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The Park–Paulino–Roesler (PPR) potential-based model is a cohesive constitutive model formulated to be consistent under a high degree of mode-mixity. Herein, the PPR’s generalization to three-dimensions is detailed, its implementation in a finite element framework is discussed, and its use in single-core and high performance computing (HPC) applications is demonstrated. The PPR model is shown to be an effective constitutive model to account for crack nucleation and propagation in a variety of applications including adhesives, composites, linepipe steel, and microstructures.