Lahbib Bousshine

Limit analysis theorems for implicit standard materials : Application to the unilateral contact with dry friction and the non-associated flow rules in soils and rocks

A new class of materials called Implicit Standard Materials was proposed in a previous work. It allows one to generalize Fenchels inequality and then to recover flow rule normality for non-standard behaviours, in particular for soils and unilateral contact with dry friction. In this work an extension of the limit analysis theorems to this news class of materials is presented. Some relevant features are pointed out, such as non-uniqueness of the limit load and coupling of the lower and upper bound problems. Some analytical and numerical solutions are presented to illustrate the theory.

A new approach to shakedown analysis for non-standard elastoplastic material by the bipotential

Abstract On the basis of the implicit standard materials that introduces a function, called bipotential, depending on both the stress and plastic strain rate, this paper is devoted to present a new approach of shakedown analysis for non standard elastoplastic materials. The bipotential theory was successfully applied to geomaterials with non-associated flow rule and Coulombs dry friction law. The present analysis is different to the Melans potential and it is based on a corner stone inequality satisfied by the bipotential and the existence of time-independent residual stress field. The deduction of bound theorems, static and kinematic, is detailed in the present article.

Plastic limit load of plane frames with frictional contact supports

On the basis of the bipotential theory, published in previous contributions, the objective of the work presented in this paper is to establish an extended formulation of limit analysis theory for frames in presence of the unilateral contact with Coulombs dry friction at supports. The kinematic and static approaches are formulated by the calculation of the total dissipation power of the frame. As it will be shown, on account of the presence of contact with friction, the two approaches are coupled in the sense that the kinematic limit analysis contains static variables and converse. To deal with, an iterative algorithm, based on successive approximations method, will be described here. The study of a simple example, consisting of a rectangular frame, demonstrates that the coefficient of friction value affects the plastic limit state and therefore the limit load and the collapse mechanism taking place too.

Implicit Standard Materials

We present a formulation for the non associated constitutive laws based on a generalization of Fenchel’s inequality and the concept of bipotential. Then, the normality rule appears as an implicit relation between dual variables. Examples of applications to the plasticity of soils and rocks, the cyclic plasticity of metals, the frictional contact and the plasticity with damage are presented.

Kinematic Limit Analysis of Nonassociated Perfectly Plastic Material by the Bipotential Approach and Finite Element Method

Limit analysis is one of the most fundamental methods of plasticity. For the nonstandard model, the concept of the bipotential, representing the dissipated plastic power, allowed us to extend limit analysis theorems to the nonassociated flow rules. In this work, the kinematic approach is used to find the limit load and its corresponding collapse mechanism. Because the bipotential contains in its expression the stress field of the limit state, the kinematic approach is coupled with the static one. For this reason, a solution of kinematic problem is obtained in two steps. In the first one, the stress field is assumed to be constant and a velocity field is computed by the use of the kinematic theorem. Then, the second step consists to compute the stress field by means of constitutive relations keeping the velocity field constant and equal to that of the previous step. A regularization method is used to overcome problems related to the nondifferentiability of the dissipation function. A successive approximation algorithm is used to treat the coupling question. A simple compression-traction of a nonassociated rigid perfectly plastic material and an application of punching by finite element method are presented in the end of the paper.

A MESHLESS METHOD ANALYSIS OF ELASTO-PLASTIC CONTACT PROBLEMS WITH FRICTION

We present a theoretical and numerical analysis of incremental elasto-plastic problems based on the meshless method and the mathematical programming. This study is done on an elasto-plastic material with isotropic hardening obeying to the von Mises criterion. The transformation method is adopted to impose the essential boundary condition. The Coulombs dry friction contact is used to implement the frictional boundary conditions and is formulated by the bipotential method which leads to only one principle of minimum in displacement. The numerical analysis results obtained by the method proposed in this paper are in good agreement with those obtained by FEM.

Numerical simulation of orthogonal cutting by incremental elastoplastic analysis and finite element method

Abstract The present work is devoted to numerical simulation of orthogonal metal cutting process by an incremental elastoplastic model taking into account the presence of the unilateral contact law with Coulomb’s dry friction on the tool/chip interface. The cutting problem is considered as a steady state in plane strain condition. The contact law in the interface is described by the bipotential concept leading us to minimise a one principle of minimum. In this model, the finite element method and the mathematical programming are used to perform numerical solutions. The numerical results obtained are compared with theoretical and experimental ones.

Solving Frictional Contact Problems within the Bipotential Framework

The main objective of this paper is to present a theoretical and numerical analysis of frictional contact problems for large deformation elasto-plastic based on the finite element method (FEM) and the mathematical programming. The study is done on an elasto-plastic material obeying to the von Mises criterion. The Coulomb’s friction contact is used to implement the frictional boundary conditions and is formulated by the bipotential concept leading us to minimize only one variational principle of minimum in displacement. In order to follow up the sequences of large deformations, we have used the sequential analysis procedure; it consists in the updating of material properties and geometrical configuration after each sequence.

Etats limites plastiques en presence de l’écrouissage isotrope

Que ce soit dans un objectif de conception de structures ou de mise en forme par déformation plastique, l’analyse limite est parmi les méthodes directes d’estimation des états limites plastiques les plus connues. En se basant sur l’approche cinématique au sens de l’analyse limite et en se servant de la méthode des éléments finis, l’objectif principal de ce travail consiste à aborder les grandes déformations plastiques du modèle de von Mises en considérant l’écrouissage isotrope. Afin de surmonter la difficulté engendrée par la nondifférentiabilité de la dissipation plastique, nous avons particularisé une méthode de régularisation initialement développée pour les matériaux compressibles. Dans le but de suivre les séquences de grandes déformations, la notion d’analyse limite séquentielle qui consiste en la mise à jour des propriétés des matériaux et de la géométrie de configuration après chaque séquence est appliquée.

Modelization by Finite Elements of Cutting and Punching Problems Using an Algorithm Based on the Implicit Standard Materials, Applied to the Friction

A new class of materials called Implicit Standard Materials is proposed. It allows to generalize Fenchel’s inequality, and then to recover normality law for non standard behaviour, in particular for unilateral contact with dry friction and granular materials. In terms of finite element method, an algorithm based on the non linear mathematical programming is used to solve every step of the incremental problem. The numerical applications show the convergence of the method. The significative sensitivity of the solution to the non associativity of the soil flow rule can be quotted.