174
K. Miller et al.
outputs 2850 individual boundary conditions, which are easily transferred to the
INP file containing the part and element definitions, before loading into Abaqus
CAE for analysis.
The loading is applied gradually over a period of 10 seconds using the smooth
step amplitude function in Abaqus, which implements a 345 polynomial [1]. This
is necessary to prevent excessive distortion in the elements resulting from large
displacement increments in each time step.
7.2.5 Material Properties
As explained in Chap. 6 of this book and our papers [15, 26], for problems where
loading is prescribed as forced motion of boundaries, the unknown deformation
field within the domain depends very weakly on the mechanical properties of the
continuum. This feature is of great importance in biomechanical modelling where
there are always uncertainties in patient-specific properties of tissues. Therefore
we use a simple neo-Hookean [26] constitutive model with Young’s modulus of
3000 Pa. To account for approximate incompressibility of brain tissue (see Chap. 4
of this book), we chose a Poisson’s ratio of 0.49.
7.2.6 Solution Algorithm and Software
Although the analysis is static, an explicit algorithm is the preferred solver because
the nonlinearity of the model makes it difficult and computationally expensive
to achieve convergence in every time step (see Chap. 10). The model is run in
Abaqus Explicit for 100 simulation seconds to allow sufficient time for a steadystate solution to be achieved. To ensure stability, a minimum time step has been
estimated from the characteristic length of the mesh and the dilatational wave speed
[1] to be ca. 4 × 10 −5 seconds. The default parameters for linear and quadratic
bulk viscosity are used, providing a means of damping to control high-frequency
oscillations in the solution.
The element formulations available in Abaqus Explicit include linear or quadratic
elements. For efficiency, the linear reduced integration hexahedrons (C3D8R) and
tetrahedrons (C3D4) are chosen with default hourglass and distortion control (for
discussion about appropriate element types for explicit analysis of approximately
incompressible materials, see also Chaps. 6 and 10 of this book). The skull is
assigned rigid triangular facet elements (R3D3).
K. Miller et al.
outputs 2850 individual boundary conditions, which are easily transferred to the
INP file containing the part and element definitions, before loading into Abaqus
CAE for analysis.
The loading is applied gradually over a period of 10 seconds using the smooth
step amplitude function in Abaqus, which implements a 345 polynomial [1]. This
is necessary to prevent excessive distortion in the elements resulting from large
displacement increments in each time step.
7.2.5 Material Properties
As explained in Chap. 6 of this book and our papers [15, 26], for problems where
loading is prescribed as forced motion of boundaries, the unknown deformation
field within the domain depends very weakly on the mechanical properties of the
continuum. This feature is of great importance in biomechanical modelling where
there are always uncertainties in patient-specific properties of tissues. Therefore
we use a simple neo-Hookean [26] constitutive model with Young’s modulus of
3000 Pa. To account for approximate incompressibility of brain tissue (see Chap. 4
of this book), we chose a Poisson’s ratio of 0.49.
7.2.6 Solution Algorithm and Software
Although the analysis is static, an explicit algorithm is the preferred solver because
the nonlinearity of the model makes it difficult and computationally expensive
to achieve convergence in every time step (see Chap. 10). The model is run in
Abaqus Explicit for 100 simulation seconds to allow sufficient time for a steadystate solution to be achieved. To ensure stability, a minimum time step has been
estimated from the characteristic length of the mesh and the dilatational wave speed
[1] to be ca. 4 × 10 −5 seconds. The default parameters for linear and quadratic
bulk viscosity are used, providing a means of damping to control high-frequency
oscillations in the solution.
The element formulations available in Abaqus Explicit include linear or quadratic
elements. For efficiency, the linear reduced integration hexahedrons (C3D8R) and
tetrahedrons (C3D4) are chosen with default hourglass and distortion control (for
discussion about appropriate element types for explicit analysis of approximately
incompressible materials, see also Chaps. 6 and 10 of this book). The skull is
assigned rigid triangular facet elements (R3D3).