A study on the thermodynamic consistency of the Park–Paulino–Roesler (PPR) cohesive fracture model

The damage parameters consistent with the PPR model are functions of two internal history parameters, κn and κt, representing the maximum normal opening and absolute tangential opening in the history of loading.

“The damage parameters consistent with the PPR model are functions of two internal history parameters, κ n and κ t , representing the maximum normal opening and absolute tangential opening in the history of loading, respectively.”

The history variables κn and κt must evolve irreversibly to ensure thermodynamic consistency.

“Given that κ n and κ t represent, respectively, the maximum normal and absolute tangential crack openings over the loading history, and the damage parameters are required to be irreversible to ensure thermodynamic consistency (Spring et al., 2016), the history variables themselves must also evolve irreversibly.”

Spring et al. (2016) demonstrated the thermodynamic consistency of the PPR CZM under pure loading conditions and introduced new unloading-reloading relationships that ensure the PPR model is thermodynamically consistent under arbitrary mixed-mode loading.

“Spring et al. (2016) demonstrated the thermodynamic consistency of the PPR CZM (Park et al., 2009) under pure loading conditions and introduced new unloading-reloading relationships that ensure the PPR model is thermodynamically consistent under arbitrary mixed-mode loading.”

Spring et al. (2016) showed that the normal and tangential damage parameters, dn and dt, defined in Equation (10), are monotonically increasing functions of κn and κt.

“Spring et al. (2016) showed that the normal and tangential damage parameters, dn and dt, defined in Equation (10), are monotonically increasing functions of κn and κt.”