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The finite-element evaluation of nonlinear cracks in power-hardening materials involves some numerical difficulties: the incompressibility in the plane-strain condition and the representation of the nonlinear crack singularity. In the present paper, the eigenmodes of Hutchinson-Rice-Rosengren (HRR) singularity at the nonlinear crack tip are obtained numerically by the finite-element eigenfunction calculation. Superposing the singularity functions thus obtained on the finite-element displacement, the J-integral values for various structures are determined directly from a coefficient of the superposed function. As for the numerical examples, we take the center-cracked plate, the double-edge-cracked plate, and the single-edge-cracked plate. Several comparison studies are made between the present and the other relevant results.
crack analysis, finite-element method, power hardening material, Hutchinson-Rice-Rosengren (HRR) singularity, penalty function, superposition method, incompressibility, numerical eigenfunction calculation, J-integral value, crack-opening displacement, residual load-point displacement, elastic-plastic fracture
Associate professor, Faculty of Engineering, University of Tokyo, Tokyo,
Research associate, University of Tokyo, Tokyo,