Analysis of dynamic stress fields in finite strain deformations of compressible materials with moving cracks

In this study, an asymptotic analysis of plane strain deformation and associated stress fields in the vicinity of a steady moving crack tip in a class of compressible hyperelastic materials is formulated. It is assumed that the semi-infinite crack is in a homogeneous Ciarlet-Geymonat material under general mixed mode I/II loads. The crack tip deformation, stress and the Jacobian determinant fields are developed up to the third order in order to guarantee the strict positivity of the Jacobian determinant in the vicinity of the moving crack tip. These higher-order elastodynamics fields predict new deformed crack-face profiles possibilities. These results indicate that the crack opens up in the vicinity of its tips even when the applied loading is antisymmetric about the plane of the crack which generalize Stephenson's result to the dynamic case. The Cauchy stresses components versus current polar coordinates are non-separables forms and the singularities depend upon the spatial polar angle coordinate. This highlights the difference with the steady dynamic LEFM theory and others previous nonlinear studies. Finally, the constant appearing in the first order elastodynamics fields is determined by linking the singular hyperelastic fields to the singular linear elastic ones using the J-Integral.