A 3D computational model of electrospun networks and its application to inform a reduced modelling approach

Abstract

In this contribution, a full 3D finite element model of electrospun networks is presented. The model explicitly accounts for the specific microstructure of these networks by generating representative volume elements through a particular fibre deposition method inspired by the process of network formation during electrospinning. The modelled fibre material and structural properties, such as different fibre shapes and distributions in diameter, can vary over a wide range, and mutual fibre contact is considered in addition to permanent cross-links. In addition to the homogenized mechanical response to macroscopic in-plane loads, the model provides access to structural information which can hardly be determined in experiments, such as fibre disposition and interconnectivity. In the present work, this asset is used to inform a recent 2.5D modelling approach (Zündel et al., 2017) and to validate inherent assumptions on network structure. The comparison between the responses of the two approaches reveals that for networks of high porosity, the reduced 2.5D model captures well the mechanical behaviour in plane stress load cases. At lower porosities though, the increasing out-of-plane orientation of fibre segments leads to effects that cannot be captured by planar approaches and necessitate a 3D approach.

Random auxetics from buckling fibre networks

“…ref. 25 ). As a consequence, transverse fibre segments are subjected to compressive loads and, eventually, buckle 26,27 .…”

“…The sets were characterised by thickness t N and segment length a of 19:14 ± 0:04 μm and 17.67 ± 0:48 μm (straight), and 19:59 ± 0:4 μm and 17:34 ± 0:5 μm (undulated), respectively (mean and standard deviation). The fibre material behaviour was defined by Young's modulus E F = 1500 MPa and Poisson's ratio ν F = 0.4 in the elastic case and additionally with the hardening slope K p F = 150 MPa and yield stress σ p F = 30 MPa for the elastic-plastic case 25 in a geometrically non-linear frame. The generated networks were used to conduct simulations of uniaxial tension experiments with Abaqus/Explicit by prescribing the elongation (λ 1 ) of the virtual network through homogeneous displacements at two opposite cross-sections, homogeneous displacements and overall zero traction at the two lateral boundaries, and unconstrained bottom and top surfaces 25 .…”

“…In particular, multiscale models allow virtual testing and thus provide access to information beyond experimental feasibility. To showcase this, we studied the effects of fibre tortuosity and inelasticity on the auxetic behaviour by means of a 3D finite element model of electrospun networks 25 , that overcomes the assumptions of affinity and prescribed buckling modes inherent to the idealised analytical model. Uniaxial tension simulations for a reference material with low fibre curvature, i.e., nearly straight segments and mean segment aspect ratio a = 17.67 qualitatively capture the in-plane fibre reorientation ( Fig.…”

On the homogeneity and isotropy of planar long fibre network computational models

“…2c) are defined through a random walk, or a chain of links with length l [19,25,32,33], and l = 4 × 10 −3 is chosen here. In particular, following our previous work [19,26] a worm-like model [34,35] is used. Thus the first link is introduced at each seeding point with random orientation ∼ Uni(0, 2 ) , and consecutive links are added until the fibre reaches a boundary of Ω c .…”

“…Both deterministic, e.g. straight or sinusoidal, and non-deterministic random curves can be used to model the shape of the single fibre centre lines [19]. For the generation of the network models, the single fibres need to be distributed within the modelling domain Ω c , for which the network properties of interest are computed.…”