Calibration of material parameters for the Chang-Mander model for unconfined concrete

The current basic OpenSees distribution includes several uniaxial models for concrete. Among them, the model proposed by Chang and Mander in 1994 offers a comprehensive setting applicable both to confined and unconfined concrete, by a proper selection of material parameters. The model offers the possibility to smoothly combine Tsai equation, for the first part of the curve, with a linear branch for the final part. This option is useful to model spalling of unconfined concrete while keeping the smoothness of the curve. Two basic parameters of the Chang-Mander model for compression, denoted by n and r, govern initial and post-peak stiffness of the Tsai equation, respectively. Besides them, there is a further parameter, denoted by α, which received less attention in the literature and determines the position of the switch between nonlinear and linear parts of the curve. In the first part of this work, the calibration of the parameters n and r is discussed in some detail. In the second part, the problem of the calibration of α is analyzed. Changes in the value of α may produce large variations in the evaluation of the spalling strain for unconfined concrete. After some comparative analyses with existing models, a simple expression to calibrate α parameter is finally proposed.