ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

3.2 Verification of meshless algorithm for soft tissue fragmentation modelling
We modelled uniaxial elongation of a rectangular specimen (dimensions of 0.1 m by 0.1
m) of soft (Young’s modulus of 3000 Pa) nearly incompressible (Poisson’s ratio of
0.49) continuum (Fig. 3). The results obtained using our algorithm were compared with
those from the well-established non-linear finite element procedures available in
ABAQUS finite element code.
As discussed in Introduction, finite element method does not facilitate robust and
accurate simulation of propagation of discontinuities due to fragmentation of soft
continua. Therefore, to eliminate the need for simulation of such propagation, modelling
of discontinuity in the finite element model shown in Fig. 3a started from introducing
the notch with geometry corresponding to that of the fully propagated notch in the
meshless model. Then elongation of 0.02 m was applied. On the other hand, in the
model implemented using our meshless algorithm, the fragmentation was initiated by
introducing a small notch in the deformed (elongated by 0.02 m i.e. 20%) meshless grid
(Fig. 3b). The discontinuity in the analysed continuum was propagated by adding nodes
on the notch edges.
a) b)
Fig. 3 Verification of the meshless algorithm for soft tissue modeling: simulation of 2-D
specimen of soft tissue-like hyperelastic material (the neo-Hookean constitutive model was
used) subjected to uniaxial elongation (on edge B) and rigidly constrained on edge A. The
specimen dimensions are 0.1 m by 0.1 m. a) Finite element model (ABAQUS solver was
used) with notch; b) Deformed meshless model with notch (the points shown are field nodes
of the meshless discretisation).
3.3 Evaluation of meshless algorithm performance: Modelling of pia-arachnoid complex
elongation
We applied our meshless algorithm with visibility criterion for fragmentation modelling
to simulate the experiments on in-plane elongation of pia-arachnoid complex (PAC)
samples conducted by Jin et al. [13] (Fig. 4) and compared the nominal stress–strain
histories predicted by the algorithm with the experimental results.
To facilitate modelling of tissues with fibrous/composite structure (such as the brain
meninges), we implemented a hyperelastic transverse isotropic material model
according to [14]. We focused on the responses at a very small strain rate of 0.05 s -1 and