Hi Chris,
Could you describe what is the material of the solid body (plate) where the line bodies are connected to? I suggest using rigid behavior for the tooling as the resulting deformation of the supports appears undesired to you. You can at least increase the Young's modulus of the current tooling to evaluate whether the response is moving into the right direction. I assume you employed linear elastic behavior for all materials.
Also, try using a frictional contact type as it is better in line with reality. This is particularly important as you seem to be planning to compare your simulation results with actual experiments.
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