Yield surface of the CDPM model

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The yield surface ($f=0$) of the damage plasticity model CDPM proposed in Grassl and Jirasek (2006) is based on the failure criterion proposed in Menetrey and Willam (1995). It depends on an eccentricity parameter $e$ and a hardening parameter $q_{\rm h}$. In the videos below, the influence of these two parameters is investigated. Firstly, the influence of the eccentricity $e$ is varied from 0.5 to 1 for the failure surface ($q_{\rm h}=1$). At the beginning of the movie, for eccentricity values close to 0.5, the deviatoric section of the yield surface has an almost triangular shape for low confinement (close to the origin). For $e=1$, a circular deviatoric section is obtained. For concrete, $e$ values close to 0.5 are used, so that for low hydrostatic stress the deviatoric section is almost triangular, but is still smooth at the compressive meridians.

In the second illustration, the hardening parameter $q_{\rm h}$ was varied from 0.1 to 1, while keeping $e=0.51$. For hardening values less than 1, the yield surface is closed on the hydrostatic axis.