Effective Computation of Higher-Order Averaged Structure Tensors in Biomechanics

Abstract eng:
For 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.

• Export as: BibTeX | MARC | MARCXML | DC | EndNote | NLM | RefWorks
• Add to your basket