Exact Analytic Solutions of the Plastic Spin Equations in Simple Shear

Panayotounakos, DE; Theotokoglou, EE; Sotiropoulos, NB; Sotiropoulou, AB

dc.contributor.author	Panayotounakos, DE	en
dc.contributor.author	Theotokoglou, EE	en
dc.contributor.author	Sotiropoulos, NB	en
dc.contributor.author	Sotiropoulou, AB	en
dc.date.accessioned	2014-03-01T01:33:27Z
dc.date.available	2014-03-01T01:33:27Z
dc.date.issued	2010	en
dc.identifier.issn	1081-2865	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20427
dc.subject	Abel equations	en
dc.subject	Nonlinear ordinary differential equations	en
dc.subject	Plastic spin equations	en
dc.subject	Simple shear	en
dc.subject.classification	Materials Science, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	Abel equation	en
dc.subject.other	Analytic solution	en
dc.subject.other	Differential systems	en
dc.subject.other	Exact analytic solutions	en
dc.subject.other	First-order	en
dc.subject.other	Functional transformation	en
dc.subject.other	Mathematical solutions	en
dc.subject.other	Nonlinear differential systems	en
dc.subject.other	Nonlinear ordinary differential equation	en
dc.subject.other	Normal form	en
dc.subject.other	Parametric forms	en
dc.subject.other	Plastic spin	en
dc.subject.other	Simple shear	en
dc.subject.other	Volterra	en
dc.subject.other	Functional polymers	en
dc.subject.other	Integral equations	en
dc.subject.other	Ordinary differential equations	en
dc.subject.other	Plastics	en
dc.subject.other	Spin dynamics	en
dc.subject.other	Nonlinear equations	en
dc.title	Exact Analytic Solutions of the Plastic Spin Equations in Simple Shear	en
heal.type	journalArticle	en
heal.identifier.primary	10.1177/1081286508095193	en
heal.identifier.secondary	http://dx.doi.org/10.1177/1081286508095193	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	We prove that the first-order nonlinear differential system governing the plastic spin response in simple shear (Dafaliasgs equations) is reduced to an equivalent equation of the Abel normal form by means of admissible functional transformations. In similar Abel equations result also the original and the generalized Volterra differential systems, describing the problem of two populations conflicting with one another. The above reduced Abel equations do not admit exact analytic solutions in terms of known (tabulated) functions, since only very special cases of these types of equations can be analytically solved in parametric form. We provide a mathematical solution methodology leading to the construction of exact implicit analytic solutions of the above-mentioned type of equations. Since the plastic spin nonlinear differential system results in a special unsolvable form of Abelgs equation of the normal form, we perform the exact implicit analytic solution of this system too. © 2010 Sage Publications.	en
heal.publisher	SAGE PUBLICATIONS LTD	en
heal.journalName	Mathematics and Mechanics of Solids	en
dc.identifier.doi	10.1177/1081286508095193	en
dc.identifier.isi	ISI:000274912800001	en
dc.identifier.volume	15	en
dc.identifier.issue	2	en
dc.identifier.spage	147	en
dc.identifier.epage	164	en