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New contact boundary modelling is achieved with a basic set of 2 and 3 dimension contact primitives. Contact constraints are originally introduced in the variational equations and associated Newton—Raphson scheme via an external penalty formulation using primitive equations. Consequently, penalty part of external load vector and tangent stiffness matrices are developed for all contact primitives. In this way, contact prescribed boundary displacements are also taken into account. Contact treatment is then completed with Newton—Raphson elements for elastic and plastic regularized friction constitutive models. In this paper, the process is extended to elastoplastic models. Finally, we propose a self acting procedure with contact algorithms (interiority, sliding and contact loss) and related subroutines for implementation in finite element framework. We illustrate these developments by means of two‐dimensional open die forging and three‐dimensional plate coining typical benchmarks with reference to bulk elastoplastic and viscoplastic constitutive models.

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.

Presents a modular method for obtaining either a quick or a precise calculation for three‐dimensional structure assemblies with local non‐linearities, such as unilateral contact with friction, or technological components, such as prestressed bolt joints. An iterative method, including a domain‐decomposition technique, is proposed to solve such quasi‐static problems in small perturbations. Two types of entities are introduced: sub‐structures and interfaces. A local and a global stage are successively carried out by an iterative algorithm until convergence. The linear problem in the global stage is solved by a FEM (3D case) or by another approach using Trefftz functions (2D axisymmetrical case). Applications developed with AÉROSPATIALE‐Les Mureaux are presented and concern the study of structure joints with different types of flanges.

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.

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.

The purpose of this paper is to investigate the application of the element‐free Galerkin (EFG) method to the simulation of metal forming processes and to propose a strategy to deal with volumetric locking problem in this context.

The J₂ elastoplastic material model, employed in the work, assumes a multiplicative decomposition of the deformation gradient into an elastic and a plastic part and incorporates a non‐linear isotropic hardening response. The constitutive model is written in terms of the rotated Kirchhoff stress and the logarithmic strain measure. A Total Lagrangian formulation of the problem is considered in order to improve the computational performance of the proposed algorithm. The imposition of the essential boundary conditions and also of the unilateral contact with friction condition are made by the application of the Augmented Lagrangian method. Here, aspects related to the volumetric locking are investigated and an F‐bar approach is applied.

The results show that the proposed approach presents no volumetric locking phenomenon when using the mean dilation approach. Moreover, differently from finite element approximations, no hour‐glass instabilities in the deformation pattern are observed, avoiding in this way the need to devise additional stabilization procedures in the proposed procedure.

This paper demonstrates the implementation and validation of the mean dilation approach, in the scope of the EFG, which was successful in coping with the volumetric locking phenomena and presented no hour‐glass instabilities in the problem cases considered in this work.

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.

This paper extends the linear complementarity problem formulation of [7] and [8] for normal impact of planar deformable bodies in multibody systems. In the kinematics of impact we consider the normal gaps between the impacting bodies in terms of the generalized coordinates. Then, the generalized coordinate’s vector is formulated in terms of the impact forces using the 5th order implicit Runge‐Kutta approach RADAU5. Substituting the generalized coordinates in the relation of normal gaps together with the complementarity relations of unilateral contact constraints leads to a linear complementarity problem where its solution results in the solution of the impact problem including impact forces and normal gaps. Then, alternatively another formulation on velocity level based on the 4th order explicit Runge‐Kutta is presented. In the presented approach no coefficient of restitution is used for treatment of energy loss during impact and, instead, the material damping is responsible for energy loss. A good agreement between the results of our approach with the results of FEM for soft planar deformable bodies was shown in [7]. Here, we improve the results for stiff planar deformable bodies and show that with a proper selection of eigenmodes, the results on both position and velocity level approach the precise results of FEM provided that an optimal time step of the integration is chosen. We also investigate the effect of considering material damping and some higher eigenfrequencies on the amount of energy which is dissipated during impact based on our approach.

Purpose – The aim of this work is to provide a global 3D finite element (FE) model devoted to the modelling of superficial soil ploughing in the large deformation range and for a vast class of soil treatment tools. Design/methodology/approach – We introduced soil constitutive equation in a FE software initially designed for the metal forming. We performed the numerical integration of the non‐linear ploughing problem. Non‐linearities encountered by the problem can be summed up: as soil constitutive equation (idealized with non‐associated compressible plastic law), unilateral frictional contact conditions (with a rigid body), geometrical non‐linearities (the ploughing tool) and large deformation range. To handle such difficulties we performed several numerical methods as implicit temporal scheme, Newton‐Raphson, non‐symmetric iterative solver, as well as proper approximation on stress and strain measures. Findings – Main results deal with the validation of the integration of the non‐linear constitutive equation in the code and a parametric study of the ploughing process. The influence of tool geometric parameters on the soil deformation modes and on the force experienced on the tools had been point out. As well, the influence of soil characteristics as compressibility had been analyzed. Research limitations/implications – This research is devoted to perform a numerical model applicable for a large range of soil treatment tools and for a large class of soil. However, taking into account all kind of soil is utopist. So limitations met are essentially related to the limit of the accuracy of the elasto‐plastic idealization for the soil. Practical implications – In practice the numerical model exposed in the paper can clearly help to improve and optimize any process involving superficial soil submitted to the mechanical action of a rigid body. Originality/value – The original value of the paper is to provide a global and an applicable numerical model able to take into account the main topics related to the ploughing of superficial soils. Industrials in geotechnics, in agriculture or in military purposes can benefit in using such numerical model.