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This paper aims to study the relationship between normal contact stiffness and contact load. It purpose a new calculation model of the normal contact stiffness of joint surfaces by considering the elastic–plastic critical deformation change of asperities contact.

The paper described the surface topography of joint surfaces based on fractal geometry, and fractal parameters and of fractal function derived from measurement data. According to the plastic–elastic contact theory, the contact deformation characteristic of asperities was analyzed; the critical deformation estimation model was presented, which expressed critical deformation as the function of fractal parameters and contact deformation; the contact stiffness calculation model of single asperity was brought forward by considering critical deformation change.

The paper combined the surface topography description function, analyzed the asperity contact states by considering the critical deformation change, and calculated normal contact stiffness based on fractal theory and contact deformation analysis. The comparison between theoretical contact stiffness and experimental data indicated that the theoretical normal contact stiffness agreed with the experimental data, and the estimation model for normal contact stiffness was appropriate.

Owing to the possibility of plastic deformation during the loading process, the experimental curve between the contact stiffness and the contact load is nonlinear, resulting in an error between the experimental results and the theoretical calculation results.

The paper established the relationship between critical deformation and fractal surface topography by constructing asperity distribution function. The paper proposed a new normal contact stiffness calculation model of joint surfaces by considering the variation of critical deformation in contact process.

This paper aims to propose a normal and tangential contact stiffness model to investigate the contact characteristics between rough surfaces of machined joints based on fractal geometry and contact mechanics theory considering surface asperities interaction.

The fractal geometry theory describes surface topography and Hertz contact theory derives the asperities elastic, elastic-plastic and plastic contact deformation. The joint normal and tangential contact stiffness are obtained. The experiment method for normal and tangential contact stiffness are introduced.

The relationship between dimensionless normal contact load and dimensionless normal and tangential contact stiffness are analyzed in different plasticity index. The results show that they are nonlinear relationships. The normal and tangential contact stiffness are obtained based on theoretical and experimental methods for milling and grinding machined specimens. The results indicate that the present model for the normal and tangential contact stiffness are consistent with experimental data, respectively.

The normal and tangential contact stiffness models are constructed by using the fractal geometry and the contact mechanics theory considering surface asperities interaction, which includes fully elastic, elastic-plastic and fully plastic contacts deformation. The present method can generate a more reliable calculation result as compared with the contact model no-considering asperities interaction.

The purpose of this study is to develop a normal contact stiffness (NCS) model among three disks of the assembled rotor system, which systematically considers the friction coefficient, the asperities interaction and the elastoplastic contact regime.

Based on the revised fractal theory, considering the friction effect, the elastoplastic contact regime and the asperities interaction in a simple way, the total NCS among three disks of the rod-fastening rotor bearing system is established. Effects of fractal dimension and roughness, friction coefficient, asperities interaction and material properties on the normal stiffness are investigated by simulations and the relevant comparisons are given for examining the reasonability of the proposed model.

NCS will decrease when asperities interaction and friction are included. As the load increases, the influences of asperities interaction and friction on stiffness become serious. NCS will be enhanced when the elastoplastic regime is considered.

A comprehensive NCS model is developed. It provides a theoretical basis for the modeling of the NCS for multi-interfaces.

The purpose of this paper is to establish a mathematical model to investigate the propagation of waves at an imperfect boundary between heat conducting micropolar elastic solid and fluid media.

Wave propagation and reflection methods have been applied to solve the problem. The expressions for reflection and transmission coefficients are obtained. The corresponding derivation for the normal force stiffness, transverse force stiffness, transverse couple stiffness and perfect bonding has also been included.

A computer program is developed and numerical results are computed to obtain the reflection and transmission coefficients of various reflected waves with incident waves. Some special and particular cases are also discussed.

In this paper, stiffness effect on these amplitude ratios with the angle of incidence has been observed and depicted graphically.

The tensile test is one of the fundamental experiments used to evaluate material properties. Simulating a tensile test can be a replacement of experiments to determine mechanical parameters of a continuous material. The paper aims to discuss these issues.

This research uses a new approach to model a tensile test of a high-carbon steel on the basis of discrete element method (DEM). In this research, the tensile test specimen was created by using a DEM packing theory. The particle-particle bond model was used to establish the internal forces of the tensile test specimen. The particle-particle bond model was first tested by performing two-particle tensile test, then was adopted to simulate tensile tests of the high-carbon steel by using 3,678 particles.

This research has successfully revealed the relationships between the DEM parameters and mechanical parameters by modelling a tensile test. The parametric study demonstrates that the particle physical radius, particle contact radius and bond disc radius can significantly influence ultimate stress and Young’s modulus of the specimen, whereas they slightly impact elongation at fracture. Increasing the normal and shear stiffness, the critical normal and shear stiffness can enable the increase of ultimate stress, however, up to maximum values.

To improve the particle-particle bond model to simulate a tensile test for high-carbon steel, the damping factors for compensating energy loss from transition of particle motions and failure of bonds are required.

This work reinforces the knowledge of applying DEM to model continuous materials.

This research illustrates a new approach to model a tensile test of a high-carbon steel on the basis of DEM.

The purpose of this paper is to establish a stiffness model of fixed joint considering self-affinity and elastoplasticity of asperities.

The proposed model considers that asperities of different scales are interrelated rather than independent. For elastoplastic contact, a spring-damper model and an elastic deformation ratio function were proposed to calculate the contact stiffness of asperities.

A revised fractal asperity model was proposed to calculate the contact stiffness of fixed joint, the impacts of the fractal dimension, the fractal roughness parameter and the Meyer index on the contact stiffness were discussed, and the present experimental results and the Jiang’s experimental results showed that the stiffness can be well predicted by proposed model.

The contradiction between the Majumdar and Bhushan model and the Morag and Etsion model can be well explained by considering the interaction among asperities of different scales. For elastoplastic contact, elastic deformation ratio should be considered, and the stiffness of asperities increases first and then decreases with the increasing of interference.

To use distinct element simulation (PFC2D) to investigate the relationships between microparameters and macroproperties of the specimens that are modeled by bonded particles. To determine quantitative relationships between particle level parameters and mechanical properties of the specimens.

A combined theoretical and numerical approach is used to achieve the objectives. First, theoretical formulations are proposed for the relationships between microparameters and macroproperties. Then numerical simulations are conducted to quantify the relationships.

The Young's modulus is mainly determined by particle contact modulus and affected by particle stiffness ratio and slightly affected by particle size. The Poisson's ratio is mainly determined by particle stiffness ratio and slightly affected by particle size. The compressive strength can be scaled by either the bond shear strength or the bond normal strength depending on the ratio of the two quantities.

The quantitative relationships between microparameters and macroproperties for parallel‐bonded PFC2D specimens are empirical in nature. Some modifications may be needed to model a specific material. The effects of the particle distribution and bond strength distribution of a PFC2D specimen are very important aspects that deserve further investigation.

The results will provide guidance for people who use distinct element method, especially the PFC2D, to model brittle materials such as rocks and ceramics.

This paper offers some new quantitative relationships between microparameters and macroproperties of a synthetic specimen created using bonded particle model.

This paper aims to simulate a punch shear test of partly consolidated ice ridge keel by using a three-dimensional discrete element method. The authors model the contact forces between discrete ice blocks with Hertz–Mindlin contact model. For freeze bonds between the ice blocks, the authors apply classical linear cohesion model with few modifications. Based on punch shear test simulations, the authors are able to determine the main characteristics of an ice ridge from the material parameters of the ice and freeze bonds.

The authors introduced a discrete model for ice that can be used for modelling of ice ridges. The authors started with short introduction to current status with ice ridge modelling. Then they introduced the model, which comprises Hertz–Mindlin contact model and freeze bond model with linear cohesion and softening. Finally, the authors presented the numerical results obtained using EDEM is commercial Discrete Element Modeling software (EDEM) and analysed the results.

The Hertz–Mindlin model with cohesive freeze bonds and linear softening is a reasonable model for ice rubble. It is trivial that the ice blocks within the ice ridge are not spherical particles, but according to results, the representation of ice blocks as spheres gave promising results. The simulation results provide information on how the properties of freeze bond affect the results of punch shear test. Thus, the simulation results can be used to approximate the freeze bonds properties within an ice ridge when experimental data are available.

As the exact properties of ice rubble are unknown, more research is required both in experimental and theoretical fields of ice rubble mechanics.

Based on this numerical study, the authors are able to determine the main characteristics of an ice ridge from material parameters of ice and freeze bonds. Furthermore, the authors conclude that the model creates a promising basis for further development in other applications within ice mechanics.

Contact problems are central to solid mechanics as contact is the principal method of applying loads to a deformable body and the point with resulting stress concentration is often the most critical point within the body. This paper presents a finite element model for the elastic contact between two cylinders at several positions. The effects of friction and surface roughness have been considered. The contact between two skew cylinders is also investigated. Results from finite element model show a good agreement with those of analytical solutions available in the literature. It was seen that the geometry of contacting bodies and orientation of applied load effect highly on contact stresses. Although the effect of surface roughness was seen to be more than that of friction, both of them can be assumed negligible in elastic contact problems.

An interface finite element for three‐dimensional problems based on the penalty method is presented. The proposed element can model joints/interfaces between solid finite elements and also includes the propagation of damage in pure mode I, pure mode II and mixed mode considering a softening relationship between the stresses and relative displacements. Two different contact conditions are considered: point‐to‐point constraint for closed points (not satisfying the failure criterion) and point‐to‐surface constraint for opened points. The performance of the element is tested under mode I, mode II and mixed mode loading conditions.