Which failure theory is appropriate for brittle materials that have little tendency to deform before fracture?

The Mohr-Coulomb stress criterion is particularly applicable to brittle materials that exhibit minimal deformation prior to fracture. This criterion is based on the concept that materials fail when the shear stress on a specific plane reaches a critical value, related to the normal stress acting on that plane. Brittle materials typically do not undergo significant plastic deformation; they tend to fail suddenly under stress.

The Mohr-Coulomb failure criterion incorporates both normal and shear stress and is effective for describing how brittle materials withstand shear failure when subjected to complex loading conditions. For these materials, the failure surface can be visualized on a Mohr's circle, allowing for easy determination of the conditions under which failure will occur.

This criterion is more suitable than the other options provided for brittle materials, which may show very little or no ductility. In contrast, the other failure theories, such as the Maximum von Mises and Maximum shear stress criteria, predominantly apply to ductile materials where plastic deformation is significant before failure. Therefore, understanding the specific behavior of brittle materials under stress helps in selecting the appropriate failure theory, making the Mohr-Coulomb stress criterion the correct choice in this scenario.