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

Although the Park–Paulino–Roesler (PPR) potential-based cohesive zone fracture model was not derived based on a thermodynamics consistency principle, we investigate the thermodynamic consistency of the PPR model under conditions of loading, unloading and reloading. First, we present a general anisotropic Helmholtz free energy function. Then, we reformulate the PPR model into the anisotropic Helmholtz form, and investigate its consistency and the various unloading/reloading relations which have been proposed for use with the model. By recasting the PPR model into the Helmholtz form, we illustrate that the PPR cohesive potential, while not designed with thermodynamic consistency in mind, is thermodynamically consistent under the pure loading conditions for which it was designed (as expected). We also demonstrate that the unloading/reloading relations, which are commonly used with the PPR model, are not thermodynamically consistent; however, through our investigation, we develop a new coupled unloading/reloading relation, which maintains the thermodynamic consistency of the PPR cohesive model. The considerations addressed in this paper are aimed at achieving a better understanding of the PPR model and other models of similar nature.