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Numerical determination of the mean value of an elasticity tensor by integration over the rotation group with Haar measure

Abstract : Let A be a 3D symmetric elasticity tensor not necessary isotropic. If µ is an invariant measure on SO(3), then µ is a convex combinaison of the Haar measure. The nearest isotropic elasticity tensor is obtained by integrating the tensor A on the rotation group SO(3). For the numerical approach, we integrate the elasticity tensor on the unit ordinary ball B(0,1).
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K. Atchonouglo, C. Vallé, Z.Q. Feng, J. Chaoui. Numerical determination of the mean value of an elasticity tensor by integration over the rotation group with Haar measure. British Journal of Mathematics and Computer Science, 2015, 10 (4), ⟨10.9734/BJMCS/2015/19480⟩. ⟨hal-02398146⟩

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