Abstract: Although researchers have proposed various size effect models, it is still one of the most challenging problems in materials science to establish a model that can fully describe different types of size effect laws. In this paper, a theoretical model is firstly proposed by systematically and in depth analyzing the variation of the local damage zone (LDZ) with specimen sizes, and further validation shows that this model can accurately describe the nonlinear size effect of LDZ. On this basis, energy balance size effect model considering the variation of local damage zone (EBM-LDZ) is established. It is found that EBM-LDZ can reflect five different types of size effect laws. Type 1: nominal compressive strength (NCS) decreases with the increase of specimen sizes, and then tend to elastic limit of uniaxial compression (ELUC); Type 2: the NCS first maintains the true compressive strength (TCS) within a certain size range, and then gradually decreases, and finally approaches the ELUC with the increasing specimen sizes; Type 3: the NCS first increase, then decreases and finally tend to the ELUC with the increasing specimen sizes; Type 4: the NCS first increases and then maintains the TCS within a certain size range, then decreases, and finally tends to the ELUC with the increasing specimen sizes; Type 5: the NCS does not vary with specimen sizes. The EBM-LDZ firstly theoretically predicts the existence of the type 4 size effect laws, which is confirmed in the size effect experiment of micro/nano-scale titanium alloy. The analysis of the EBM-LDZ shows that the competition between the relative rates of change of LDZ and specimen size is the reason that EBM-LDZ can predict the five types of size effect laws. The author has proved that the energy balance size effect model can well predict type 1, 2 and 5 size effect laws, but it cannot reflect type 3 and 4 size effect laws. Therefore, experimental data of type 3 and 4 size effect laws are utilized to validate and evaluate the EBM-LDZ and IUSEL. The results indicate that the EBM-LDZ can well predict the type 3 and 4 size effect data, but IUSEL cannot describe the type 4 size effect data. The total mean determination coefficient of the EBM-LDZ is close to that of IUSEL.