Mode I stress intensity factor and T-stress by exponential matrix method

An analytical method called Exponential Matrix Method EMM is presented for finding T-stress and Stress Intensity Factor SIF under Mode I loading, in two-dimensional stationary elasticity. First, a set of Hamiltonian dual equations is implemented. The system is then solved using EMM. This more direct, efficient and systematic method provides eigensolutions which become symplectic adjoint orthogonal to each other by means of slight mathematical transformations. Their combinations in terms of symplectic series allow a complete description of the behavior of elastic fields at the crack tip. The series coefficients, notably T-stress and SIF are obtained using Trapezoidal Integral Method TIM. Comparisons to ABAQUS solutions are given to show of the efficiency and accuracy of EMM. Numerical examples based on the choice of circular integration contours centered on the crack tip are developed.