LINEAR AND NONLINEAR UNIFIED STRENGTH THEORY

Unification of a priori unrelated concepts,methods,theories or phenomena is an important characteristic of the beauty of a scientific theory.Strength theory deals with the yield and failure of materials under the complex stress state.It includes the yield criteria(for those materials which have the same strength both in tension and compression) and failure criteria(for SD materials,i.e.strength difference of materials in tension and in compression).It is an important foundation for research on the strength of materials and structures.Strength theory is widely used in physics,mechanics and engineering.It is of great significance in theoretical research and engineering application,and is also very important for the effective utilization of materials.It is an interdisciplinary field where the physicist,civil and mechanical engineers interact in a closed loop.The unified strength theory gives a series of new failure criteria,establishes a relation among various failure criteria,and encompasses previous yield criteria and failure models as special cases.The single-shear strength theory including the famous Tresca yield criterion and the Mohr-Coulomb strength theory,the twin-shear strength theory including the twin-shear yield criterion and the twin-shear failure criterion are all special criteria of the unified strength theory.The unified strength theory has been applied to many fields.The unified strength theory is not a single criterion;it is a series of failure criteria,a system of strength theory.A series of new failure criteria and yield criteria between the single-shear theory and twin-shear theory can be introduced from the unified strength theory.The unified strength theory,however,is a combination of the linear criteria.It cannot unify the nonlinear criteria.It can only approximate nonlinear criteria.A new mechanical model and a new general unified strength theory of materials under complex stress state are proposed.It establishes a relation among various failure criteria including the linear and nonlinear criteria.The new theory encompasses the most familiar failure criteria as special cases;and a series of new criteria can be introduced.The single-shear strength theory,the twin-shear strength theory and the octahedral-shear strength theory are all special cases of the new general unified strength theory.This new unified strength theory including the linear and nonlinear criteria can be adopted for more materials.