000014150 001__ 14150
000014150 005__ 20161115100143.0
000014150 04107 $$aeng
000014150 046__ $$k2016-08-21
000014150 100__ $$aHashlamoun, Kotaybah
000014150 24500 $$aEffective Computation of Higher-Order Averaged Structure Tensors in Biomechanics

000014150 24630 $$n24.$$p24th International Congress of Theoretical and Applied Mechanics - Book of Papers
000014150 260__ $$bInternational Union of Theoretical and Applied Mechanics, 2016
000014150 506__ $$arestricted
000014150 520__ $$2eng$$aFor biological tissues reinforced by statistically oriented collagen fibres (such as articular cartilage), a probability distribution function is used to describe the orientation of the fibres. In evaluating the material response, the overall effect of the fibres is accounted for via the evaluation of averaging integrals over all possible directions in space. The averaging integral of the structure tensor (tensor product of the unit vector describing the fibre direction by itself), or the averaged structure tensor, is of high significance. Higher-order averaged structure tensors feature in several models and carry similarly important information. However, the computational cost associated with their evaluation is very high. This work proposes to introduce mathematical techniques to minimise the computational cost associated with the evaluation of higher order averaged structure tensors, for the case of a transversely isotropic distribution of orientation. Tensor and component expressions are presented.

000014150 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000014150 653__ $$a

000014150 7112_ $$a24th International Congress of Theoretical and Applied Mechanics$$cMontreal (CA)$$d2016-08-21 / 2016-08-26$$gICTAM2016
000014150 720__ $$aHashlamoun, Kotaybah
000014150 8560_ $$ffischerc@itam.cas.cz
000014150 8564_ $$s58713$$uhttps://invenio.itam.cas.cz/record/14150/files/PO.SM01-1.06.197.pdf$$yOriginal version of the author's contribution as presented on CD,  page 1717, code PO.SM01-1.06.197
.
000014150 962__ $$r13812
000014150 980__ $$aPAPER