Jean Salençon

Yield Design: A Survey of the Theory

The theory of Yield Design is based upon the obvious necessary condition for the stability of a structure that the equilibrium of that structure and the resistance of its constituents should be compatible. The static approach of the yield design theory proceeds directly from this condition, leading to lower estimates of the extreme loads. The kinematic approach is derived by dualizing the static approach through the principle virtual work, thus ensuring full mechanical consistency. The treatment of a classical example illustrates these arguments. Present and possibly future domains of practical applications of the theory are reviewed, including the full adequacy between the Yield Design Theory and the Ultimate Limit State Design concept of safety.

A numerical application of the slip line field method to extrusion through conical dies

Abstract The industrial importance of cold extrusion is now well known. Unfortunately, the productivity of the process is restricted by the manifestation of a specific defect: the central burst, which is closely linked to ductility and to a depressive stress state in the core of material. An accurate knowledge of these facts is therefore necessary to the extension of the process. In this paper, we develop a slip line field model in order to calculate exactly the hydrostatic pressure on the axis of the system. Its peculiarity is that it can be associated with a mechanical test of material ductility. This method is developed for axisymmetric extrusion through conical dies, with a perfectly plastic material, obeying Trescas yield criterion with its associated flow rule and with the Haar-Karman hypothesis. We assume that the pressure has a linear distribution along the die, which makes it possible to construct the slip line field. We then derive the velocity field, and determine by trial and error the pressure gradient along the die so that the velocity field satisfies all the boundary conditions. We apply this method to several extrusion ratios and die-angles; we compute the stress field in the deformed regions, obtaining an upper-bound for the extrusion pressure and a value for the hydrostatic pressure on the axis. Comparisons with experimental results show quite a good agreement between theoretical and experimental values of the extrusion pressure. The method will enable us in a future work to introduce friction along the die, metal work hardening and different profiles of the die.

Evaluation of global bearing capacities of structures

A synthetic presentation of the theory of yield design is illustrated by examples such as the stability analysis of reinforced soil structures and the resistance of long fiber reinforced composite materials. The classical limit analysis theory when standard elastic perfectly plastic behaviour can be assumed yields a more precise assessment of the global bearing capacities of structures and makes optimal limit design possible. Structural optimal design is also studied with respect to eigenvalues as well as Structural Topology and Design Optimization.

A Dynamic Macro-Element for Performance-Based Design of Foundations

The work is concerned with the development of an original macro-element model for shallow foundations within the context of performance-based design of structures. The macroelement can be viewed as a link element placed at the base of the structure that reproduces in a simplified, yet coherent way the non-linear interaction phenomena arising at the soil-footing interface during dynamic excitation. As such, it offers an efficient prediction of the maximum and permanent displacements at the foundation level by identifying the non-linear mechanisms that produce them. These are: (a) the sliding mechanism along the soil-footing interface, (b) the irreversible soil behaviour mechanism and (c) the foundation uplift mechanism. These non-linear mechanisms are introduced within the macro-element model in a fully coupled way. In its present state of development the model can be used for strip and circular footings in purely cohesive or purely frictional soils.

Stability analysis of reinforced soil structures through a homogenization method

The increasing use of soif reinforcement techniques in the field of geotechnical engineering, requires the elaboration of reliable as weil as practical yield design procedures for reinforced soif structures. The method presented hereafter, originates from the intuitive idea that from a macroscopic point of view, reinforced soils can be regarded as homogeneous but anisotropie materials, on account of the existence of privileged orientations due to the reinforcing inclusions. The strength criterion of such an equivalent homogeneous material can be theoretically determined starting from the strength characteristics of the reinforced soif components. Application of such a criterion, which can be explicitely formulated within the framework of a multilayered modelization for the reinforced soil, is then performed on the case of the stability analysis of sorne typical structures. Special concern has been given to reinforced earth structures, and it turns out that the theoretical estimations so obtained are in good agreement with experimental data. Despite sorne limitations which are outlined in the paper, the yield design homogenization procedure thus proposed is likely to become an appropriate design method for reinforced soif structures. * École Polytechnique, 91128 Palaiseau Cedex.

Statics of One-Dimensional Media

We shall now present two approaches to one-dimensional modelling of the continuum. The starting point for this theory of one-dimensional media must clearly be geometrical, based on the observation that many solids used as structural elements in constructions (civil or industrial engineering, ship building, aeronautics, etc.) have a slender shape (Fig. 1). This suggests that it should be possible to carry out mechanical studies on the one-dimensional geometry defined by a director curve.

Modelling the Continuum

The notion of a deformable continuous medium comes to mind when we observe the kind of solid deformations shown in Figs. 1 and 2, during cold or hot forming processes, or again the flow of a liquid, or the expansion and compression of a gas. From this kind of experience, the observer extracts the idea that certain problems can be treated on a macroscopic scale by assimilating the material to a ‘continuous’ medium, without in any way contradicting the assumptions of microscopic physics.

The Virtual Work Approach to the Modelling of Forces

The last three chapters have been devoted to geometrical modelling of the deformable continuum on the basis of our experimental intuition. In order to model the mechanics of the continuum, we must now introduce the idea of forces and establish laws governing the motion and equilibrium of a system in this model. It should be emphasised that, as in all classical textbooks, the word ‘forces’ is used here and in all that follows as a generic term. It does not imply that the corresponding actions are intended to be modelled as concentrated or distributed forces. It is the very aim of the analysis to investigate what force model is relevant.

Local Analysis of Stresses

The aim of Chap. V was to show how the virtual work method could be used to set up a representation of internal forces in the classical 3-dimensional continuum. We thus arrived at a symmetric second rank tensor field defined on the current configuration k t , which we called the Cauchy stress tensor field.

Classic Topics in Three-Dimensional Elasticity

The aim in this chapter is to present several classic problems in the study of linearised isothermal elastic equilibrium for homogeneous, isotropic materials. The initial state of the system under zero loading, taken as the reference state, is always assumed to be natural. The following points will be emphasised: statement of the problem (in particular, boundary conditions), form of the solution, remarks (e.g., other formulations of the problem), practical applications (e.g., yield point of the system).