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With the continuous development of network technology, the production and lifestyle of human beings are also quietly changing. People find that the network makes life faster and more convenient and also makes our life more “transparent.” The openness, sharing, and convenience of the network make it easier to infringe on the privacy rights of others, bringing an unprecedented impact on traditional privacy protection. This paper studied information security assurance-related algorithms and built an information security assurance model. Through this model, some privacy violation events existing in the network today were analyzed. Then, a corresponding questionnaire was constructed according to some of the problems of these events. The questionnaire is mainly used for research on people of all age groups, mainly to study their understanding of relevant legal knowledge and their views on the law. A total of 188 valid questionnaires were collected in this survey. Only 37.23% people knew a lot about the law. Most of them learned it from the Internet, and they rarely learned about it from relevant books. About 70% people believe that the law plays a big role in privacy protection, and they will choose legal help if they encounter privacy violations. However, this is inconsistent with some data obtained from the information security assurance model. Through analysis, it can be seen that although they want legal help, they lack the relevant knowledge of the law, and they do not know whether the privacy of individuals has been violated. Therefore, it is necessary to strengthen personal knowledge of privacy protection laws and improve the personal information legal protection and fair use system.

Polysaccharides are important biological macromolecules in all organisms, and have recently been studied as therapeutic agents for ulcerative colitis (UC). However, the effects of Pinus yunnanensis pollen polysaccharides on ulcerative colitis remains unknown. In this study, dextran sodium sulfate (DSS) was used to induce the UC model to investigate the effects of Pinus yunnanensis pollen polysaccharides (PPM60) and sulfated polysaccharides (SPPM60) on UC. We evaluated the improvement of polysaccharides on UC by analyzing the levels of intestinal cytokines, serum metabolites and metabolic pathways, intestinal flora species diversity, and beneficial and harmful bacteria. The results show that purified PPM60 and its sulfated form SPPM60 effectively alleviated the disease progression of weight loss, colon shortening and intestinal injury in UC mice. On the intestinal immunity level, PPM60 and SPPM60 increased the levels of anti-inflammatory cytokines (IL-2, IL-10, and IL-13) and decreased the levels of proinflammatory cytokines (IL-1β, IL-6, and TNF-α). On the serum metabolism level, PPM60 and SPPM60 mainly regulated the abnormal serum metabolism of UC mice by regulating the energy-related and lipid-related metabolism pathways, respectively. On the intestinal flora level, PPM60 and SPPM60 reduced the abundance of harmful bacteria (such as Akkermansia and Aerococcus) and induced the abundance of beneficial bacteria (such as lactobacillus). In summary, this study is the first to evaluate the effects of PPM60 and SPPM60 on UC from the joint perspectives of intestinal immunity, serum metabolomics, and intestinal flora, which may provide an experimental basis for plant polysaccharides as an adjuvant clinical treatment of UC.

The paper presents a new method to study the dynamic mechanical properties of concrete under low pressure and a high strain rate via the inversion of spherical wave propagation. The dynamic parameters of rate-dependent constitutive relation of elastic concrete are determined by measured velocity histories of spherical waves. Firstly, the particle velocity time history profiles in the low stress elastic region at the radii of 100.6 mm, 120.6 mm, 140.6 mm, 160 mm, and 180.6 mm are measured in the semi-infinite space of concrete by using the mini-explosive ball and electromagnetic velocity measurement technology. Then, based on the universal spherical wave conservation equation and the fact that the accommodation relationship in state equation satisfies linear elastic law, the inverse problem analysis of spherical waves in concrete (called “NV + T0/SW”) is proposed, which can obtain the dynamic numerical constitutive behavior of concrete in three-dimensional stress by measuring the velocity histories. The numerical constitutive relation is expressed in the form of distortion, and it is found that the distortion law has an obvious rate effect. Finally, the rate-dependent dynamic parameters in concrete are determined by the standard linear solid model. The results show that the strain rate effect of concrete cannot be ignored with the strain rate range of 102 1/s. This study can provide a feasible method to determine the dynamic parameters of rate-dependent constitutive relation of concretes. This method has good applicability, especially in the study of the dynamic behavior of multicomponent composite materials with large-size particle filler.

The present study is on the analytical solution for the elastic field due to a cuboidal inclusion of uniform eigenstrain within a transversely isotropic full-space material, and a numerical method to model inclusions of any arbitrary shapes and with any eigenstrain distributions as the integration of a set of such cuboidal inclusions. The fast Fourier transform (FFT) is applied for efficient computation. The developed method and results are implemented to analyze the elastic field in a transversely isotropic full-space material containing inclusions of different shapes, different eigenstrain distributions, and multiple cuboids of different densities. Furthermore, the effect of material anisotropy on the stress field subjected to a spherical inclusion with pure dilatant eigenstrains is explored by comparing the behavior of a transversely isotropic material with that of a corresponding isotropic one. The numerical results show that the induced stresses are drastically influenced by the Young’s moduli of transversely isotropic materials, and that material constant C 33 has a large influence on normal stress σ 33 .

The high strain rate in metal cutting significantly affects the mechanical properties of the work piece by altering its properties. This study outlines the material strain rates during elliptical vibration cutting. The finite element analysis, Taguchi method, and analysis of variance (ANOVA) were employed to analyze the effects and contributions of cutting and vibration process parameters (feed rate, rake angle, tangential amplitude, and frequency of vibration) on the variation of strain rates during machining of Inconel 718. Taguchi signal-to-noise analysis on an L18 (21 × 33) orthogonal array was used to determine the optimum parametric combination for the maximum strain rate, and ANOVA was applied to evaluate the significance of control parameter factors on the strain rate. The results of the finite element analysis under different conditions illustrated that the feed rate and rake angle were negatively related to the strain rate, whereas the tangential amplitude and frequency had a positive response. Furthermore, ANOVA results indicated that the effect of the feed rate, tool rake angle, vibration frequency, and tangential amplitude on the strain rate were all statistically significant, with a reliability level of 95%. Of these, the dominant parameter affecting the strain rate was the feed rate, with a percentage contribution of 40.36%. The estimation of the optimum strain rate and confirmation tests proved that the Taguchi method could successfully optimize the working conditions to obtain the desired maximum strain rate.

In this study, the finite element (FE) analysis, analysis of variance (ANOVA), and the back propagation neural network (BPNN) were employed to evaluate and predict the cutting forces of titanium alloy Ti-6Al-4V depending on vibration frequency, tangential amplitude, and thrust amplitude, as well as cutting speed during elliptical vibration cutting (EVC). A series of EVC simulations were conducted based on the verified FE model to evaluate the impacts of different EVC parameters on cutting forces. The results show that the tangential force decreases with increasing vibration frequency, tangential amplitude, and thrust amplitude, but with decreasing cutting speed. The positive and negative thrust forces decrease with increasing frequency and tangential amplitude, but with decreasing thrust amplitude and cutting speed. In addition, ANOVA results clearly indicated that the tangential amplitude is the dominant parameter affecting the cutting forces, and the percent contributions to cutting forces are 69.56%, 66.03%, and 62.83%, respectively. Further, the BPNN models with three different activation functions and different architectures are utilized to predict the cutting forces, and the best performance, in terms of agreement with the target outputs, can be achieved by the network using logarithmic sigmoid activation function and architecture with 15 neurons in one hidden layer. The correlation coefficients for training and testing the selected network are 0.99993 and 0.99916, and the mean square errors are 0.1963 and 2.6070, respectively, and these reveal that BPNN is fairly successful in predicting the cutting forces.

Semi-analytical models (SAMs) have been developed to analyze contact problems efficiently, including those of inhomogeneous materials, based on the equivalent inclusion method. However, understanding the behavior of microscopic inhomogeneities requires SAMs of even higher efficiency. This study builds a new semi-analytical model for high-speed simulations of contacts of materials containing distributed particles of sizes orders of magnitude smaller than that of the contact radius. The domain decomposition method is applied to construct a two-level mesh set to implement multiscale computation. The macroscopic mesh uses homogenized elements that ensure a high computing efficiency in obtaining the contact pressure distribution as a boundary condition, whereas the material microstructures are modeled using the microscopic mesh, and thus the microscopic stress and strain are obtained. New influence coefficients are derived for eigenstress and eigenstrain calculations in both mesh levels and are used to calculate the eigenstress and equivalent eigenstrains. The new model is implemented to investigate the effects of particle clustering on the contact performances of composites.

This paper reported a size-dependent semi-analytical model (SAM) on the contact involving a functionally graded elastic film indented by a rigid frictionless cylinder, where Chen-Yao's surface elastic theory is employed to account for the effects of surface energy and surface strain. The model assumes that the film is perfectly bonded to a rigid substrate, and that the shear modulus of the film varies along the thickness direction following a simple exponential form. The core fundamental solutions of the elastic displacements and stresses for such an elastic thin film with respect to the unit applied force are derived firstly, incorporating the surface effects by means of Chen-Yao's surface elastic theory. Then the frequency response functions (FRFs) and their conversion into the corresponding influence coefficients (ICs), are analytical obtained. Efficient numerical techniques, supported by the conjugate gradient method (CGM) and the fast Fourier transform (FFT), are applied to obtain the unknown pressure and stress distributions. The combined effects of shear modulus ratio, film thickness, and surface energy on the contact behavior of the thin film are explored, and a schematic map is constructed to reveal the influences of film thickness and material characteristic length, which correlates the geometric configuration (i.e. a film or a half-space) and surface behaviors (i.e. with or without considering the surface effects).

This paper reports a semi-analytical model (SAM) for simulating the dynamic contact of a rigid sphere and the surface of a multiferroic magnetoelectroelastic (MEE) film under an increasing applied force. The frequency response functions (FRFs) and their conversion into influence coefficients (ICs) for the MEE film are analytically derived, incorporating the loading velocity in a dynamic process. Fast numerical techniques, including the conjugate gradient method (CGM) and the fast Fourier transform (FFT), are employed for efficient numerical solutions to the dynamic contact behaviors, including the distributions and variations of contact pressure and electric/magnetic potentials, as well as subsurface stresses. The proposed model is implemented to analyze the influences of loading velocity, film thickness, and sphere radius on the dynamic MEE responses, including pressure/stresses and electric/magnetic potentials. An energy conversion factor is selected to evaluate the performance of MEE energy conversion. Furthermore, a sensitivity analysis is conducted to evaluate the influence of material properties and their coupling on the efficiency of mechanical–electric/magnetic energy conversion.

Semi-analytical models have been developed to analyze the contact of inhomogeneous materials based on the equivalent inclusion method. It is important to pursue a higher efficiency in numerical implementation of the semi-analytical models. This paper reports the development of a dual-grid computational scheme for further improving the efficiency of the current semi-analytical modeling. Parametric studies show that the new method can save at least 50% of the execution time with respect to the original algorithm in a considerably wide range of conditions. The new method is applied to investigate the influence of inhomogeneities on contact pressure distributions. Data regression is performed to obtain the amplitudes of contact pressure disturbances as a function of inhomogeneitys elastic modulus, size and location. Then, a criterion is developed based on the values of contact pressure disturbances to determine the circumstances in which the coupling between inhomogeneities and surface contact be ignored.

Semi-circular bend specimens are used to measure the brittle materials' fracture toughness, such as brittle metals, rocks, and ceramic materials. The quasi-static and dynamic model I fracture toughness of tungsten heavy alloy, a typical brittle metal material, are measured using the semi-circular bend specimens under quasi-static compression and dynamic impact loadings. For quasi-static cases, the specimens are loaded on a universal testing machine with a constant loading speed. While for dynamic cases, the specimens are executed on a modified split Hopkinson pressure bar system with the impact pressures from 0.2 to 0.4 MPa. The results show that the dynamic fracture toughness of tungsten alloy increases with the increase of the loading rate. Further, a rate-dependent bilinear traction-separation law is introduced to explain the dynamic fracture behaviors of tungsten alloy. The parameters of the rate-dependent law are obtained from the experiments and the finite element simulations. Finally, the dynamic simi-circular bend simulations using the cohesive element with rate-dependent cohesive law are established to simulate the crack propagation, and the simulation results are in good agreement with the test data.

Materials having two or more constituents of different mechanical properties are often seen in engineering practice. These constituents are connected through their interfaces where the material displacements and tractions are most likely discontinuous, subjected to one, or more, of the five general interface conditions, i.e., perfectly bonded, dislocation-like, force-like, spring-like, and frictionless contact. This paper focus on the contact problem of a rigid sphere sliding on a layered half-space with a spring-like interface between the layer and the substrate. The frequency-domain analytical solutions for the elastic field caused by surface pressure and shear traction are derived. Three stiffness coefficients are introduced to reflect the relationship between tractions and the difference in displacements at both sides of the interface. Further, a sliding contact problem of a rigid sphere and a layered half-space with the spring-like interface is numerically investigated, and the effects of stiffness coefficients on the contact behaviors are explored. Finally, the two-layer model for a coated surface with an inner layer is compared to the spring-like model. When the inner layer is thin and soft, the pressures, as well as stresses, obtained by both models are similar to each other, and the two models are equivalent.

The tangential fretting is explored in the present study when one of the contacting bodies distributed with multiple inhomogeneities. The tangential fretting contact of an elastic sphere with an inhomogeneous material is considered. A new numerical model based on a semi-analytical method is developed by using Eshelby’s equivalent inclusion method and fast Fourier transform algorithms. The coupling between the contact loading and inhomogeneities is fully considered. The influence of multiple inhomogeneities on tangential contact is investigated. Parametric studies are conducted for the effects of randomly distributed inhomogeneities on the contact pressure, tangential displacement, subsurface stress, etc., revealing the significance of the influences of inhomogeneity distribution parameters on tangential fretting performance.

A numerical thermal elastohydrodynamic lubrication model is developed for a coated gear pair, in which the elastic deformation is calculated through the frequency response function of Green function and the discrete-convolute fast Fourier transform. Tribological performance of the gear pair is evaluated in terms of the pressure, the film thickness, the coefficient of friction, the frictional power loss, as well as the temperature rise during meshing. Effects of the elastic modulus and the coating thickness of the coating material are studied under various working conditions. Results provide tribological guidance for engineering practice of gear coating design.

This research explores the influence of inhomogeneities on the torsional fretting via a newly developed semi-analytical method with considering the load history. The disturbances of elastic fields caused by inhomogeneities are modeled based on Eshelby’s equivalent inclusion method. Solutions are achieved iteratively through considering the coupling of surface tractions and subsurface inhomogeneities. The influences of a single inhomogeneity are investigated, revealing that the presence of an inhomogeneity causes significant surface effects on the torsional fretting. Further, the influences of inhomogeneity distribution parameters on the torsional fretting performance are quantified, demonstrating the capability of the proposed method.

Rolling contact experiments of (TiB + TiC)/Ti–6Al–4V composites reveal that inhomogeneous reinforcements reduce the materials’ rolling-contact fatigue (RCF) lives. The composite microstructures are examined and reconstructed based on the dual-beam focus ion beam scanning electron microscopy (FIB/SEM) technique. Integration of the microstructure-based stress analysis approach and Zaretsky’s RCF life prediction methodology leads to a new numerical RCF life modeling method. The newly developed mesh differential refinement scheme, together with the fast Fourier Transform techniques, is utilized to improve the efficiency and versatility of the proposed method. The RCF lives of the composites predicted by the new model are then compared with the experimental data, illustrating the effectiveness of the proposed method.

This paper reports the derivation of the explicit integral kernels for the elastic fields due to eigenstrains in two joined and perfectly bonded half-space solids or bimaterials. The domain integrations of these kernels result in the analytical solutions to displacements and stresses. When the eigenstrains are all in solid I, the kernel for the elastic fields has four groups in this solid and two groups in the other joined solid. Explicit closed-form solutions for a cuboidal inclusion with uniform eigenstrains are derived as the basic solutions, i.e., the influence coefficients. When the computational domain is meshed into cuboidal elements of the same sizes, the total elastic fields can be quickly obtained by implementing three-dimensional fast Fourier transform-based algorithms. The results for the fields due to a cuboidal, a spherical, and a cylindrical inclusion, as well as multiple cuboidal inclusions are presented and discussed. Residual stresses in an elasto-plastic contact involved a coated substrate is further analyzed with the new solution approach.

This paper presents a numerical solution approach of solving smooth- and rough-surface contact problems involving distributed inhomogeneities with arbitrary shapes and different material properties, based on the numerical equivalent inclusion method (EIM). Full 3D FFT techniques and a mesh differential refinement scheme are incorporated into the proposed solution method to enhance the efficiency and flexibility. Comparative studies referencing the FEM and a simplified method demonstrate the efficiency and accuracy of the present method. Computations of several heterogeneous contact cases verify the capability of the method in solving complicated and rough-surface contact problems involving materials with distributed inhomogeneities.

This work quantitatively explores the dependence of the truncation errors on computational mesh settings for image-inclusion approaches and proposes a corresponding amendment. The new method is based on FFT algorithms and involves four individual portions. A mesh differential refinement scheme, consisting of independent and flexible selections-combinations of the surface, source, and target domains, is conceived to assist the proposed method. Comparisons of the results produced by the new and conventional mesh schemes demonstrate the significant improvements in computational performances. The new method can facilitate the numerical evaluation of local elastic characteristics caused by distributed inclusions or defects in contacting components.

Three-dimensional fretting contacts involving multilayered or functionally graded materials are commonly seen in mechanical systems. The analyses of surface fatigue and contact failure require the knowledge of pressure, shear tractions, and stresses. This paper presents a novel method for analyzing the fretting contacts of these materials. The frictional contact equations are divided into two portions, one containing the unknown contact pressure and the other the shear tractions, solved by using the conjugate gradient method with boundary conditions enforced during the iteration. Displacements and stresses caused by the contact pressure and shear tractions are calculated through the use of the influence coefficients and by means of the fast Fourier transform. The influence coefficients are obtained from the analytical frequency response functions derived by the authors, which are the frequency-domain responses of a multilayered surface system to a unit concentrated normal or tangential force. Functionally graded coatings are modeled with multiple sufficiently thin layers; and the minimum number needed to simulate a functionally graded material is numerically determined. This modeling approach is applied to simulate the fretting contact involving multilayered materials and functionally graded coatings and to unfold the dependence of the tangential load–displacement relationship on the degree of material dissimilarity.

A mixed elastohydrodrynamic (EHL) model for journal bearings considering an axial flow due to shaft axial motion and misalignment is developed for lubrication performance evaluation. A new, faster mixed EHL computing technology utilizing the odd–even successive overrelaxation (OESOR) parallel numerical iterative method is proposed based on the red–black successive overrelaxation (RBSOR) method to minimize the execution time prolonged by the complexity caused by the axial flow and misalignments. The multithreaded computing scheme conducted by the OpenMP directive using different meshes and threads suggests that the OESOR method exhibits better efficiency. A series of transient analyses was conducted to solve the mixed EHL model with the parallel OESOR method. The results show that the axial flow and misalignments significantly affect the average pressure, hydrodynamic and asperity contact pressure, elastic deformation, and other characteristics of the journal bearings.

This research explores the influence of distributed non-interpenetrating inhomogeneities on the contact of inhomogeneous materials via a new efficient numerical model based on Eshelby’s Equivalent Inclusion Method. The half-space contact of a sphere with an inhomogeneous material is considered, and the solutions take into account interactions between all inhomogeneities. The efficiency and solution accuracy of the proposed method are demonstrated through comparative studies with those of an existing numerical method and the finite element method. The influence of spatial inhomogeneity orientations on the contact elastic field is investigated and parametric studies are conducted for the effect of arbitrarily distributed inhomogeneities on the stress field of the materials. The significance of the influences of inhomogeneity distribution parameters on the inverse volumetric stress integral is quantified and the corresponding data are fitted into selected several formulas as a step towards understanding the rolling contact fatigue life of the materials.

Rolling contact fatigue (RCF) behaviors of titanium matrix composites (TiB + TiC)/Ti–6Al–4V are investigated, including the microstructural variables, the stress distribution and the RCF life. The effect of reinforcements on RCF is observed in detail. The microstructural information, especially pertaining to the reinforcements, is obtained through scanning electron microscope. The influence of reinforcements on stress distribution is studied via analyses of subsurface stress distributions based on an approximate numerical method, in which the reinforcement distributions are taken into account. The results reveal that the existence of reinforcements causes RCF life reduction due to the stress concentration in and around the reinforcements.

Multilayer coatings are often seen in surface engineering for surface modifications. Optimal design of the multilayered materials requires the understanding of their mechanical behaviors based on deformation and stress analyses. The frequency response functions (FRFs) of the displacement and stress fields in multilayered materials under unit normal and shear loadings are the analytical cores for solving the contact of such materials. The authors have successfully derived these functions by utilizing the Papkovich–Neuber potentials and appropriate boundary conditions. Two matrix equations containing unknown coefficients in the FRFs are established by following the structure rules, and then the closed-form FRFs written in a recurrence format are established. A fast numerical semi-analytical model based on the derived FRFs is further developed for investigating the elastic contact of multilayered materials with any desired material design.

This paper presented a numerical approach to solving the problem of a flat-ended punch in contact with a half-space matrix embedded with multiple three dimensional arbitrary-shaped inhomogeneities. Based on the semi-analytical method (SAM) and the equivalent inclusion method, numerical procedures were developed and the effects of inclusion shape and distribution were analyzed. Fast Fourier transform technique was implemented to accelerate the calculation of surface deformation and subsurface stress. Interactions of inter-inclusions and inclusion-matrix were taken into account. Numerical results showed the presence of inhomogeneities (i.e., microstructures in solids) indeed had a great effect on local contact pressure and a strong disturbance to the subsurface stress field in the vicinity of inclusions. The effects were dependent on the shape and distribution of inclusions and inter-inclusion interactions. The physical significance of this study is to provide an insight into the relation between the material microstructure and its response to the external load, and the solution approach and procedures may find useful applications, for example, the analysis of fatigue and crack propagation for composite materials, prediction of stress field in solids containing material defects, and study of the mechanism of chemical-mechanical polish (CMP) for inhomogeneous materials, etc.

Solving elastohydrodynamic lubrication (EHL) problems is a complex and time-consuming process due to the interactive solutions of the Reynolds equation and contact elasticity. Analyzing journal bearing EHL problems is even more difficult due to the scale difference in the structural and surface features, which may span four orders of magnitude. This article presents a fast EHL computing technology utilizing a parallel numerical iterative method (the red–black successive overrelaxation method) and multithreaded computing scheme conducted by OpenMP directives. The fast computational approaches allow the construction of high-density EHL meshes for effective descriptions of important texture features of journal bearing surfaces.

Material wear in the contact area may lead to fatigue failure of a structural component under torsional fretting. It is necessary to investigate the wear mechanisms accompanying torsional fretting, especially during the unloading process. This paper intends to analyze the torsional stress field during loading and unloading processes and to explore the link between fretting wear and the location of material first yield, for which a parametric study on factors influencing this location, such as coefficient of friction and stick zone ratio, is committed. Because the surface shear traction is complex during the unloading process, the subsurface stress field is calculated by means of an efficient semi-analytical method. The relationship between the first yield location and wear mechanism is examined through observations of worn surfaces from a set of torsional fretting experiments.

This paper presents a new method of contact plasticity analysis, based on Galerkin vectors, to solve the stresses caused by eigenstrain or plastic strain. The plastic strain region below the contact surface is divided into a number of elementary cuboids, where the plastic strains are assumed to be constant in every cuboidal element. The influence coefficients, relating plastic strains to residual displacements or residual stresses, can be divided into four terms: one due to the plastic strains in the full space, and others due to the image plastic strains in the virtual half space. Each term can be solved quickly and efficiently by using the three-dimensional discrete convolution and fast Fourier transform or the three-dimensional combined discrete convolution and correlation and fast Fourier transform. This new method is used to analyze the contact plastic residual displacements and residual stresses for several contact cases to reveal its efficiency. Partial slip contact involving an elasto-plastic body is investigated. Results show that the stick–slip behavior is affected by the plastic strains, and the surface stresses exhibit more complex behavior than those from a pure elastic partial slip contact.

This work presents a numerical study of a spinning rigid sphere pressed against an elasto-plastic half space under combined normal and torque loading. The von Mises stresses and equivalent plastic strain under different torques are investigated. Results show that the torque shifts the maximum von Mises stress and plastic region in the half space closer to the surface at larger friction coefficient. An empirical formula to predict the contact area is suggested. The evolution of the plastic region in the half space is further examined. The region shows more complex shapes than those only under a normal load.

Quarter space problems have many useful applications wherever an edge is involved, and solution to the related contact problem requires extension to the classical Hertz theory. However, theoretical exploration of such a problem is limited, due to the complexity of the involved boundary conditions. The present study proposes a novel numerical approach to compute the elastic field of two quarter spaces, joined so that their top surfaces occupy the same plane, and indented by a rigid sphere with friction. In view of the equivalent inclusion method, the joined quarter spaces may be converted to a homogeneous half space with properly established eigenstrains, which are analyzed by our recent half space-inclusion solution using a three-dimensional fast Fourier transform algorithm. Benchmarked with finite element analysis the present method of solution demonstrates both accuracy and efficiency. A number of interesting parametric studies are also provided to illustrate the effects of material combinations, contact location and friction coefficient showing the deviation of the solution from Hertz theory.

Modern engineering design often faces severe challenges in accommodating impurities and imperfections of materials in the presence of considerable thermal expansion and plastic deformation. Based on micromechanics, a versatile and effective approach for such non-linear problems can be conceived by employing an inclusion model. This paper reports on the derivation of explicit integral kernels for the elastic fields due to eigenstrains in an elastic half-space. The domain integrations of these kernels result in analytical solutions to stresses and deformations. After dividing each general kernel into four groups, the integration is resolved into three-dimensional convolutions and correlations, which can be numerically processed with algorithms based on fast Fourier transform (FFT) to enable efficient and accurate numerical computations. The analytical solution corresponding to a cuboidal inclusion (a rectangular parallelepiped domain) is obtained in an explicit closed-form and is utilized to determine influence coefficients. The present solution and numerical implementation can be used as building blocks for analyzing arbitrarily distributed thermal strains, plastic strains and material inhomogeneities, as demonstrated by solving an illustrative example of elasto-plastic contact.

This article presents a new rolling contact solver using a semi-analytical method (SAM) to analyze three-dimensional steady-state rolling contacts, including the effects of creep. This new solver includes both the normal and tangential contact issues for the pressure and shear tractions, respectively. The accuracy and efficiency of the present method are demonstrated by comparison to existing analytical and numerical solutions. Rolling contact problems for a smooth infinite roller pressed against a half space with either a single asperity or a sinusoidal wave are investigated. The results show the complexity of pressure and shear traction. Asperities produce higher localized pressures, which demand larger local shear tractions to produce slip in such regions. Stick regions are also observed at the trailing edge of the contact.

Elastic-plastic contacts were analyzed by means of a three-dimensional numerical model based on minimization of complementary energy, in which the effect of plastic deformation is included by superimposing the plastic residual displacement on the geometry of contacting surface. The plastic strain increments are determined through the radial return method and J 2 flow theory, which are integrated with the conjugate gradient method (CGM) algorithm and the fast Fourier transform (FFT) technique for improving numerical efficiency. The results from the present numerical model were compared to those from finite element method (FEM) for three typical contacts—i.e., those of a smooth elastic-plastic ball in contact with a rigid body of different geometry: a smooth plane, a plane superposed with a single asperity, and a sinusoidal wave on the plane—which showed persistent good agreement between our model and FEM. Then, three-dimensional elastic-plastic contacts of real engineering surfaces produced by a grinding p...

For multilayered or coated substrates in elastohydrodynamic-lubricated (EHL) contacts, the subsurface stress distributions under a normal load combined with shear traction have been analyzed in this article through computer simulations. The Papkovich-Neuber potentials and Fourier transform are adopted to deduce the pressure–displacement, pressure–stress, and shear traction–stress response functions in frequency domain for the coated substrates, and to calculate distributions of pressure and subsurface stress. The results from the analysis of EHL contacts on coated substrates are compared with those from dry contact model in which shear traction is assumed to obey Coulomb’s law. Effects of the Young’s modulus of coatings, the properties of lubricants, and the magnitude of traction are discussed. Similar to the results in dry contacts, hard coatings in lubricated cases tend to increase the von Mises stress, whereas soft coatings decrease the stress. Shear traction makes the max von Mises stress increasing and moving closer to surface. However, the changes in subsurface stress due to shear traction are less obvious in lubricated contacts. Comparison between EHL and dry contact models reveals that lubrication can reduce the von Mises stress in the coating layer due to smaller shear traction. The analyses show that pressure, film thickness, and subsurface stress distributions are influenced by surface coatings, sliding velocity, rheological models, and pressure–viscosity behaviors.