Singularities of homogeneous deformations in finite elasticity

Lazopoulos, KA

dc.contributor.author	Lazopoulos, KA	en
dc.date.accessioned	2014-03-01T01:27:15Z
dc.date.available	2014-03-01T01:27:15Z
dc.date.issued	2007	en
dc.identifier.issn	1468-1218	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/18365
dc.subject	Bifurcation	en
dc.subject	Continuum mechanics	en
dc.subject	Maxwell's sets	en
dc.subject	Singularity theory	en
dc.subject	Two-phase strain	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	Anisotropy	en
dc.subject.other	Bifurcation (mathematics)	en
dc.subject.other	Classification (of information)	en
dc.subject.other	Continuum mechanics	en
dc.subject.other	Elasticity	en
dc.subject.other	Maxwell equations	en
dc.subject.other	Nonlinear analysis	en
dc.subject.other	Maxwell's sets	en
dc.subject.other	Singularity theory	en
dc.subject.other	Two phase strain	en
dc.subject.other	Deformation	en
dc.title	Singularities of homogeneous deformations in finite elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.nonrwa.2006.07.001	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.nonrwa.2006.07.001	en
heal.language	English	en
heal.publicationDate	2007	en
heal.abstract	Is classification of the singularities of the potential, concerning the homogeneous deformations in Finite Elasticity, an important material property? The present study demonstrates that the answer to the question is positive. Since the type of singularity prescribes Maxwell's sets in the neighborhood of a singularity, the emergence of multiphase strain states depends on the performed classification. Bifurcation analysis and singularity classification for homogeneous deformations of any hyperelastic, anisotropic, homogeneous material under any type of conservative quasi-static loading is performed. Critical conditions for branching of the equilibrium paths are defined and their post-critical behavior is studied. Singularities corresponding to simple and compound branching are classified according to Arnold's classification. Unconstrained materials are only considered. Special attention is given to the compound branching (D-k) cases requiring elaborate mathematical techniques. The geometry of the umbilics is described with the equilibrium paths and the cusp lines. With the help of Maxwell's sets in the neighborhood of the umbilics, the emergence of discontinuous strain fields is demonstrated. The theory is applied to orthotropic and transversely isotropic materials as well. The proposed method may directly be applied to crystals stability problems. (c) 2006 Elsevier Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Nonlinear Analysis: Real World Applications	en
dc.identifier.doi	10.1016/j.nonrwa.2006.07.001	en
dc.identifier.isi	ISI:000247859300011	en
dc.identifier.volume	8	en
dc.identifier.issue	4	en
dc.identifier.spage	1208	en
dc.identifier.epage	1223	en