Virtual design of electrospun-like gelatin scaffolds: The effect of three-dimensional fibre orientation on elasticity behaviour

Remarkable mechanical performance of biological tissues is explained by a hierarchical fibrous structure. Designing materials that have similar properties is challenging because of the need to assess complex deformation mechanisms. In order to shed more light on architectural possibilities of biopolymer fibrous networks, we propose a numerical study that relates the fibre arrangement to the elastic modulus of a gelatin scaffold obtained using electrospinning. The adopted approach is based on the virtual designing of scaffolds using all possible combinations of Euler angles that define fibre orientations including preferable alignment. The generated networks are converted into a finite element model and the predicted elastic behaviour is examined. Predictions show that the fibre alignment achieved experimentally in biopolymer fibrous networks is for most of the fibres exhibiting an orthotropic behaviour. Some particular combinations of Euler angles allow transverse isotropic architectures while only limited cases are isotropic. A large sensitivity of Young's moduli to Euler angles is achieved describing multiple scenarios of independent anisotropic behaviours. An anisotropy ratio of the elastic behaviour is suggested based on a suitable combination of elastic moduli. Such a ratio exhibits a wide variation depending on individual and coupled effects of Euler angles. The finite element model predicts 2D, 3D and 4D maps representing all possible configurations of fibre alignment and their consequences on elastic behaviour. The predicted fibre orientation representing the observed anisotropic behaviour of electrospun gelatin networks demonstrates unbalanced contributions of in-plane and out-of plane fibres for a large range of processing conditions