Vol. 10, No. 3, 2015

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Antiplane shear field for a class of hyperelastic incompressible brittle material: Analytical and numerical approaches

Claude Stolz and Andres Parrilla Gomez

Vol. 10 (2015), No. 3, 395–410
DOI: 10.2140/jomms.2015.10.395
Abstract

This paper reconsiders the problem of determining the elastostatics fields near the tip of a crack in a body deformed by an antiplane shear for a class of incompressible, homogeneous, isotropic materials. The study is generalized to the formation of a quasicrack under the same conditions of loading for brittle material that cannot support any further loading when a critical strength is reached. The crack is then replaced by a totally damaged zone where the stress is identically zero. The shape of the boundary between the damaged and undamaged body is found analytically. A numerical approach is proposed to address the problem for more general constitutive law. The analytical solution is recovered by a process of shape optimization.

Keywords
antiplane shear, brittle material, crack-tip fields, hyperelasticity
Milestones
Received: 7 March 2014
Revised: 6 February 2015
Accepted: 2 March 2015
Published: 26 August 2015
Authors
Claude Stolz
Génie civil et Mécanique
UMR CNRS 6183
1 rue de la Noë
44321 Nantes
France
IMSIA EDF UMR CNRS 9219
1 avenue Charles de Gaulle
92141 Clamart
France
Andres Parrilla Gomez
Génie civil et Mécanique
UMR CNRS 6183
1 rue de la Noë
44321 Nantes
France