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.

The stress Concentration Near a Rigid Line Inclusion in a Pre-stressed, Elastic Material. Part I Full Field Solution and Asymptotics / Dal Corso, Francesco; Bigoni, Davide; Gei, Massimiliano. - In: JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS. - ISSN 0022-5096. - STAMPA. - 56:3(2008), pp. 815-838. [10.1016/j.jmps.2007.07.002]

The stress Concentration Near a Rigid Line Inclusion in a Pre-stressed, Elastic Material. Part I Full Field Solution and Asymptotics

Dal Corso, Francesco;Bigoni, Davide;Gei, Massimiliano
2008

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.
3
Dal Corso, Francesco; Bigoni, Davide; Gei, Massimiliano
The stress Concentration Near a Rigid Line Inclusion in a Pre-stressed, Elastic Material. Part I Full Field Solution and Asymptotics / Dal Corso, Francesco; Bigoni, Davide; Gei, Massimiliano. - In: JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS. - ISSN 0022-5096. - STAMPA. - 56:3(2008), pp. 815-838. [10.1016/j.jmps.2007.07.002]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/69307
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