Analysis of crack parameters under pure Mode II loading by modified exponential matrix method. (February 2021) - Nianga, J.M.; Mejni, F.; Kanit, T.; Li, J.; Imad, A.
Highlights: New analytical method for calculating the Stress Intensity Factor (SIF) under Mode II loading is presented. The crack problem is formulated as a system of Hamiltonian equations, solved based on a new method for determining eigensystems. The linear combination of these eigensolutions allows a good description of the expected solution. The SIF under Mode II loading is calculated using the trapezoidal integration method. Abstract: A new analytical method for calculating the Stress Intensity Factor (SIF) under Mode II loading is presented in the framework of two-dimensional stationary elasticity. Starting from the linear elasticity equations, the crack problem is formulated as a system of Hamiltonian equations, solved based on a new method for determining eigensystems, called Exponential Matrix Method (EMM). The obtained eigensolutions satisfy the adjoint symplectic orthogonality by means of performing an angular stress variation with respect to the radial stress. The linear combination of these eigensolutions then allows a good description of the expected solution. Related to one of the asymptotic expansion coefficients, the SIF under Mode II Loading is calculated using the trapezoidal integration method (TIM). The implemented methodology validation is carried out by comparing the obtained results with those provided by the literature review.