Rational implementation of the Mohr criterion in its general form

The Mohr criterion is successfully implemented for brittle materials in its general form based on failure envelopes formulated using quadratic functions. This is probably the first time when the criterion has been made comprehensive enough and yet convenient enough to apply since its publication over 120 years ago. To facilitate the formulation, all stress states at failure are partitioned into two groups and all materials are classified into those of higher and lower brittleness. A failure envelope is constructed rationally for each class of materials without resorting to either an oversimplistic and unreasonable linearisation or an overcomplicated and nonlinear formulation. For materials of higher brittleness, the envelope can be defined using a single parabola, whilst for those of lower brittleness, the envelope is defined in a piecewise manner. A new concept of the terminating Mohr's circle (TMC) is introduced which sits at the tensile end as a part of the envelope to terminate the parabola whilst joining the parabolic part of the envelope smoothly. Its diameter varies with the brittleness of the material. It is instrumental both in the partition of stress states and in the classification of materials. The required input data for such formulated Mohr criterion are tensile and compressive strengths only. The procedure of actual applications of the criterion to the assessment of material failure is relatively simple and straightforward as demonstrated in the paper and the schematic is also provided. The failure mode can be predicted in terms of the orientation of failure plane. The formulation is verified for its self-consistency and validated through comparisons with existing criteria and experimental data. The criterion can now be employed in practical failure predictions as a useful means supporting engineering design, especially when brittle materials are concerned.