Dear Zhao Cheng,
Based on the CDP concrete model, the stress obtained in a uniaxial compression test should be scaled by the factor (1−D), where D is the damage variable. Consequently, the nominal (real) stress cannot reach the maximum compressive strength fc_m; instead, the peak stress should be approximately (1−D) fc_m.
However, in the FLAC3D uniaxial compression examples, the reported stress (not the effective stress) reaches fc_m. This raises a fundamental question regarding the calibration strategy used. If damage initiates at fc_0, then reaching fc_m with the nominal stress should not be possible—only the effective stress would reach this value.
Could you clarify how the calibration was performed? Specifically:
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Did you assume a constant beta parameter, or did you use an evolving beta controlling the expansion or contraction of the yield surface based on the ratio of the current compressive and tensile strengths?
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If the latter approach was used, how did you address the numerical difficulties that arise when the tensile strength ft becomes very small, causing beta to increase sharply and often leading to convergence issues or failure of the Newton–Raphson solver?
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Alternatively, did you adopt an internal calibration strategy, such as using an increased fc_m in the effective stress formulation and accounting for damage at peak compression (e.g., Dc,peak)?
I would appreciate clarification on which approach was used and how these issues were handled.
Many thanks,
Mojtaba