Difference in peel test results between MOOSE CZM InterfaceKernel (Constitutive model: BiLinearMixedModeTraction ) and ABAQUS

[asurovi]

Greetings!

I am trying to validate a 2D plane strain peel test problem results from MOOSE (using Cohesive Zone Action System, constitutive law: BiLinearMixedModeTraction) with ABAQUS Result.

Problem Statement: Two double cantilever beams, each 100 mm long (x-direction), 1.5 mm thick (y-direction) and 20 mm wide (out-of-plane-thickness) is bonded by an adhesive layer of negligible (zero) thickness. Material properties of beams: $E_{1} = 135.3 e 9$ Pa, $nu = 0.24$. Material properties of cohesive layer in MOOSE: penalty_stiffness $= 570 e 12$ Pa/m, normal_strength = shear_strength = $5.7e7$ Pa, $G_{Ic} = G_{IIC} = 280 J/m^{2}$, eta $= 2.284$, Material properties of cohesive layer in ABAQUS: $E/K_{nn} = E/K_{ss} = E/K_{tt} = 570 e12$, $\sigma_{I}^{0} = \sigma_{II}^{0} = \sigma_{III}^{0} = 5.7e7 Pa$, $G_{Ic} = G_{IIC} = G_{IIIc} = 280 J/m^{2}$, B-K law power = 2.284. The right edge is fixed in the x-direction (disp_x = 0) and time-dependent vertical displacements are applied at the top and bottom points as disp_y = $\pm$ 0.006 * t. The option use_displaced_mesh = false is used to ensure the displacements are imposed in the reference configuration.

Issue 1:
Important Points:

• I have used:
  • Same mesh and element type
  • Same material properties
  • Same interface properties
  • Same boundary conditions
• I checked the underlying CZM theory of the MOOSE Interface Kernel and ABAQUS cohesive elements and found that they are theoretically the same.
• However, I got different results for reaction force (computed from NodalSum of save_in r_y at top point and scaled by (1/2* out-of-plane-thickness * 1/2) due to symmetry BCs disp_x = 0 and equal division in both sides' interface) and stress_yy (using ElementalVariableValue) at top element as attached:

Issue 2:
Since I will need mortar interface definition to deal with non-conforming mesh adhesive contact problem, I have also tried to validate the same problem with BilinearMixedModeCohesiveZoneModel userobject. Though I was able to get a converged solution up to an applied displacement of 0.003 m after trying all possible solver setups, I am attaching the results here in the hope of getting insight into the convergence issue and the reaction-force mismatch between the CZM InterfaceKernel and Bilinear UserObject.

I am attaching input files of the peel test from ABAQUS and MOOSE (Cohesive Zone Action, BilinearMixedModeCohesiveZoneModel userobject)
peeltest_input_files.zip

Specific Questions:

1. Are the CZM properties that I used as MOOSE input comparable with those in ABAQUS?
2. What can be the reason that peak values are almost same but the elastic slope and softening behavior is different?
3. How can I resolve the convergence issue with BilinearMixedModeCohesiveZoneModel?

Thanks a lot for your time and help in advance.

Kind Regards,
Agnila Ghosh Surovi

[GiudGiud]

@arovinelli @hugary1995 if you have insights on the matter.
Thanks!

[hugary1995]

Very good questions!

Are the CZM properties that I used as MOOSE input comparable with those in ABAQUS?

I suspect not. I cannot say for sure without seeing the Abaqus theory manual on the cohesive traction-separation law. One easy way to check is to set up a simple two element test: Make a mesh consisting of two elements, introduce CZM along the element interface, apply a displacement control to pull the two elements apart. Do the same thing in MOOSE and Abaqus, and compare the force-displacement curves. That way we can know for sure whether the TSLs are equivalent, at least in the mode-I sense.

What can be the reason that peak values are almost same but the elastic slope and softening behavior is different?

One explanation is the TSLs in MOOSE and Abaqus could have different softening response but same peak traction.

How can I resolve the convergence issue with BilinearMixedModeCohesiveZoneModel?

There is a parameter called lag_displacement_jump that could help with convergence. However, when using this parameter you need to make sure the load increment size is small enough.