Analytic parametric solutions for the HRR nonlinear elastic field with low hardening exponents

Sotiropoulou, A; Panayotounakou, N; Panayotounakos, D

dc.contributor.author	Sotiropoulou, A	en
dc.contributor.author	Panayotounakou, N	en
dc.contributor.author	Panayotounakos, D	en
dc.date.accessioned	2014-03-01T01:23:36Z
dc.date.available	2014-03-01T01:23:36Z
dc.date.issued	2006	en
dc.identifier.issn	0001-5970	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17043
dc.subject	Asymptotic Solution	en
dc.subject	Nonlinear Elasticity	en
dc.subject	Normal Form	en
dc.subject	Ordinary Differential Equation	en
dc.subject	Strain Hardening	en
dc.subject	Second Order	en
dc.subject.classification	Mechanics	en
dc.subject.other	Asymptotic solutions	en
dc.subject.other	Hardening exponents	en
dc.subject.other	Nonlinear elastic (plastic) fractures	en
dc.subject.other	Ordinary differential equation (ODE)	en
dc.subject.other	Differential equations	en
dc.subject.other	Fracture	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Plasticity	en
dc.subject.other	Rigidity	en
dc.subject.other	Strain hardening	en
dc.subject.other	Elasticity	en
dc.title	Analytic parametric solutions for the HRR nonlinear elastic field with low hardening exponents	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00707-006-0315-x	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00707-006-0315-x	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	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.	en
heal.publisher	SPRINGER WIEN	en
heal.journalName	Acta Mechanica	en
dc.identifier.doi	10.1007/s00707-006-0315-x	en
dc.identifier.isi	ISI:000238019800005	en
dc.identifier.volume	183	en
dc.identifier.issue	3-4	en
dc.identifier.spage	209	en
dc.identifier.epage	230	en