Advances in strength theories for materials under complex stress state in the 20th Century

It is 100 years since the well-known Mohr-Coulomb strength theory was established in 1900. A considerable amount of theoretical and experimental research on strength theory of materials under complex stress state was done in the 20th Century. This review article presents a survey of the advances in strength theory (yield criteria, failure criterion, etc) of materials (including metallic materials, rock, soil, concrete, ice, iron, polymers, energetic material, etc) under complex stress, discusses the relationship among various criteria, and gives a method of choosing a reasonable failure criterion for applications in research and engineering. Three series of strength theories, the unified yield criterion, the unified strength theory, and others are summarized. This review article contains 1163 references regarding the strength theories. This review also includes a brief discussion of the computational implementation of the strength theories and multi-axial fatigue.