Finite strain analysis of crack tip fields in Yeoh-model-based rubber-like materials which are loaded in plane stress

摘要

The dominant asymptotic stress field near the tip of a Mode-I crack of Yeoh-model-based rubber-like materials is determined. The analysis bases on the fully nonlinear equilibrium theory of incompressible hyperelastic solids. First, The nonlinear PDE (partial differential equation) governing the leading behavior of y_2 is transformed to a linear PDE. Then the linear PDE is solved and the solution of y_2 is obtained. With the solution of y_2 and boundary conditions the numerical solution of y_1 is obtained, too. Finally, the analysis solution in polar coordinate of the first Kirchhoff Stress in plane stress state is obtained.