Modelling Small Deformations of Polycrystals

The scientific work of Jean Mandel has been exceptionally rich in the area of the mechanics of solids; the subjects which he has treated have been extremely diverse, from the theory of plasticity, buckling, soil mechanics, visco-elasticity, the theory of reduced models, and thermo- dynamics, to percolation in porous media. But throughout this com- prehensive work Jean Mandel has always maintained his interest in forming connections between the properties of materials (strength, deformability, viscosity) and the properties of their basic constituents. What is sometimes referred to in materials science as the transition from the microscopic to the macroscopic has for him been a very constant direction of research, which he never ceased to encourage in the Laboratoire de Mecanique des Solides of which he was the director. It is known that in the plasticity of metals permanent deformations must be sought in intercrystalline slip and more generally in disloca- tions and the various microstructural defects. Before deformation of polycrystals is tackled, it is necessary to understand the mechanisms which take place within the crystal: the different systems of slip which may be activated and also the elementary mechanisms of twinning. Jean Mandel has shown how to make the transition from the behaviour of the single crystal to that of the polycrystal and has given the relation- ships between the overall permanent deformation of the polycrystal and the plastic deformation of the single crystal.