Micro cracking in solid material is a phenomenon of solid plane bifurcation with incompatible micro-rotation. Therefore it is important to analysis the micro-rotation field in a strained material in fractute mechanics. On the basis of strain-rotation (S-R) decomposition theorem, the geometric criterion of cracking has been established. In order to verify its validity, using grating experimental method the thin compact tension specimens were investigated. The analysis results show a good agreement between the experimental and geometric criterion.

Localized deformation and instability is the focal point of research in mechanics. The most typical problem is the plastic analysis of cylindrical bar necking and shear band under uniaxial tension. Traditional elasto-plastic mechanics of infinitesimal deformation can not solve this problem successfully. In this paper, on the basis of S(strain)-R(rotation) decomposition thorem, the authors obtain the local strain distribution and progressive state of axial symmetric finite deformation of cylindrical bar under uniaxial tension adopting nonlinear gauge approximate method and computer modeling technique.