Due to its significant non-linear softening characteristics and its wide variety of use cases, concrete has received considerable attention for the modeling of its mechanical behavior. The non-linear simulation of linear concrete structures is often associated with mesh dependency, the resolution of which requires some form of regularization. While most of the past research has focused on tension energy regularization for better mesh-objectivity, the compression behavior has been partly left out, even though it may have a significant impact for particular applications. By starting from the failed attempt to simulate a pushout test from the literature, this paper focuses on the enhancements brought by the energetic regularization in compression to an isotropic damage model based on Mazars’ equivalent strain. The resulting model is applied in three representative case studies where the enhanced mesh-objectivity is shown relative to the load–displacement behaviors and the damage patterns that are produced, and compared to those obtained by the classical model.