Cosserat, Eugène and François

The Cosserat theory of elasticity, also deserving the names of micropolar elasticity, the micropolar theory of elasticity, or micropolar continuum mechanics, incorporates a local rotation of material points as well as the translation assumed in classical elasticity and a couple stress (a torque per unit area) as well as the force stress (force per unit area). This theory was motivated by the discrepancy observed between the results of classical theory of elasticity and experiments performed for solid bodies sowing pronounced effects of an underlying microstructure, like in granular media, and multimolecular bodies, like polymers, or in the vicinity of cracks and notches. It was proposed in 1887 by Voigt who tried to remove the shortcomings of classical elasticity theory by assuming that the mutual interaction of two parts of a solid body is mediated not only by a force vector associated to Cauchy stress but also by an internal moment vector due to additional couple stresses (Fig. 1).

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