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This book focuses on the unified solutions and analysis for the problems in soil mechanics based on the unified strength theory, which is a new theory on the yield and failure of materials under multi-axial stresses. Then, it provides a system of yield and failure criteria adopted for most materials, from metallic materials to rocks, concretes, soils, polymers, etc. It includes the Tresca criterion, Mohr–Coulomb theory, and Mises criterion as well, which are special cases or linear approximation of the UST.

This book thoroughly describes a theory concerning the yield and failure of materials under multi-axial stresses – the Unified Strength Theory, which was first proposed by the author and has been frequently quoted since. It provides a system of yield and failure criteria adopted for most materials, from metals to rocks, concretes, soils, and polymers. This new edition includes six additional chapters: General behavior of Strength theory function; Visualization of the Unified Strength Theory; Equivalent Stress of the UST and Comparisons with other criteria; Economic Signification of the UST; General form of failure criterion; Beauty of Strength Theories. It is intended for researchers and graduate students in various fields, including engineering mechanics, material mechanics, plasticity, soil mechanics, rock mechanics, mechanics of metallic materials and civil engineering, hydraulic engineering, geotechnical engineering, mechanical engineering and military engineering.

It has been ten years since I presented the paper entitled “A new model and theory on yield and failure of materials under the complex stress state” at the Sixth Conference on Mechanical Behaviour of Materials held at Kyoto, Japan in 1991. The proceedings edited by Jono and Inoue were published by Pergamon Press in 1991. At that conference Professor Murakami and I were invited to act as the chairperson and co-chairperson of a session, and I presented the paper at another session. Few days before the conference, I had given a seminar regarding the tw- shear strength theory and the unified strength theory at Nagoya Technological University. These were the first two presentations of the unified strength theory, although I had completed the research of the unified strength theory in 1990. The paper “Twin-shear strength theory and its generalization” was published in the English edition of Sciences in China, the top journal in China, in 1985. The th original generalized twin-shear strength theory was presented at the 16 International Theoretical and Applied Mechanics Congress held at Copenhagen in Denmark and MPA (MaterialPrüfungsAnstalt) at Stuttgart University, Germany in 1984. After this Congress I visited the MPA and School of Civil Engineering of Stuttgart University, and gave a seminar regarding the generalized twin-shear strength theory at MPA of Stuttgart University. Professor Otto Mohr (1835–1918) has had worked at the Stuttgart University. He was a very good professor, his lectures aroused great interest in his students.