11 Meshless Algorithms for Computational Biomechanics of the Brain
293
Fig. 11.15 Verification of the MTLED algorithm through modelling of indentation of cylindrical
samples made from soft incompressible material (Sylgard 527 silicone gel by Dow Corning) with
properties similar to the brain tissue. (a) Experimental set-up. (b) Overall deformation of the
meshless model for the indentation depth of 10 mm (the displacement scale in the figure is in
metres). The interpolating nodes were connected to form the triangles to visualise the deformed
model surface. (c) Comparison of the force—indentation depth relationship obtained using the
MTLED framework (green dotted line), non-linear finite element procedures available in ABAQUS
finite element (FE) code (blue dotted line) and the experimental data (black solid line)—average
from three experiments. Using ABAQUS finite element code [31], we were able to obtain the
results for the indentation depth of up to only 4 mm after which the solution diverged. For the
indentation depth of up to 4 mm, the results obtained using the MTLED framework and ABAQUS
code are very close and cannot be visually distinguished. (Adapted from Wittek et al. [68])
countermeasure. Therefore, when obtaining the reference solution for verification of
the MTLED framework with the visibility criterion using the established non-linear
procedures available in the ABAQUS finite element code [31], surgical dissection
could not be directly modelled. Instead, the elongation was applied to the finite
element model of a specimen of soft hyperelastic material (with the brain tissue
properties) with a predefined dissection/cut (detailed description is in Jin et al.
[20]). The edges of the elements were aligned and separated along the dissection
(Fig. 11.18). The analysis using the ABAQUS finite element code was conducted for
implicit integration in time domain with the default parameters and linear (i.e. with
linear shape functions) quadrilateral plain strain elements with hybrid formulation
293
Fig. 11.15 Verification of the MTLED algorithm through modelling of indentation of cylindrical
samples made from soft incompressible material (Sylgard 527 silicone gel by Dow Corning) with
properties similar to the brain tissue. (a) Experimental set-up. (b) Overall deformation of the
meshless model for the indentation depth of 10 mm (the displacement scale in the figure is in
metres). The interpolating nodes were connected to form the triangles to visualise the deformed
model surface. (c) Comparison of the force—indentation depth relationship obtained using the
MTLED framework (green dotted line), non-linear finite element procedures available in ABAQUS
finite element (FE) code (blue dotted line) and the experimental data (black solid line)—average
from three experiments. Using ABAQUS finite element code [31], we were able to obtain the
results for the indentation depth of up to only 4 mm after which the solution diverged. For the
indentation depth of up to 4 mm, the results obtained using the MTLED framework and ABAQUS
code are very close and cannot be visually distinguished. (Adapted from Wittek et al. [68])
countermeasure. Therefore, when obtaining the reference solution for verification of
the MTLED framework with the visibility criterion using the established non-linear
procedures available in the ABAQUS finite element code [31], surgical dissection
could not be directly modelled. Instead, the elongation was applied to the finite
element model of a specimen of soft hyperelastic material (with the brain tissue
properties) with a predefined dissection/cut (detailed description is in Jin et al.
[20]). The edges of the elements were aligned and separated along the dissection
(Fig. 11.18). The analysis using the ABAQUS finite element code was conducted for
implicit integration in time domain with the default parameters and linear (i.e. with
linear shape functions) quadrilateral plain strain elements with hybrid formulation