ABSTRACT

The mechanical and statistical aspects are deeply related and it is not possible to separate their consequences at the macro-scale level. It can only be said that neither a purely statistical model (not describing the mechanical nature of the phenomenon), neither a purely deterministic damage model (without any statistical aspect) can really account for size-effect. However, they will practically work in certain cases. Breysse and Saouridis [4] have explained for what reasons volume effects (decrease of strength with increasing size, under uniform loading) and gradient effects (increase of strength with a higher concentrated loading) can be explained by similar mechanisms. For instance, the so-called gradient effect can be induced by a non uniform external loading (gradient of stress), or by the presence of a geometrical stress concentrator (a notch for instance). However, due to the fact that the micro-properties change at each point, even a uniform external loading results in gradient of stresses/strains at the micro-scale. It comes that it may seem artificial to distinguish between volume effect and gradient effect, and that a wholly general understanding of the underlying mechanisms is preferable.