On multiscale boundary conditions in the computational homogenization of an RVE of tendon fascicles

Abstract

Present study provides a numerical investigation on multiscale boundary conditions in the computational homogenization of a representative volume element (RVE) of tendon fascicles. A three-dimensional hexagonal-helicoidal finite element RVE composed of two material phases (collagen fibers and cells) and three finite strain viscoelastic models (collagen fibrils, matrix of fibers and cells) compose the multiscale model. Due to the unusual helical geometry of the RVE, the performance of four multiscale boundary conditions is evaluated: the linear boundary displacements model, the minimally constrained model and two mixed boundary conditions allying characteristics of both, linear and minimal models. Numerical results concerning microscopic kinematic fields and macroscopic stress-strain curves point out that one of the mixed models is able to predict the expected multiscale mechanics of the RVE, presenting sound agreement with experimental facts reported in literature, for example: characteristic non-linear shape of the stress-strain curves; macroscopic energy loss by hysteresis; axial rotation of fascicles observed in tensile tests; collagen fibrils are the main load-bearing components of tendons; cells contribute neither to the stiffness nor to the macroscopic energy loss. Moreover, the multiscale model provides important insights on the micromechanics of tendon fascicles, predicting a non-homogeneous and relevant strain localization on cells, even under physiological macroscopic strain amplitudes.

Keywords: Finite element method; Homogenization; Multiscale; Soft tissues; Tendon; Viscoelastic.