Summary
In this paper, we restore the already constructed approximate asymptotic solutions extracted in [10] concerning the HRR [1] strongly nonlinear fourth-order ordinary differential equation (ODE) for plane strain conditions in nonlinear elastic (plastic) fracture. It is proved that the above equation, for low strain hardening exponents (0 < N « 1), is reduced to a strongly nonlinear ODE of the second order. The method of the total differentials is used so that the last equation is reduced to Abels' equations of the second kind of the normal form, that can be analytically solved in parametric form. In addition, the case of rigid perfect-plasticity (N=0) is extensively investigated and several important results are extracted.
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Sotiropoulou, A., Panayotounakou, N. & Panayotounakos, D. Analytic parametric solutions for the HRR nonlinear elastic field with low hardening exponents. Acta Mechanica 183, 209–230 (2006). https://doi.org/10.1007/s00707-006-0315-x
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DOI: https://doi.org/10.1007/s00707-006-0315-x