Numerical assessment of T-stress computation using a p-version finite element method

Two path independent integrals for T-stress computations, one based on the Betti-Rayleigh reciprocal theorem and the other based on Eshelby's energy m omentum tensor are studied. Analytical as well as numerical equivalence bet ween the two integrals is found. To quantify and assess the accuracy of com puted values, error analysis for the proposed numerical computation of the T-stress is presented. Specifically, it is found that the error of the comp uted T-stress is proportional to the ratio of the stress intensity factor d ivided by the square root of the characteristic dimension of the integratio n domain where the path independent integral is evaluated. Using a highly a ccurate hierarchical p-version finite element method, the convergence and a ccuracy of computed values are easily monitored, and it is shown for numeri cal examples that the error of the computed T-stress complies with the desc ribed error analysis. We conclude that path independent integrals, in conju nction with hierarchical p-version finite element methods, provide a powerf ul and robust tool to obtain highly accurate numerical results for the T-st ress.