Computational prediction of ideal strength for a material

The ideal strength is crucial for predicting material behavior under extreme conditions, which can provide insights into material limits, guide design and engineer for enhanced performance and durability. In this work, we present a method within an allows for the estimation of tensile, shear, and indentation strengths in any crystallographic direction or plane. We have examined the strain-stress relationships of several well-known structures and compared our findings with previous work, demonstrating the effectiveness of our approach. Moreover, we performed extensive investigations into the indentation strength of hexagonal WC, \b{eta}-SiC, and MgA$l_2O_4$. The current study uncovers the modes of structural deformation and the underlying atomistic mechanisms. The insights gained from this study have significant implications for the further exploration and design of superhard materials.