4.1 Sandwich core
45
coating. The third approach tries to overcome this by implementing a three-layered
property set with a brittle material model for the phenolic resin coating and an elastoplastic material model for the inner aramid paper [Fis09], [Kil13], [Bar11], [Liu15],
[Liu15]. This approach promises a more realistic failure progression. Based on the reviewed literature, a suitable modelling approach for detailed meso-scale models is developed. This is described in the following.
Model description
Four-node planar elements of the S4R type are implemented for the cell walls. The cell
geometry is defined according to the cross-sectional measurements given in Table 5.
Mesh convergence studies show that a mesh size of 0.4 mm (equivalent to 5 elements
along cell wall width) provides a good trade-off between convergence and computational effort in particular for application in larger sandwich models [See14]. Since on constituent level solely the sandwich core is investigated, a mesh size of 0.25mm (8 elements
along cell wall width) is implemented in order to increase computational accuracy. This
mesh size is comparable to previous studies on Nomex meso scale modelling [Roy14],
[Gig12], [Hei08]. The honeycomb core is modelled excluding the face sheets. Rigid bond
between face sheet and core is assumed. Therefore, the nodes in the top and bottom
plane are each defined as rigid body. The bottom rigid body is constrained in all six degrees of freedom (DoF). The boundary conditions of the top nodes depend on the load
case. In compression and tension a constant velocity is prescribed in T direction, while
all remaining DoF are constrained. In case of transverse shear, a constant velocity is prescribed in W/L direction and all remaining DoF are constrained excluding the T direction.
These boundary conditions are summarized in Figure 35. It should be noted that Figure
35 illustrates the FE-models using a coarse mesh for clarity on the displayed nodal constraints. Due to the fact that an explicit solver is applied for quasi-static simulations, mass
scaling and increased loading rates are implemented to reduce the computational time.
Appropriate parameters for both model parameters have been established through sensitivity studies, in order to make sure that the simulation results are not affected. In addition, hourglass control is activated using the ABAQUS default settings. Another measure for keeping the computational time within manageable limits is reducing the total
model size if compared to the tested specimens. In case of honeycomb cells, this is generally done by defining a unit cell (UC) along with appropriate boundary conditions,
which represent the periodicity of the cellular core. The boundary conditions depend on
the implemented unit cell geometry and on the load case, while the defined unit cell
geometries of the present work are illustrated in Figure 36. The considerations that lead
to these unit cells have been described in [See17]. All simulations throughout the present
thesis were performed using ABAQUS 6.14-1.
45
coating. The third approach tries to overcome this by implementing a three-layered
property set with a brittle material model for the phenolic resin coating and an elastoplastic material model for the inner aramid paper [Fis09], [Kil13], [Bar11], [Liu15],
[Liu15]. This approach promises a more realistic failure progression. Based on the reviewed literature, a suitable modelling approach for detailed meso-scale models is developed. This is described in the following.
Model description
Four-node planar elements of the S4R type are implemented for the cell walls. The cell
geometry is defined according to the cross-sectional measurements given in Table 5.
Mesh convergence studies show that a mesh size of 0.4 mm (equivalent to 5 elements
along cell wall width) provides a good trade-off between convergence and computational effort in particular for application in larger sandwich models [See14]. Since on constituent level solely the sandwich core is investigated, a mesh size of 0.25mm (8 elements
along cell wall width) is implemented in order to increase computational accuracy. This
mesh size is comparable to previous studies on Nomex meso scale modelling [Roy14],
[Gig12], [Hei08]. The honeycomb core is modelled excluding the face sheets. Rigid bond
between face sheet and core is assumed. Therefore, the nodes in the top and bottom
plane are each defined as rigid body. The bottom rigid body is constrained in all six degrees of freedom (DoF). The boundary conditions of the top nodes depend on the load
case. In compression and tension a constant velocity is prescribed in T direction, while
all remaining DoF are constrained. In case of transverse shear, a constant velocity is prescribed in W/L direction and all remaining DoF are constrained excluding the T direction.
These boundary conditions are summarized in Figure 35. It should be noted that Figure
35 illustrates the FE-models using a coarse mesh for clarity on the displayed nodal constraints. Due to the fact that an explicit solver is applied for quasi-static simulations, mass
scaling and increased loading rates are implemented to reduce the computational time.
Appropriate parameters for both model parameters have been established through sensitivity studies, in order to make sure that the simulation results are not affected. In addition, hourglass control is activated using the ABAQUS default settings. Another measure for keeping the computational time within manageable limits is reducing the total
model size if compared to the tested specimens. In case of honeycomb cells, this is generally done by defining a unit cell (UC) along with appropriate boundary conditions,
which represent the periodicity of the cellular core. The boundary conditions depend on
the implemented unit cell geometry and on the load case, while the defined unit cell
geometries of the present work are illustrated in Figure 36. The considerations that lead
to these unit cells have been described in [See17]. All simulations throughout the present
thesis were performed using ABAQUS 6.14-1.