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effective tensor of a polycrystal
Posted Dec 4, 2014, 4:35 p.m. EST 0 Replies
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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 bit.do/vmisesfisher (called orientation distribution function of fibers) . i must change the probability density in equation (28) bit.do/e28 with the von mises-fisher than i must follow the steps listed in the article bit.do/effectivetensor1 , bit.do/effectivetensor2 , 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
Hello Khaled Alyani
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