Stress-based Insertion in Vertical Interface Specimen

In order to more clearly observe the adaptive capabilities of our dynamic insertion algorithm we have selected a simple mode I problem composed of two different materials separated by a vertical interfaces, as seen in Figure 4.27. The bulk material of the pre-notched region has a Young's modulus $E_1 = 3.24 \times 10^9 Pa$ and the maximum normal and shear stress for its cohesive elements is $\sigma_{max,1} = 3.24 \times 10^7 Pa$. The second region is $100$ times stronger with $E_2 = 100 E_1$ and $\sigma_{max,2} = 100 \sigma_{max,1}$, while the interface cohesive elements are weakened by $100$ times. Figures 4.28 through 4.30 are snapshots of the solution at various time steps during the $72000$ time step simulation using the $45\%$ stress insertion criteria. From these figures we can see the build-up of the cohesive elements - and consequently the stresses - both at the crack tip as well as far field along the vertical interface. As the main crack begins to propagate through the solution, the build-up of stresses near the interface causes it to delaminate, prior to the arrival of the main crack. But once the main crack finally reaches the interface, it becomes trapped and grows in both directions along the interface till complete failure of the system occurs.

Figure 4.27: Schematic representation of interface test specimen with boundary conditions.

Figure 4.28: Deformation after 5000 time steps for stress insertion of 45% (10x exaggeration).
Figure 4.29: Deformation after 17500 time steps for stress insertion of 45% (10x exaggeration).
Figure 4.30: Deformation after 25500 time steps for stress insertion of 45% (10x exaggeration) (edge key: thin = normal edge, dark = cohesive element, dashed = failing cohesive element, bold = failed cohesive element).