Abstract:
An approximate solution of nonlinear eigenvalue problem arising from the Mode I crack problem in a nonlinear power-law medium is obtained. The perturbation technique is used. The method allows to find the analytical formula expressing the eigenvalue as the function of parameters of constitutive law and eigenvalue corresponding to the linear undisturbed problem.
Keywords:nonlinear eigenvalue problem, stress-strain state near the crack tip, stress singularity, multiscale fracture model, perturbation method, analytical solution.
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