scholarly journals 3D Muscle Deformation Mapping at Submaximal Isometric Contractions: Applications to Aging Muscle

2020 ◽  
Vol 11 ◽  
Author(s):  
Vadim Malis ◽  
Usha Sinha ◽  
Shantanu Sinha
Keyword(s):  
Extracellular Matrix ◽  
Strain Rate ◽  
Shear Strain ◽  
Compressive Strain ◽  
Strain Tensor ◽  
Medial Gastrocnemius ◽  
Strain Rate Tensor ◽  
Shear Strain Rate ◽  
Velocity Mapping ◽  
Lateral Transmission

3D strain or strain rate tensor mapping comprehensively captures regional muscle deformation. While compressive strain along the muscle fiber is a potential measure of the force generated, radial strains in the fiber cross-section may provide information on the material properties of the extracellular matrix. Additionally, shear strain may potentially inform on the shearing of the extracellular matrix; the latter has been hypothesized as the mechanism of lateral transmission of force. Here, we implement a novel fast MR method for velocity mapping to acquire multi-slice images at different % maximum voluntary contraction (MVC) for 3D strain mapping to explore deformation in the plantar-flexors under isometric contraction in a cohort of young and senior subjects. 3D strain rate and strain tensors were computed and eigenvalues and two invariants (maximum shear and volumetric strain) were extracted. Strain and strain rate indices (contractile and in-plane strain/strain rate, shear strain/strain rate) changed significantly with %MVC (30 and 60% MVC) and contractile and shear strain with age in the medial gastrocnemius. In the soleus, significant differences with age in contractile and shear strain were seen. Univariate regression revealed weak but significant correlation of in-plane and shear strain and shear strain rate indices to %MVC and correlation of contractile and shear strain indices to force. The ability to map strain tensor components provides unique insights into muscle physiology: with contractile strain providing an index of the force generated by the muscle fibers while the shear strain could potentially be a marker of lateral transmission of force.

scholarly journals The Behavior of Melts with Vanishing Viscosity in the Cone-and-Plate Rheometer

2019 ◽  
Vol 10 (1) ◽  
pp. 172
Author(s):  
Lihui Lang ◽  
Sergei Alexandrov ◽  
Elena Lyamina ◽  
Van Manh Dinh
Keyword(s):  
Strain Rate ◽  
Shear Strain ◽  
Constitutive Equations ◽  
Material Flow ◽  
Analytic Solution ◽  
Theoretical Solution ◽  
Qualitative Behavior ◽  
Strain Rate Tensor ◽  
Shear Strain Rate ◽  
Vanishing Viscosity

A semi-analytic solution for material flow in the cone-and-plate rheometer is presented. It is assumed that the viscosity is solely a function of the second invariant of the strain rate tensor. A distinguishing feature of the constitutive equations used is that the viscosity is vanishing as the shear strain rate approaches infinity. This feature of the constitutive equations affects the qualitative behavior of the solution. Asymptotic analysis is carried out near the surface of the cone to reveal these features. It is shown that the regime of sliding must occur and the shear strain rate approaches infinity under certain conditions. It is also shown that the asymptotic behavior of the viscosity as the shear strain rate approaches infinity controls these qualitative features of the theoretical solution. Some of these features are feasible for experimental verification. An interpretation of the theoretical solution found is proposed.

High shear strain rate rheometry of polymer melts

2009 ◽  
Vol 114 (2) ◽  
pp. 864-873 ◽  
Author(s):  
A. L. Kelly ◽  
T. Gough ◽  
B. R. Whiteside ◽  
P. D. Coates
Keyword(s):  
Strain Rate ◽  
Shear Strain ◽  
Polymer Melts ◽  
Shear Strain Rate ◽  
High Shear

Rheology of colloids

Surfactants ◽  
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.

scholarly journals Erebus Glacier Tongue, Mcmurdo Sound, Antarctica

1974 ◽  
Vol 13 (67) ◽  
pp. 27-35 ◽  
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.

scholarly journals Deformation in the Vicinity of Ice Divides

1983 ◽  
Vol 29 (103) ◽  
pp. 357-373 ◽  
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.

scholarly journals Dynamics and Structure of Griesgletscher, Switzerland

1980 ◽  
Vol 25 (92) ◽  
pp. 215-228 ◽  
Author(s):  
M. J. Hambrey ◽  
A. G. Milnes ◽  
H. Siegenthaler
Keyword(s):  
Strain Rate ◽  
Flow Line ◽  
Compressive Strain ◽  
Local Deformation ◽  
Strain History ◽  
Strain Rates ◽  
Shear Strain Rate ◽  
Maximum Shear Strain ◽  
Alpine Valley ◽  
Ablation Area

AbstractA detailed investigation has been carried out on the dynamics of an Alpine valley glacier of relatively simple shape and the results are considered in relation to the development of secondary structures. Ice velocity reaches a maximum near the top of a small ice fall (40 m a−1) which also coincides approximately with the equilibrium line. Flow lines converge in the accumulation area but are roughly parallel in the ablation area. The “regional” strain-rate pattern is rather complex. Approximate longitudinal extension is evident in the accumulation area and strain-rates reach high values at the south margin and in the ice fall (up to 0.12 a−1). In the ablation area, strain-rates are comparatively small and in general indicate longitudinal compression. “Local” deformation rates obtained in the area beneath the ice fall and along a flow line near one of the margins reveal complex patterns of deformation within small areas.There is no clear relationship between foliation and strain-rates (and by analogy stresses), except in the case of longitudinal foliation in marginal areas which, if actively developing, lies approximately parallel to a direction of maximum shear strain-rate. It is more important to consider the relationship of this structure to strain history. Results from this study indicate that, regardless of the initial orientation of the foliation in relation to the strain ellipse, it attains approximate parallelism with the long axis of the ellipse as deformation progresses.It is also shown that many foliations originate from pre-existing layered structures such as stratification or crevasse traces. This problem is discussed particularly with reference to an arcuate foliation which originates in the ice fall and is believed to represent tensional veins, subsequently subjected to compressive strain within and below the ice fall.

scholarly journals The theory of plane plastic strain for anisotropic metals

1949 ◽  
Vol 198 (1054) ◽  
pp. 428-437 ◽  
Keyword(s):  
Plastic Strain ◽  
Strain Rate ◽  
Shear Strain ◽  
Plane Strain ◽  
Yield Criterion ◽  
Elliptic Functions ◽  
Shear Strain Rate ◽  
Maximum Shear Strain ◽  
Geometrical Properties ◽  
Plane Plastic

A yield criterion and plastic stress-strain relations are formulated for anisotropic metals deformed under conditions of plane strain. The equations are shown to be hyperbolic, the characteristics coinciding with the directions of maximum shear strain-rate. When the anisotropy is uniformly distributed, the variation of the stresses along the characteristics is expressed in terms of elliptic functions, and geometrical properties of the field of characteristics are established. The theory is applied to the problem of indentation by a flat die.

A Corotational Elastoplastic Formulation With Subloading Surface Model for Hardening Materials

Volume 1 ◽  
2004 ◽  
Author(s):  
Ali Reza Saidi ◽  
Koichi Hashiguchi
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Simple Shear ◽  
Deformation Theory ◽  
Elastoplastic Deformation ◽  
Strain Tensor ◽  
Surface Model ◽  
Strain Rate Tensor ◽  
Hencky Strain ◽  
Stress Components

In this paper a corotational constitutive model for the large elastoplastic deformation of hardening materials using subloading surface model is formulated. This formulation is obtained by refining the large deformation theory of Naghdabadi and Saidi (2002) adopting the corotational logarithmic (Hencky) strain rate tensor and incorporating it into the subloading surface model of Hashiguchi (1980, 2003) falling within the framework of the unconventional plasticity. As an application of the proposed constitutive model, the large Elastoplastic deformation of simple shear example has been solved and the results have been compared with classical elasto-plastic model using the Hencky strain tensor. Also the effect of the choice of corotational rates on stress components has been studied.

scholarly journals Measurement of the Deformation of Ice in a Tunnel at the Foot of an Ice Fall

1956 ◽  
Vol 2 (20) ◽  
pp. 735-746 ◽  
Author(s):  
J. W. Glen
Keyword(s):  
Strain Rate ◽  
Compressive Stress ◽  
Compressive Strain ◽  
Longitudinal Direction ◽  
Strain Rate Tensor ◽  
Surface Slope ◽  
Local Surface ◽  
Maximum Compressive Stress

AbstractDuring the Cambridge Austerdalsbre Expedition 1955, a tunnel was dug horizontally into the ice at the foot of a large ice fall, and its subsequent movements were surveyed. The axis of the tunnel was rotating very fast, as might be expected from the change in surface slope under the ice fall, but as well as this the tunnel was being bent, i.e. the tunnel axis was an active anticline. As the local surface of the glacier above the tunnel was convex, this bending was tending to increase the convexity, and as it is in this region that waves form across the glacier under the ice fall this observation is interpreted as showing that the wave ogives are actually being formed in the ice surrounding the tunnel. The distances between pegs in the tunnel walls were also measured. There was a compressive strain occurring along the tunnel axis (i.e. the tunnel was decreasing in length) and the tunnel was also closing far more rapidly than would be predicted from the weight of overlying ice alone. These two observations suggest that a large compressive stress is acting in the glacier in a longitudinal direction. Measurements on surface stakes, though not of the same accuracy as the internal measurements, confirmed these predictions, and also allow the strain rate tensor to be estimated. From this the magnitude of the stresses can be computed, and the longitudinal compressive stress is estimated to be about 3 bars. Observations of the banding on the walls of the tunnel showed that the fine bands were within 10° of being perpendicular to the maximum compressive stress.

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