finite element model of the bracket-archwire combinations was developed with contact boundary conditions. The deformation between tie wings and the slot was analyzed for various angles of twist. For SS archwires at 30° angle of twist, the tie wings deformation in 0.018-in and 0.022-in brackets were 48.67μm and 34.87μm, respectively. The slot deformations of 0.018-in and 0.022-in brackets were 66.33μm and 45.69μm, respectively. Similarly, the amount of deformation in the bracket-titanium molybdenum alloy archwire combinations were also presented. The slot deformation was more than the tie wings deformation as the slot walls bear the immediate torque force. Thus, orthodontic researchers should know that the torque-relevant bracket deformation should ideally be evaluated in the slot region rather than the tie wings.

A membrane equivalent method to reproduce the macroscopic mechanical responses of steel wire-ring nets under rockfall impact

Steel wire-ring nets, which have complex nonlinear mechanical behaviour, are widely used in rockfall protection engineering. At present, the circular beam model with a discrete contact boundary is the most accurate method to simulate steel wire-ring nets’ mechanical responses, but its computational efficiency is low. This paper hereby proposes a membrane equivalence-based continuum simulation method: the membrane equivalent method (MEM)11MEM: abbreviation of the membrane equivalent method proposed in this paper to reproduce the macroscopic mechanical behaviour of steel wire-ring nets.. This study’s aim is to greatly improve the computational efficiency of numerical models through the MEM without compromising computational accuracy in macroscopic mechanical behaviour, compared to the circular beam model. According to the out-of-plane loading experimental results of the net panel and membrane analytical model of orthogonal tension belts, an exponential hardening constitutive model of the equivalent membrane was derived. The MEM’s material parameters were corrected in numerical models for a less than 10% error between the simulated and experimental results. Under the rigid boundary condition, the net panel impact simulation results established by the MEM agreed with extant literature’s experimental results, the peak acceleration error was 4.3%, and the rebound characteristic of the net was reproduced. Under the flexible boundary condition, the MEM’s obtained maximum impact displacement and impact force errors were 10.3% and 7.7%, respectively, compared to 3000 kJ full-scale impact experimental results. The MEM’s computational efficiency can be increased almost tenfold compared to that of the circular beam model.

Numerical Simulation of a High-Speed Impact of Metal Plates Using a Three-Fluid Model

The process of wave formation at the contact boundary of colliding metal plates is a fundamental basis of explosive welding technology. In this case, the metals are in a pseudo-liquid state at the initial stages of the process, and from a mathematical point of view, a wave formation process can be described by compressible multiphase models. The work is devoted to the development of a three-fluid mathematical model based on the Baer–Nunziato system of equations and a corresponding numerical algorithm based on the HLL and HLLC methods, stiff pressure, and velocity relaxation procedures for simulation of the high-speed impact of metal plates in a one-dimensional statement. The problem of collision of a lead plate at a speed of 500 m/s with a resting steel plate was simulated using the developed model and algorithm. The problem statement corresponded to full-scale experiments, with lead, steel, and ambient air as three phases. The arrival times of shock waves at the free boundaries of the plates and rarefaction waves at the contact boundary of the plates, as well as the acceleration of the contact boundary after the passage of rarefaction waves through it, were estimated. For the case of a 3-mm-thick steel plate and a 2-mm-thick lead plate, the simulated time of the rarefaction wave arrival at the contact boundary constituted 1.05 μs, and it was in good agreement with the experimental value 1.1 μs. The developed numerical approach can be extended to the multidimensional case for modeling the instability of the contact boundary and wave formation in the oblique collision of plates in the Eulerian formalism.