In this study,with the meso-scale model reliably validated in our previous work (Construction and Building Materials,2018),the waveform features of plain concrete under various loading conditions and especially with considering stress non-equilibrium are reliably reproduced and predicted.Associating with waveform features,the violation indicator of the specimen stress equilibrium in the split Hopkinson pressure bar test is identified for concrete-like damage softening materials.The concrete material behaviors for stress non-equilibrium are further analyzed,e.g.the dynamic increase factor (DIF)and damage development,etc.The conception of“damage failure volume” is introduced,and a new method of defining the development of concrete dynamic damage is given in the numerical study.What's more,the “compression wave” and “double peak” phenomena observed in the experiment are further interpreted based on the means of numerical simulation.Waveform features how to reflect the concrete material properties is also concluded.The results show that,the disappearance of the “double peak” phenomenon of reflection curve under high strain rate can be regarded as the indicator of the violation of stress equilibrium.After the violation of the stress equilibrium,the relevant DIFs of the concrete specimen will not change significantly.Especially,the concrete specimen will turn into structural response from material response.The conception of “damage failure volume” can well explain the generation of the “double peak” phenomenon of the reflection curve.The “compression wave” phenomenon of reflection curve under lower strain rates is derived from the unloading expansion recovery of the concrete specimen.Furthermore,under the same loading condition,the amplitude of the first peak of the reflection curve can be used as the evaluation standard of the bonding quality between mortar and aggregates.