# About the Cosserats’ Book of 1909

## Abstract

The Cosserat brothers published in 1909 an original book where they favour a variational formulation of continuum mechanics together with an invariance which they call “Euclidean invariance” of the Lagrangian-Hamiltonian action. This strategy places on an equal footing translations and possible rotational degrees of freedom, yielding in a natural way what is now commonly called the theory of Cosserat or oriented—or polar—continua with asymmetric stresses and the new notion of couple stresses. Here their landmark work is replaced in its epoch making context underlining the influences they benefited from and the influence they have exerted on their direct contemporaries and much later on (in the second-half of the twentieth century). The sociological scientific environment of the early twentieth century and the typical publication strategy of the time are outlined, explaining thus the Cosserats’ own strategy. The further reception of their work from 1909 to the Second World War and the revival of interest in it in the nineteen-fifties are examined critically. Finally, the formalization of their work in a new landscape of continuum thermo-mechanics created essentially by Truesdell is evoked together with other influences and further developments.

### Keywords

Cosserat continua Euclidean invariance Couple stress Variational formulation Generalized continua### References

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