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i have a problem that i wanted to share with you

if we consider a polycrystal made of cylindrical fibers following a von mises-fisher distribution equation (17) in http://bit.do/vmisesfisher (called orientation distribution function of fibers) . i must change the probability density in equation (28) http://bit.do/e28 with the von mises-fisher than i must follow the steps listed in the article http://bit.do/effectivetensor1 , http://bit.do/effectivetensor2 , http://bit.do/effectivetensor3 so that by using orientation averaging, i find the effective (elasticity) tensor of the polycrystal

it s an optimization problem

arg min of the integral over rotation group of the von mises-fisher distribution multiplied by the distance between the effective tensor of the polycrystal (what we are looking for) and the one of a single cylindrical fiber (given).

if any one could give ideas about how can i start solving this optimization problem to find the effective tensor of the polycrystal

.

thank you

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# Effective tensor of a polycrystal

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