Exact Analytical Representation of Fiber Stress Tensor Based on Angular Integration (AI) Through Cellular Level Probabilistic Equations

Coban G., Celebi M. S.

International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Rhodes, Greece, 22 - 28 September 2014, vol.1648 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1648
  • Doi Number: 10.1063/1.4912568
  • City: Rhodes
  • Country: Greece


An analytical representation of the structural stress tensor which describes the fiber dispersion in soft biological tissue has been represented. The mathematical form is computationally efficient compared to the angular integration schemes and it interelates the cellular scale fiber rotation concept with macroscopic deformation of the tissue. It has been shown that, based on well known cellular rotation concepts, the steady state second Piola-Kirschoff stress tensor can be described by a set of structural and remodeling variables, and the current strain tensor.