A new damage constitutive model for rock strain softening based on an improved Logistic function

• Introduces a flexible S-shaped damage evolution model based on an improved Logistic function that captures the full damage process during rock deformation—maintenance, onset, acceleration, deceleration, and termination—in a unified expression. • Establishes a constitutive model integrating damage mechanics and effective medium theory that accurately describes complete pre-peak compaction and post-peak strain softening behavior across multiple rock types. • Validated against uniaxial and trial compression tests on Miluo granite, yellow sandstone, mudstone, and glutenite, demonstrating close agreement between theoretical curves and experimental data and significant advantages over existing models. • The damage model parameters a, r, and β have clear physical meanings and competitive interactions, jointly controlling the shape of the theoretical stress-strain curve and enabling practical calibration for engineering applications.