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It seems like you've made a comprehensive effort to set up your analysis for 2-material fiber composites using APDL 2021 R1. The convergence issue you're facing at large displacements, such as 150 or 200, can be due to several factors. Here are some steps you can take to diagnose and potentially resolve the problem:

Check Material Properties: Ensure that the material properties you've defined for both material 1 and material 2 are accurate and appropriate for large displacements. Double-check the values of Young's modulus, Poisson's ratio, and the hyperelastic parameters.

Convergence Settings: Increase the convergence tolerance settings to see if it helps the solver converge at larger displacements. You can adjust settings like "AUTOTS,ON" and "NSUBST" to make the convergence criteria more relaxed.

Element Quality: Examine the quality of your mesh elements, especially in regions with large displacements. Poorly shaped elements can lead to convergence problems. Consider refining the mesh in critical areas.

Solver Iterations: It might require more solver iterations to reach convergence at larger displacements. You can increase the maximum number of iterations or use adaptive techniques to control convergence.

Boundary Conditions: Ensure that your boundary conditions are correctly applied for large displacements. Sometimes, improper constraints can hinder convergence.

Output and Monitoring: Add more output requests during the solution to monitor the convergence progress. This will help you identify which step is causing the issue. You can use the /OUTPR command to control the output frequency.

Contact or Bonding: If your model involves contact between different parts, make sure that the contact or bonding settings are appropriate for large displacements.

Element Type: Depending on your specific problem, consider using different element types or formulations that are better suited for large deformation analyses, such as shell elements or 3D solid elements with enhanced formulations.

Solver Documentation: Refer to the documentation for APDL 2021 R1 to see if there are any specific recommendations or limitations for large displacement problems.

Numerical Instabilities: Large displacements can sometimes lead to numerical instabilities. Ensure that your time-stepping strategy and nonlinear analysis settings are appropriate for your problem.

Consult Experts: If the issue persists, consider consulting with experts in finite element analysis or the ANSYS support team. They may be able to provide specific guidance based on your model and setup.

Remember to back up your current setup before making significant changes and document any modifications you make for future reference. Troubleshooting convergence issues can be complex, and it often involves a combination of adjusting settings, refining the model, and careful analysis of the results.