Reviews on research progress of strength theories for materials

Strength theory is a mechanical theory that studies the mechanism and principle governing the yielding or failure of materials under multiaxial stresses, which is one of the most fundamental contents in the research of solid mechanics. This theory holds great significance in theoretical research, engineering application and material utilization, and has been widely used in physics, mechanics, earth science, material science and engineering. The author systematically categorizes and summarizes various material strength theories, providing an overview and comment of the theoretical perspectives of these strength theories, as well as pointing out their respective scopes of application, advantages, and disadvantages. Strength theories are classified into the isotropic strength theory and the anisotropic strength theory. Isotropic strength theories encompass principal stress strength theory, shear stress strength theory and other strength theories. The principal stress strength theories further include maximum tensile stress strength theory, Mises yield theory, minimum energy dissipation principle strength theory, and damage ratio strength theory. Shear stress strength theories are divided into single-shear strength theory, twin-shear strength theory, and triple-shear strength theory. Other strength theories include maximum tensile strain strength theory, spatially mobilized plane strength theory, mesoscopic strength theory, and other theories. Anisotropic strength theory is the extension of isotropic strength theory, which is discussed according to three categories: metal materials, composite materials and geotechnical materials respectively. The strength theories for metal materials and composite materials are divided into macroscopic strength strength criteria and micro-and meso-scopic strength criteria. Meanwhile, the strength theories for geotechnical materials are divided into four categories: Mohr-Coulomb series, Hoeke-Brown series, Matsuoka-Nakai series and other empirical model series. Additionally, the theoretical viewpoint, parameter definition, and physical significance of the damage ratio strength theory are summarized. It is noted that this theory serves as a quantitative indicator for various failure modes, including tensile brittle failure, uniaxial compressive crushing, and triaxial compressive plastic flow of brittle materials such as rocks and concrete. The theory reveals that the failure of brittle materials is caused by inelastic volume expansion. Moreover, it elucidates the principle that under high hydrostatic pressure, the decrement of damage ratio parameters causes a reduction in inelastic volume expansion, leading to the transition of brittle materials towards plastic behavior. Finally, a prospective outlook on the development of the strength theory is provided, indicating that the damage ratio strength theory is expected to become the development direction of macroscopic strength theories. This theory holds the potential for further refinement and application to other isotropic materials and anisotropic materials. Furthermore, by integrating macroscopic strength theory with micro-and meso-scopic strength theory models and artificial intelligence strength theory models, it is possible to calibrate parameters in micro-and meso-scopic strength models and adjust major parameters in macroscopic strength theories. This integration can make the realization of a unified framework encompassing macroscopic strength theories, micro-and meso-scopic strength models, and artificial intelligence strength models.