Reduced kinematic multiscale model for tissue engineering electrospun scaffolds

Abstract

To this day, there is still a need for a direct relationship between the microscopic material properties and network microstructure configuration with the macroscopic mechanical response in order to optimize the design loops of biomimetic electrospun grafts. Multiscale mechanical modeling arises as a useful alternative, which allows to represent the individual nanofibers mechanical response and how the interaction between fibers results in the final macroscopic behavior. In this work, a micromechanical model that accounts for fiber interaction, progressive straightening (i.e. progressive recruitment) and reorientation is presented. An RVE is generated by means of a virtual deposition algorithm that mimics the electrospinning process itself, thus obtaining geometries that resemble the observed electrospun microstructure. These geometries were then validated by comparison with analysis of SEM images, taking special interest in the diameter, orientation and tortuosity distributions. Then, an elastic–plastic constitutive law for the nanofibers is implemented along with a simplified kinematic description that results in a significant reduction of the number of Degrees of Freedom of the discretized mechanical equilibrium problem. Finally, the micromechanical model is validated against uniaxial tensile tests of electrospun PLLA bone-shaped samples, reproducing the experimentally observed behavior while employing realistic geometric and constitutive parameters to characterize the fibers.