Geodesic
Asymptotic methods of nonlinear fracture mechanics: results, contemporary state and perspectives
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2013), pp. 156-168

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In the paper the brief review of the important results of nonlinear fracture mechanics recently obtained by the asymptotic methods and perturbation techniques is given. The asymptotic solutions of the whole class of crack problems are discussed. Applications of the asymptotic analysis for crack problems of nonlinear fracture mechanics such that crack tip fields in damaged medium, fatigue crack growth problems in damaged medium, nonlinear eigenvalue problems arising from fracture mechanics analysis, nonlinear eigenvalue analysis including higher order terms are elucidated.
Keywords: asymptotic methods, nonlinear fracture mechanics, crack tip stress field, nonlinear eigenvalue problems. 
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L. V. Stepanova; E. M. Adylina. Asymptotic methods of nonlinear fracture mechanics: results, contemporary state and perspectives. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2013), pp. 156-168. http://geodesic.mathdoc.fr/item/VSGTU_2013_2_a17/