Abstract: Deformation and strain are the objective mechanical responses of materials when the stress or external environment changes, and the description of this property is subjective. The conventional representation of strain state consists of three normal strains and three shear strains, which is inconvenient in testing and expression. In order to find a new method to express the strain state——a more universal shear strain generalized angular strain is proposed based on the shear strain. In this paper, the generalized angular strain is defined as the change of radian at any angle and is no longer limited to the right angle. On this basis, the relationship between the generalized angular strain and the expression of the conventional strain state is established based on the expression of the change of any angle in the strain theory, and the conditions and specific methods for the calculation of the conventional strain state from the generalized angular strain are given. By considering the uniform distribution of directions, the generalized angular strain representation based on tetrahedron and equal right angle tetrahedron are studied. According to the given method, the conventional strain state can be expressed as these two generalized angular strains, and the corresponding conventional strain state can also be obtained from these two generalized angular strains. Thus, a single representation of strain state is realized, that is, only six generalized angular strains can be used to represent three-dimensional strain state without the joint form of three positive strains and three shear strains. The research results of this paper provide a new idea for the development of strain state testing methods and the research of constitutive model.

Key words: strain state, shear strain, generalized angular strain, tetrahedron, dihedral angle