Nonlinear strain energy based (NSEB) criterion for quasi-brittle materials under multiaxial stress states

An equivalent-failure plane model is developed to accommodate the macro-failure phenomenon of quasi-brittle materials under multiaxial stress states. On this basis, strain energy based (SEB) criterion is proposed based on the comprehensive and systematic analysis of strain energy release and dissipation as well as inhibition and acceleration from the normal stress and material itself. In the SEB criterion, the strain energy release is controlled by part of distortional and volumetric strain energy in the block, strain energy dissipation is a function of distortional strain energy, the work of inhibition or acceleration is described as strain energy of normal stress, and the inhibition of materials itself is part of critical shear and cleavage energy density in the block. Then, a nonlinear strain energy based (NSEB) criterion is developed by considering the impact of normal stress on inhibited or accelerated parameters. The NSEB criterion is adopted to predict the multiaxial failure and yield stress of different quasi-brittle materials. The results indicate that the NSEB criterion can predict multiaxial failure and yield stress successfully. Further research indicates that predicted parameters not only are located in the pre-specified range, but also can manifest the micro/meso-experimental phenomenon of different quasi -brittle materials failure. For the purpose of comparison, Hsieh-Ting-Chen, Parabolic Mogi and Bresler-Pister criteria are used to predict the multiaxial failure and yield stress. It can be found that the NSEB criterion gives a better prediction than Hsieh-Ting-Chen, Parabolic Mogi and Bresler-Pister criteria. The determination coefficients R2 of these criteria are also determined. It is noted that the NSEB criterion has a maximum R2 compared with other criteria. Therefore, it is concluded that the NSEB criterion can give a more reliable pre-diction for multiaxial failure and yield of quasi-brittle materials.