Heriot-Watt Mathematics Report Series
HWM04-26, 17 Nov 2004
Shear Band Formation for a Non-Local Model of Thermo-Viscoelastic Flows
J W Bebernes and A A Lacey
Many materials exhibit narrow bands of plastic deformation under extreme
loading conditions. These shear bands are observed in very thin zones and are regarded as a precursor to material failure. Shear band formation is caused by the heat generated in regions with high strain-rate loading. With insufficient times for diffusion of this heat, a localised thermal softening of the material occurs, enhancing plastic flow in thin zones. A one-dimensional thermoviscous model for shear bands has previously been considered. Assuming a constitutive equation for the material to be of Maxwell type, a thermo-viscoelastic version of this model leads to a highly non-local and nonlinear parabolic equation.
This model exhibits various possibilities for shear band formation.
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