<p>The present study employs and investigates in detail several energy decompositions to capture the tension-compression asymmetric damage behavior of ductile materials based on a gradient-extended two-surface damage-plasticity framework. A series of methodological innovations are proposed to address the complex coupling between plasticity and tension-compression asymmetric damage. More specifically, both the elastic and plastic energy densities are decomposed by three representative energy decompositions: the volumetric-deviatoric decomposition, the spectral decomposition, and the star-convex decomposition. Since the stress-like quantities derived from the decomposed strain energy are governed by different damage degradation functions, the von Mises yield criterion is reformulated in terms of the components of Cauchy stress and back stress. Subsequently, thermodynamically consistent plastic evolution laws are derived to account for the influence of asymmetric damage. In addition, the Macaulay bracket is employed within the damage criterion to prevent undesired interaction between positive and negative contributions of the damage driving force. Several numerical examples are presented to investigate the characteristics of the three energy decompositions. Moreover, the limitations of the existing two-surface damage-plasticity model are examined and addressed in four aspects: damage nucleation, damage propagation, crack-like behavior, and flexibility.</p>