You're facing a common challenge in numerical modeling: replicating results from one software package in another, especially when dealing with complex nonlinear material behavior like that of rubble stone masonry. You're right to suspect that differences in the underlying numerical formulations, particularly regarding crack modeling, could be the primary source of the discrepancy between your SAP2000 results and Proença et al.'s (2018) DIANA results.

Here's a breakdown of potential issues and considerations:

Crack Modeling Differences:

• Total Strain Rotating Crack Model (DIANA): This model is sophisticated and tracks the crack orientation as the deformation progresses. It's well-suited for capturing the anisotropic behavior of cracking in materials like masonry.
• SAP2000's Layered Shells and Nonlinearity: While SAP2000 allows for layered shells and material nonlinearity (including tension softening), it doesn't directly implement a "rotating crack" model in the same way as DIANA. The tension softening you're applying is likely based on a fixed crack approach, where the crack direction is determined at the onset of cracking and remains fixed throughout the analysis. This simplification can lead to differences in the predicted response, especially in shear-dominated problems where crack rotation is significant.

Material Model Implementation:

Constitutive Model Details: Even if both software packages offer "linear elastic in compression and exponential softening in tension," the specific implementation details can vary. Pay close attention to:

• Tension Softening Parameters: The shape of the exponential softening curve (e.g., the fracture energy, Gf, and the tensile strength, ft) is crucial. Small differences in these parameters can significantly affect the post-cracking behavior. Ensure you're using exactly the same values as Proença et al. (2018).
• Compression Behavior Beyond Elasticity: While you're using linear elastic compression, it's worth considering if any damage or crushing behavior is implicitly included in the DIANA model that you might be missing in SAP2000.
• Shear Retention: The reduction of shear stiffness after cracking is a critical parameter in masonry models. Ensure you are accounting for this in SAP2000. There are different approaches to model shear retention, and the specific method used in DIANA might differ from the one available in SAP2000.

Mesh Sensitivity:

• Element Size and Type: The mesh density and element type can influence the results, especially in nonlinear analyses. Ensure your SAP2000 mesh is sufficiently refined, particularly around the opening where stress concentrations and cracking are expected. Compare the element size used in DIANA if possible.
• Integration Points: You mentioned you've tried varying the number of integration points. This is important, but be aware that increasing the number of integration points beyond a certain point may not significantly improve accuracy and can increase computational cost.

Solution Algorithm and Convergence:

Nonlinear Solution Control: The nonlinear solution algorithms (e.g., Newton-Raphson, arc-length) and convergence criteria used in the two software packages can differ. These differences can affect the accuracy and stability of the solution, particularly in highly nonlinear problems.

Some recommendations that can be given to you are as follows.

• Focus on Material Calibration: The most likely source of the discrepancy is the material model and its parameters. Double-check every parameter of the constitutive model, especially those related to tension softening and shear retention. If possible, try to calibrate your SAP2000 model against simpler experimental tests (e.g., direct tension or shear tests) on similar masonry specimens to ensure the material behavior is accurately captured.
• Investigate SAP2000's Crack Modeling Capabilities: While SAP2000 doesn't have a dedicated "rotating crack" model, explore any advanced material models or options that might offer a closer approximation. Look for options related to smeared cracking or damage plasticity models.
• Consider a Simplified Approach for Comparison: As a sanity check, you could try a simplified model in SAP2000, such as a smeared crack model with fixed crack direction, to see if you can at least capture the general trend of the capacity curve. This would help isolate whether the issue is primarily due to crack modeling differences or other factors.
• Document Everything: Keep meticulous records of all your model parameters, mesh details, and analysis settings. This will be invaluable for troubleshooting and comparing results.

In summary, it's highly probable that the differences in crack modeling between DIANA and SAP2000 are the main reason for the discrepancies you're observing. While you might not be able to achieve a perfect match, focusing on accurate material calibration and understanding the limitations of SAP2000's nonlinear capabilities should help you improve your results and draw more meaningful conclusions.