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Nonlinear fracture mechanics for an elastic Bell material. (English) Zbl 1030.74564
Within the framework of finite elasticity, a crack analysis is formulated for a material subjected to the Bell constraint. The kinematical characterization of the Bell constraint and its restrictions on the full range of compatible deformations are presented and the constitutive equations for an isotropic, hyperleastic Bell material are given. General far-field loading (mixed-mode loading) and conditions ensuring vanishing tractions at the crack faces are considered. A system of coupled partial differential equations, governing the elastostatics finite plane-stress problem for a compressible Mooney-RivIin material under the Bell constraint, is derived. By means of an asymptotic procedure, the deformation and stress fields near the crack tip are computed, showing how these cease to be singular. These field equations are expressed in terms of polar coordinates. The global and the local formulations of a crack problem are discussed. An asymptotic procedure is applied to compute the deformation field in the proximity of the crack tip. An emphasis is placed in proving Stephenson’s result, R. A. Stephenson [J. Elast. 12. 65-99 (1982)] in the author’s context, in describing the crack profile after deformation and in evaluating the asymptotic Piola-Kirchhoff and Cauchy stress fields. Some comparisons with the existing solutions in the literature are made.

MSC:
74Rxx Fracture and damage
74B20 Nonlinear elasticity
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