Numerical Determination of the Mean Value of an Elasticity Tensor by Integration over the Rotation Group with Haar Measure
Kossi Atchonouglo, Claude Vallee, Zi-Qiang Feng, Jamal Chaoufi
Journal of Advances in Mathematics and Computer Science · pp. 1–9 · Published 19 Jul 2015
10.9734/BJMCS/2015/19480Abstract
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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