A Discrete Fiber Dispersion Model with Octahedral Symmetry Quadrature for Applications in Skin Mechanics

Abstract

Advanced simulations of the mechanical behavior of soft tissues frequently rely on structure-based constitutive models, including smeared descriptions of collagen fibers. Among them, the so-called Discrete Fiber Dispersion (DFD) model is based on a discrete integration of the fiber-strain energy over all the fiber directions. In this paper, we recall the theoretical framework of the DFD model, including a derivation of the stress and stiffness tensors required for the finite element implementation. Specifically, their expressions for incompressible plane stress problems are obtained. The use of a Lebedev quadrature, built exploiting the octahedral symmetry, is then proposed, illustrating the particular choice adopted for the orientation of the integration points. Next, the convergence of this quadrature scheme is assessed by means of three numerical benchmark tests, highlighting the advantages with respect to other angular integration methods available in the literature. Finally, we propose as applicative example a simulation of Z-plasty, a technique commonly used in reconstructive skin surgery, considering multiple geometrical configurations and orientations of the fibers. Results are provided in terms of key mechanical quantities relevant for the surgical practice.