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A consistent formulation for unilateral contact problems including frictional work hardening or softening is proposed. The approach is based on an augmented Lagrangian approach coupled to an implicit quasi‐static Finite Element Method. Analogous to classical work hardening theory in elasto‐plasticity, the frictional work is chosen as the internal variable for formulating the evolution of the friction convex. In order to facilitate the implementation of a wide range of phenomenological models, the friction coefficient is defined in a parametrised form in terms of Bernstein polynomials. Numerical simulation of a 3D deep‐drawing operation demonstrates the performance of the methods for predicting frictional contact phenomena in the case of large sliding paths including high curvatures.

Because of the specific structure and working mechanism, piston speed is only half of its shaft, which causes severally friction between piston and cylinder. Therefore, the main purpose of this paper is to investigate the friction and wear characteristics of the incomplete spherical piston in spherical pump comprehensively. Finally, to search the low-friction and wear-resistance structural pattern of the piston, and enhance the durability of spherical pump.

The non-linear frictional moment model for incomplete spherical piston in spherical pump was derivated quantificationally. Parameter sensitivity analyses were conducted to find the low-friction structural pattern of the piston. The theoretical wear model of piston–cylinder pair is proposed as well.

To reduce the frictional moment between incomplete piston and cylinder, the optimised diameter ratio between piston pin and piston should be 0.12 based on the parameter sensitivity analyses. The maximum frictional moment is approximately 2.5 times of the minimum. The total efficiency should be considered synthetically based on the thickness of specific working medium.

The proposed non-linear frictional moment model offers the quantitative estimations. Parameter sensitivity analyses were conducted to find the low-friction structural pattern of the piston. The wear behaviours of the piston and cylinder were analysed to investigate the wear characteristics of the piston.

Rotary disc is a key component in the compact spherical pump, connecting shaft and piston, bearing hydraulic force conformally and constituting dynamic working chambers alternatively. Motion of rotary disc comprises two components. One is rotating around its own axis and the other is sliding on a cone surface. Therefore, it is necessary to investigate the friction and wear mechanism between rotary disc and cylinder under a complicated operation condition.

Structural properties of rotary disc are analyzed first. Frictional moment of rotary disc is modeled based on its structural characteristics and working mechanism, and the constraints of the structural parameters are considered. Besides, the concept of dimensionless contact area is proposed. Comparison is performed between the proposed concept and the frictional moment to determine an optimized beginning angle for spherical pump with a given displacement. The wear model of rotary disc is also established based on its kinematic property, a velocity coefficient is proposed and its common values are presented.

Effects of structural parameters, i.e. beginning angle and ending angle on the frictional moment, are obtained quantitatively. The frictional moment increases with beginning and ending angle with different rates. While the dimensionless contact area decreases with beginning angle. The larger the piston angle, the larger the velocity coefficient will be. The rotary disc wears severely with a larger beginning angle and smaller ending angle, while it has the smallest wear rate under a smaller beginning angle and a larger ending angle.

The originality lies in modeling the complex contact force of rotary disc based on its specific structure. These conclusions can be used to optimize the structural parameters of rotary disc.

This paper aims to investigate the effect of frictional materials and surface texture on the energy conversion efficiency and the mechanical output performance of the ultrasonic motor (USM).

A newly designed testing system was set up to measure the mechanical output performance of the USM. The influence of different frictional materials on the output performance of the USM was studied under the same assembly process and parameters. The surface texture was fabricated by laser ablation processing. The effects of surface texture and input parameters on the energy conversion efficiency and mechanical output performance of the USM were studied.

The results show that polyimide (PI) composites as frictional material can significantly improve the output performance of the USM compared to polytetrafluoroethylene (PTFE) composites. When the pre-load is 240 N, the energy conversion efficiency of the USM using textured PI composites as frictional material can reach 41.93 per cent, increased by 29.21 per cent compared to PTFE composites, and the effective output range of the USM is increased to 0.7-1.1 N m. Besides, the pre-load and surface texture have a great influence on the output performance of the USM.

PI composites can improve the mechanical output performance of the USM. Surface texture can also improve the interface tribological properties and the energy conversion efficiency based on the advanced frictional materials, which will contribute to the increment of the output performance of the USM under the same input conditions.

The purpose of this paper is to expand the previously published fuzzy logic controller for contact method to normal frictionless contact for solving mechanical frictional contact problems. The secondary aim is to integrate a reduction model for each component in contact to decrease the size of the global finite element contact problem.

The proposed strategy relies on the design of two fuzzy logic controllers currently used in the automation domain. These controllers are considered to link normal and tangential gaps (for sticking conditions) with normal and tangential contact loads. A direct consequence of integrating a control-based approach into the numerical solving approach is the decomposition of the non-linear problem into a set of linear problems.

With this new strategy, no tangent or coupling matrix is defined for the contact problem that allows to consider a projection matrix to reduce the size of each component in contact and subsequently to decrease the associated computational time. As in condensation techniques, this matrix is composed of both modal bases of each component in contact and static modes that capture behaviors at the contact interface. Moreover, the proposed numerical application highlights the efficiency of the proposal in terms of computation time and precision of contact data.

The developments are currently implemented in Matlab only for 2D static numerical applications. Therefore, as obtained results are very promising in terms of precision and computational time, the objective is to complete the proposed method in future research to manage frictional contact for 3D finite element models in a dynamic context.

In conclusion, this paper highlights the interest of studying mechanical frictional contact problems by considering fuzzy logic control approaches.

The fundamental friction studies of rubber have generally dealt with single contact sliders or rollers. It has been demonstrated abundantly that the lubricated friction of rubber is mainly the ‘deformation loss’ component of friction. At moderate sliding speeds where thin film lubrication exists and the interface shear drag is small, the friction is the same as in rolling. The rubber substrate is continually deforming ahead of, and recovering behind, the contact in both rolling or sliding cases. Since the deformation of rubber is partially irreversible, energy is lost which is irreversible, energy is lost which is reflected as the ‘deformation loss’ component of friction at the contact. This deformation loss component of friction has been correlated with the “elastic hysteresis” or the “visco‐elastic losses”. The elastic hysteresis consideration alone does not fully explain rubber substrate deformation and friction behaviour. The assumptions used are incompatible. For example, the delayed or incomplete recovery of the rubber substrate behind the contact leads to residual strains which result in the contact area asymmetry as shown in Fig. 1. In contrast, the elastic hysteresis approach assumes Hertzian elastic contact which is symmetric. It may be noted that all ‘lossy’ materials whether plastic or visco‐elastic in nature must involve frictional contact area asymmetry. Various simplified visco‐elastic considerations of the rolling contact have been illustrated, only qualitatively, the contact deformation and frictional loss behaviour. Direct experimental and quantitive verifications have not been attempted, however. Some rigorous visco‐elastic, two dimensional, continuum analyses of the rolling contact are available in the literature and are very complex. It is difficult to use the results of these analyses to the problem of frictional loss evaluation, primarily because linear and simplified visco‐elastic models have been employed. Moreover, for the general friction problem of rubberlike elastomers which are nonlinear visco‐elastic solids of complex descriptions, physical quantification and interpretation of the parameters used in the above analyses are not possible. Employing the method of a visco‐elastic operator, a semi‐analytical technique has been used recently to express the asymmetry of the sliding contact area and the associated deformation loss component of friction. The results of the analyses agree reasonably with the experimental observations. Dynamic material property parameters used in the analyses are obtained from an indentation test arrangement under closely controlled conditions.

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.

This paper aims to describe the application of the virtual element method (VEM) to contact problems between elastic bodies.

Polygonal elements with arbitrary shape allow a stable node-to-node contact enforcement. By adaptively adjusting the polygonal mesh, this methodology is extended to problems undergoing large frictional sliding.

The virtual element is well suited for large deformation contact problems. The issue of element stability for this specific application is discussed, and the capability of the method is demonstrated by means of numerical examples.

This work is completely new as this is the first time, as per the authors’ knowledge, the VEM is applied to large deformation contact.

Following earlier work on the combined finite/discrete element simulation of shot peening process in 2D case, 3D representation of the problem is established with respect to DE modelling and contact interaction laws. An important relevant computational issue regarding the critical time step is carefully studied, and a new time stepping scheme that can ensure both short and long term stability of the contact models is developed. Numerical tests are performed to evaluate the proposed normal and frictional contact interaction laws with various model parameters. The influences of single and multiple shot impact, as well as element sizes are also numerically investigated. The established contact interaction laws can also be applied to other multi‐body dynamic simulations.

This paper is concerned with the calibration and validation of a finite‐element model of dry sliding wear in metals. The model is formulated within a Lagrangian framework capable of accounting for large plastic deformations and history‐dependent material behavior. We resort to continuous adaptive meshing as a means of eliminating deformation‐induced element distortion, and of resolving fine features of the wear process such as contact boundary layers. Particular attention is devoted to a generalization of Archard’s law in which the hardness of the soft material is allowed to be a function of temperature. This dependence of hardness on temperature provides a means of capturing the observed experimental transition between severe wear rates at low speeds to mild wear rates at high speeds. Other features of the numerical model include: surface evolution due to wear; finite‐deformation J₂ thermoplasticity; heat generation and diffusion in the bulk; non‐equilibrium heat‐transfer across the contact interface; and frictional contact. The model is validated against a conventional test configuration consisting of a brass pin rubbing against a rotating steel plate.