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

•New method called Modified Exponential Matrix is presented.•Computation of T-stress and Stress Intensity Factor.•Comparison with numerical solutions. An analytical method called Exponential Matrix Method EMM is presented for finding T-stress and Stress Intensity Factor SIF under Mode I loading, in...

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Bibliographic Details
Published in:Theoretical and applied fracture mechanics 2019-10, Vol.103, p.102287, Article 102287
Main Authors: Nianga, J.-M., Mejni, F., Kanit, T., Imad, A., Li, J.
Format: Article
Language:English
Subjects:
Combinations (mathematics)
Computer simulation
Crack tips
Elasticity
Engineering Sciences
Exponential matrix method
Finite element method
Matrix methods
Mode I
Stress intensity factor
Stress intensity factors
Symplectic method
T-stress
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Summary:•New method called Modified Exponential Matrix is presented.•Computation of T-stress and Stress Intensity Factor.•Comparison with numerical solutions. 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.
ISSN:0167-8442
1872-7638
DOI:10.1016/j.tafmec.2019.102287