The stress concentration near a rigid line inclusion in a prestressed, elastic material. Part I. Full-field solution and asymptotics

Dal Corso, Francesco, Bigoni, Davide and Gei, Massimiliano ORCID: https://orcid.org/0000-0003-3869-7504 2008. The stress concentration near a rigid line inclusion in a prestressed, elastic material. Part I. Full-field solution and asymptotics. Journal of the Mechanics and Physics of Solids 56 (3) , pp. 815-838. 10.1016/j.jmps.2007.07.002

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Abstract

A lamellar (zero-thickness) rigid inclusion, so-called ‘stiffener’, is considered embedded in a uniformly prestressed (or prestrained), incompressible and orthotropic elastic sheet, subject to a homogeneous far-field deformation increment. This problem is solved under the assumption of plane strain deformation, with prestress principal directions and orthotropy axes aligned with the stiffener. A full-field solution is obtained solving the Riemann–Hilbert problem for symmetric incremental loading at infinity (while for shear deformation the stiffener leaves the ambient field unperturbed). In addition to the full-field solution, the asymptotic Mode I near-tip representation involving the corresponding incremental stress intensity factor are derived and these results are complemented with the Mode II asymptotic solution. For null prestress, the full-field stress state is shown to match correctly with photoelastic experiments performed by us (on two-part epoxy resin samples containing an aluminum lamina). Our experiments also confirm the fracture patterns for a brittle material containing a stiffener, which do not obey a hoop-stress criterion and result completely different from those found for cracks. Issues related to shear band formation and evaluation of energy release rate for a stiffener growth (or reduction) are deferred to Part II of this article.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Engineering
Subjects:	T Technology > TA Engineering (General). Civil engineering (General)
Publisher:	Elsevier
ISSN:	0022-5096
Last Modified:	28 Oct 2022 09:18
URI:	https://orca.cardiff.ac.uk/id/eprint/74052

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