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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