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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.

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.

The interaction between rock mass structural planes and dynamic stress levels is important to determine the stability of rock mass structures in underground geotechnical engineering. In this work, the authors aim to focus on the degradation effects of fracture geometric parameters and unloading stress paths on rock mechanical properties.

A three-dimensional Particle Flow Code (PFC3D) was used for a systematic numerical simulation of the strength failure and cracking behavior of granite specimens containing prefabricated cracks under conventional triaxial compression and triaxial unilateral unloading. The authors demonstrated the unique mechanical response of prefabricated fractured rock under two conditions. The crack initiation, propagation, and coalescence process of pre-fissured specimens were analyzed in detail.

The authors show that the prefabricated cracks and unilateral unloading conditions not only deteriorate the mechanical strength but also have significant differences in failure modes. The degrading effect of cracks on model strength increases linearly with the decrease of the dip angle. Under the condition of true triaxial unilateral unloading, the deterioration effect of peak strength of rock is very significant, and unloading plays a role in promoting the instability failure of rock after peak, making the rock earlier instability failure. Associating with the particle vector diagram and crack coalescence process, the authors find that model failure mode under unilateral loading conditions is obviously distinct from that in triaxial loading. The peak strain in the unloading direction increases sharply, resulting in a new shear slip.

This study is expected to improve the understanding of the strength failure and cracking behavior of fractured rock under unilateral unloading.

The purpose of this paper is to present a new way to solve numerically a mechanical frictionless contact problem within a context of multiple sampling, frequently used to design robust structures.

This paper proposes to integrate a control-based approach, currently used in automation domain, for the solving of non-linear mechanical problem. More precisely, a fuzzy logic controller is designed to create a link between the normal gaps identified between the bodies and the normal contact pressures applied at the interface.

With this new strategy, the initial non-linear problem can be decomposed into a set of reduced linear problems solved using the finite element method. A projection built from the modal bases of each component in contact is considered to reduce computational time. Moreover, the proposed numerical applications highlight an interesting compromise between computation time and precision of contact data.

Currently, the proposed Fuzzy Logic Controller for Contact method has been developed for a frictionless contact problem in the case of 2D numerical applications. Therefore, as obtained results are very interesting, it will be possible to expand on these works in a future works for more complex problems including friction, 3D model and transient dynamic responses by adding other controllers.

In conclusion, this paper highlights the interest of studying a contact problem by considering automation approaches and defines the basis of future multidisciplinary works.

Inside the finite element framework of LAGAMINE code, the contact conditions are introduced with specific two‐node interface elements and four‐node quadrangular elements or four‐node one point quadrature elements. A non‐associated flow rule is involved for sliding unilateral contact modelling. Two methods of penalty factor computations in the penalty contact algorithms are presented. These methods are then used for contact modelling of two isothermal examples: axisymmetric tube expansion and asymmetric slab bending, the material bulk constitutive equation being isotropic and elasto‐plastic.

In order not to affect the highway and railway traffic under the bridge during the construction process, bridges adopting swivel construction method are increasingly used at areas where the traffic is heavy. Previous studies are mostly conducted by assuming that the bridge is under its own stability conditions, without considering the impact of construction error, changes of external condition and wind-induced vibration on the stability of the bridge, which poses serious challenges to the bridge construction process. This paper aims to analyze the extent to which static load and fluctuating wind effect influence structural stability and to test the credibility of the structure.

A finite element calculation method is used to analyze a T-shaped rigid frame swivel bridge. A full bridge model was built, and a local model of the turntable structure established; the two are then combined means of node coupling. Subsequently, the three sensitivity indexes – deflection rate, stress change rate and the change rate of spherical hinges – are used to evaluate in what way the bridge stability is influenced under various factors.

It is found that the stability of the swivel bridge is quite sensitive to unilateral overweight, steel beam tension and wind-induced vibration effects but less sensitive to the change of bulk density. Also found is that the change of elastic modulus exerts some effects on deflection but has negligible effects on other stability indexes. Furthermore, the transverse unbalanced torque on the bridge generated by wind-induced vibration is an important factor in determining the size of the turntable, indicating that it is not just controlled by the weight of the bridge.

All factors affecting the stability of swivel construction are analyzed, and solutions to reduce the influence are proposed. The influence of wind-induced vibration effects on swivel construction is analyzed for the first time. It is pointed out that wind-induced vibration effects have great influence on the structure, and its influence could not be neglected.

The purpose of this paper is to investigate the influence of the resolution with which interfaces of fractal geometry are represented, on the contact area and consequently on the contact interfacial stresses. The study is based on a numerical approach. The paper focuses on the differences between the cases of elastic and inelastic materials having as primary parameter the resolution of the interface.

A multi‐resolution parametric analysis is performed for fractal interfaces dividing a plane structure into two parts. On these interfaces, unilateral contact conditions are assumed to hold. The computer‐generated surfaces adopted here are self‐affine curves, characterized by a precise value of the resolution δ of the fractal set. Different contact simulations are studied by applying a horizontal displacement s on the upper part of the structure. For every value of s, a solution is taken in terms of normal forces and displacements at the interface. The procedure is repeated for different values of the resolution δ. At each scale, a classical Euclidean problem is solved by using finite element models. In the limit of the finest resolution, fractal behaviour is achieved.

The paper leads to a number of interesting conclusions. In the case of linear elastic analysis, the contact area and, consequently, the contact interfacial stresses depend strongly on the resolution of the fractal interface. Contrary, in the case of inelastic analysis, this dependence is verified only for the lower resolution values. As the resolution becomes higher, the contact area tends to become independent from the resolution.

The originality of the paper lies on the results and the corresponding conclusions obtained for the case of inelastic material behaviour, while the results for the case of elastic analysis verify the findings of other researchers.

As it is widely known, corrosion is a major deterioration factor for structures which are located on coastal areas. Corrosion has a great impact on both the durability and seismic performance of reinforced concrete structures. In the present study, two identical reinforced concrete columns were constructed and mechanical tests were organized to simulate seismic conditions. Prior to the initiation of the mechanical tests, the base of one of the two columns was exposed to predetermined accelerated electrochemical corrosion (at a height of 60 cm from the base). After the completion of the experimental loading procedure, the hysteresis curves – for unilateral and bilateral loadings – of the two samples were presented and analyzed (in terms of strength, displacement and dissipated energy). The paper aims to discuss this issue.

In the present study, two identical reinforced concrete columns were constructed and mechanical tests were organized to simulate seismic conditions. The tests were executed under the combination of a constant vertical force with horizontal, gradually increasing, cyclic loads. The implemented displacements, of the free end of the column, ranged from 0.2 to 5 percent. Prior to the initiation of the mechanical tests, the base of one of the two columns was exposed to predetermined accelerated electrochemical corrosion (at a height of 60 cm from the base). After the completion of the experimental loading procedure, the hysteresis curves of the two samples were presented and analyzed (in terms of strength, displacement and dissipated energy).

Analyzing the results, for both unilateral and bilateral loadings, a significant reduction of the seismic performance of the corroded column was highlighted. The corrosion damage imposed on the reference column resulted in the dramatic decrease of its energy reserves, even though an increase in ductility was recorded. Furthermore, more attention was paid to the consequences of the uneven corrosion damage, recorded on the steel bars examined, on ductility, hysteretic behavior and damping ratio.

In the present paper, the influence of the corrosion effects on the cyclic response of structural elements was presented and analyzed. The simulation of the seismic conditions was achieved by imposing, at the same time, a constant vertical force and horizontal, gradually increasing, cyclic loads. Finally, an evaluation of the performance of a column, under both unilateral and bilateral loadings, took place before and after corrosion.

A finite‐element model for calculating the die temperature profile for a hot‐forging operation is presented. The workpiece is modelled as a thermo‐viscoplastic material, while the dies are considered undeformable. Heat transfer between the dies and the workpiece is modelled using an iteratively coupled, fixed‐point calculation of the temperature in each domain. Transfer of temperature boundary conditions across contact interfaces is performed for non‐coincident meshes, using a boundary integration point contact analysis. Two industrial‐type examples are presented. In the first example, the effectiveness of the transfer of the temperature boundary conditions for a non steady‐state forging process is evaluated and determined to be satisfactory. Then weakly‐ and strongly‐coupled temperature resolutions are compared. It was found that the strongly‐coupled resolution may be necessary in order to obtain reasonably accurate results. In the second example, the weakly‐coupled resolution is compared to a constant‐temperature die approach for a relatively slow forging process, which shows the influence of the die temperature on the flow of the material.

In this paper, the influence of fractal interface geometry to the evolution of the friction mechanism is studied. The paper is based on fractal approaches for the modeling of the multiscale self‐affine topography of these interfaces. More specifically, these approaches are based on scale‐independent parameters such as the fractal dimension. Here, friction between rough surfaces is assumed to be the result of the gradual plastification of the fractal interface asperities. In order to study the resulting highly nonlinear problem a variational formulation is used in order to describe contact between the interfaces. The numerical method used here leads to the successive solution of quadratic optimization problems. Finally, structures with different fractal interfaces are analyzed in order to obtain results for the relation between the fractal dimension and the overall response of the structures.