Impact comminution of solids due to local kinetic energy of high shear strain rate: II–Microplane model and verification

The apparent increase of strength of concrete at very high strain rates experienced in projectile impact (10 s −1 to 10 6 s −1 ), called ‘dynamic overstress’, has recently been explained by the theory of release of local kinetic energy of shear strain rate in finite size particles about to form. This theory gives the particle size and the additional kinetic energy density that must be dissipated in finite-element codes. In previous research, it was dissipated by additional viscosity, in a model partly analogous to turbulence theory. Here it is dissipated by scaling up the material strength. Microplane model M7 is used and its stress–strain boundaries are scaled up by factors proportional to the −4/3rd power of the effective deviatoric strain rate and its time derivative. The crack band model with a random tetrahedral mesh is used and all the artificial damping is eliminated. The scaled M7 model is seen to predict the crater shapes and exit velocities of projectiles penetrating concrete walls of different thicknesses as closely as the previous models. The choice of the finite strain threshold for element deletion criterion, which can have a big effect, is also studied. It is proposed to use the highest threshold above which a further increase has a negligible effect.

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Rheology of colloids

Surfactants ◽

10.1093/oso/9780198828600.003.0015 ◽

2019 ◽

pp. 400-424

Author(s):

Bob Aveyard

Keyword(s):

Strain Rate ◽

Shear Strain ◽

Shear Thickening ◽

Rheological Behaviour ◽

Maxwell Model ◽

Colloidal Dispersions ◽

Shear Strain Rate ◽

Plastic Behaviour ◽

Shear Thickening Fluids ◽

External Forces

Lyophobic colloidal dispersions, aggregated surfactant systems, and polymer solutions, as well as foams and emulsions, can all be deformed by weak external forces; rheology is the study of deformation and flow of materials. Various rheological quantities arising from the response of a material to shear are defined. For liquids the stress, τ‎, applied is related to the rate of deformation, that is, the shear strain rate, γ̇. For Newtonian fluids τ‎ and γ̇ are linearly related and τ‎ / γ̇ is the viscosity, η‎. Other nonlinear relationships correspond to shear thinning and shear thickening fluids and to plastic behaviour in which there is a yield stress. Viscoelastic systems exhibit both viscous and elastic properties; such behaviour is often treated using the simple Maxwell model. Some illustrative experimentally observed rheological behaviour is presented.

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Erebus Glacier Tongue, Mcmurdo Sound, Antarctica

Journal of Glaciology ◽

10.1017/s0022143000023340 ◽

1974 ◽

Vol 13 (67) ◽

pp. 27-35 ◽

Cited By ~ 39

Author(s):

G. Holdsworth

Keyword(s):

Shear Stress ◽

Strain Rate ◽

Shear Strain ◽

Longitudinal Strain ◽

Strain Rates ◽

Shear Strain Rate ◽

Mcmurdo Sound ◽

Glacier Tongue ◽

The Past ◽

Image Position

Examination of the past and present behaviour of the Erebus Glacier tongue over the last 60 years indicates that a major calving from the tongue appears to be imminent. Calculations of the regime of the tongue indicate that bottom melt rates may exceed 1 m a−1. By successive mapping of the ice tongue between the years 1947 and 1970, longitudinal strain-rates were determined using the change in distance between a set of 15 teeth, which are a prominent marginal feature of the tongue. Assuming a flow law for ice of the form where τ is the effective shear stress and is the effective shear strain-rate, values of the exponent n = 3 and B = 1 × 108 N m−2 are determined. These are in fair agreement with published values.

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Deformation in the Vicinity of Ice Divides

Journal of Glaciology ◽

10.3189/s0022143000030288 ◽

1983 ◽

Vol 29 (103) ◽

pp. 357-373 ◽

Cited By ~ 30

Author(s):

Charles F. Raymond

Keyword(s):

Finite Elements ◽

Laminar Flow ◽

Velocity Profile ◽

Strain Rate ◽

Shear Strain ◽

Vertical Velocity ◽

Flow Theory ◽

Numerical Calculations ◽

Shear Strain Rate ◽

Horizontal Shear

AbstractNumerical calculations by finite elements show that the variation of horizontal velocity with depth in the vicinity of a symmetric, isothermal, non-slipping ice ridge deforming on a flat bed is approximately consistent with prediction from laminar flow theory except in a zone within about four ice thicknesses of the divide. Within this near-divide zone horizontal shear strain-rate is less concentrated near the bottom and downward velocity is less rapid in comparison to the flanks. The profiles over depth of horizontal and vertical velocity approach being linear and parabolic respectively. Calculations for various surface elevation profiles show these velocity profile shapes are insensitive to the ice-sheet geometry.

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