On the Effect of Stress Concentration in Cosserat Continua

Abstract

The theories of continuum mechanics use idealised models mostly based on the assumption of a continuous distribution of matter. Only in this way the fundamental definitions can be introduced as there are the continuous and differentiable displacement and rotation vectors, the stress and strain tensors and the necessary material constants characterising the deformation behaviour. All these quantities represent statistical mean values taken over very small ranges of volume and time. Consequently continuum theories cannot give satisfying predictions of the behaviour of the material within very small ranges of volume and time, if high gradients of stress and strain occur; especially these theories cannot describe processes with dominating structure effects since all material qualities producing effects of such kind had been eliminated by introducing the idealised models. In consequence of this situation a restrictive condition must be respected with regard to the applicability of continuum theories in very small ranges of volume and time. There are some analogies to the physical restrictive condition of Heisenberg.