Atherosclerosis is a prevalent cardiovascular disease and defined as plaque formation inside the arterial intima layer. The atherosclerotic plaque is characterized as anisotropic, soft tissue and a potential plaque rupture could result in life-threatening clinical events, such as ischemic attack or stroke. The plaque rupture mechanism is still poorly understood due to the lack of real-time, in-vivo observations. Aiming to predict and describe the plaque damage behavior, numerical damage models have been implemented. This study focused on developing a theoretical and computational framework of Strain Energy Density Function (SEDF) with energy limiter damage model with atherosclerotic plaque-mimicking tissue-engineered applications. The generated damage model was implemented in Neo-Hookean and Holzapfel-Gasser-Ogden (HGO) SEDF via material user subroutines (UMAT codes) in finite element software. The computational models simulated 8 different experimental ruptured cases based on idealized and realistic geometrical models. In the material characterization process an iterative optimization algorithm was developed. The findings demonstrated that the case-specific computational models with SEDF with energy limiter damage model reproduced the plaque-mimicking rupture as they fitted the experimental crack initiation and propagation patterns. The results revealed that the anisotropic HGO material model generated the highest amount of Cauchy stresses and strain energy density. In addition, the geometrical configuration sensitivity of the damage model was emphasized as all cracks initiated from the inclusion and the results between idealized and realistic geometrical models deviated. A parametric study was conducted to investigate the influence of various energy limiters in matrix and fibers components via the SEDF and resulted in a matrix-dominated damage model. The SEDF with energy limiter model could be further optimized by developing a fully automated damage model and validated with clinical applications.