The shape of a traction-separation relation in the cohesive zone model is essential for accurately capturing the nonlinear fracture process of a material. In particular, to account for a relatively large fracture process zone of quasi-brittle materials, multi-linear softening models are typically adopted, e.g., bilinear and trilinear softening models [1]; however, these models are generally limited to mode-I. To extend multi-linear softening models to mixed-mode fracture, this study employs a potential-based cohesive zone modeling formulation. The cohesive constitutive relation is derived from a potential-energy function [2–3], where the functions are superposed to introduce kink points in a multi-linear softening response. The proposed formulation is implemented within an extrinsic cohesive zone modeling framework, in which cohesive surface elements are adaptively inserted along arbitrary crack paths. The results demonstrate the applicability of the potential energy-based softening formulation to a wide range of quasi-brittle materials (e.g., plain concrete and fiber reinforced concrete), where the model parameters are obtained from experimental results. As a summary, the present work provides a unified framework for mixed-mode fracture analysis of quasi-brittle materials in different softening descriptions and can be a foundation for future extensions to other material fracture analysis. REFERENCES [1] Park, K., Paulino, G. H., & Roesler, J. (2010). Cohesive fracture model for functionally graded fiber reinforced concrete. Cement and Concrete Research, 40(6), 956-965. [2] Jeon, S., Park, K. (2026). Extrinsic cohesive zone modeling using potential-based PPR model for mixed-mode problems. In preparation. [3] Park, K., Paulino, G. H., & Roesler, J. R. (2009). A unified potential-based cohesive model of mixed-mode fracture. Journal of the Mechanics and Physics of Solids, 57(6), 891-908.