Spatial patterning in shear bands
- Universite de Metz (France)
- Shell Research, Rijswijk (Netherlands)
Localization of the deformation in shear bands is frequently observed in a variety of solids such as metals and rocks. For strain-rate-independent solids, the condition of loss of ellipticity of the incremental governing equations was first considered to determine the orientation of these bands and the critical conditions of their onset. Another option is to introduce a characteristic length scale directly in the constitutive model as in non-local theories. In both cases, the results of these usually 1-D analyses have shed new light on the shear band thicknesses and their spacings. Nevertheless, due to the 1-D assumption of these analyses, very little information has been gathered concerning thickness variations along the shear bands and the development of a possible structure in the shear zones has never been identified. We present the results of two studies on spatial patterning in shear zones. The first model considered is that of a non-Newtonian material with then-no-mechanical coupling. We studied the stability of laminar steady-state solutions of a plane-Couette flow to 2-D perturbations. In the absence of any Benar-type of instability, we found that the dominant mode of instability is either 1-D or 2-D depending on the exact values of the rheological parameters. The second model considered is that of a hyperelastic material with a modified potential that depends on higher-order deformation gradients. Instability in a shear-band mode are obtained from a 2-D bifurcation analysis for a layer of infinite extent and sustaining a simple shear mode of deformation. It is shown that the first bifurcation along the fundamental path is 1-D followed by 2-D bifurcations with a continuous spectrum.
- OSTI ID:
- 175398
- Report Number(s):
- CONF-950686-; TRN: 95:006111-0370
- Resource Relation:
- Conference: Joint applied mechanics and materials summer meeting, Los Angeles, CA (United States), 28-30 Jun 1995; Other Information: PBD: 1995; Related Information: Is Part Of AMD - MD `95: Summer conference; PB: 520 p.
- Country of Publication:
- United States
- Language:
- English
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