scholarly journals Dynamic recrystallization during deformation of polycrystalline ice: insights from numerical simulations

2017 ◽  
Vol 375 (2086) ◽  
pp. 20150346 ◽  
Author(s):  
Maria-Gema Llorens ◽  
Albert Griera ◽  
Florian Steinbach ◽  
Paul D. Bons ◽  
Enrique Gomez-Rivas ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Dynamic Recrystallization ◽  
Numerical Simulations ◽  
Simple Shear ◽  
Basal Slip ◽  
Pure Shear ◽  
Ice Sheets ◽  
Shear Direction ◽  
Slip Systems ◽  
Ice Sheet Dynamics

The flow of glaciers and polar ice sheets is controlled by the highly anisotropic rheology of ice crystals that have hexagonal symmetry (ice lh). To improve our knowledge of ice sheet dynamics, it is necessary to understand how dynamic recrystallization (DRX) controls ice microstructures and rheology at different boundary conditions that range from pure shear flattening at the top to simple shear near the base of the sheets. We present a series of two-dimensional numerical simulations that couple ice deformation with DRX of various intensities, paying special attention to the effect of boundary conditions. The simulations show how similar orientations of c -axis maxima with respect to the finite deformation direction develop regardless of the amount of DRX and applied boundary conditions. In pure shear this direction is parallel to the maximum compressional stress, while it rotates towards the shear direction in simple shear. This leads to strain hardening and increased activity of non-basal slip systems in pure shear and to strain softening in simple shear. Therefore, it is expected that ice is effectively weaker in the lower parts of the ice sheets than in the upper parts. Strain-rate localization occurs in all simulations, especially in simple shear cases. Recrystallization suppresses localization, which necessitates the activation of hard, non-basal slip systems. This article is part of the themed issue ‘Microdynamics of ice’.

ON BOUNDARY CONDITIONS IN THE FINITE VOLUME LATTICE BOLTZMANN METHOD ON UNSTRUCTURED MESHES

1999 ◽  
Vol 10 (06) ◽  
pp. 1003-1016 ◽  
Author(s):  
GONGWEN PENG ◽  
HAOWEN XI ◽  
SO-HSIANG CHOU
Keyword(s):  
Shear Flow ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Lattice Boltzmann Method ◽  
Finite Volume ◽  
Simple Shear ◽  
Lattice Boltzmann ◽  
Unstructured Meshes ◽  
Simple Shear Flow ◽  
Boltzmann Method

Boundary conditions in a recently-proposed finite volume lattice Boltzmann method are discussed. Numerical simulations for simple shear flow indicate that the extrapolation and the half-covolume techniques for the boundary conditions are workable in conjunction with the finite volume lattice Boltzmann method for arbitrary meshes.

Reorientation of inclusions by combination of pure shear and simple shear

1976 ◽  
Vol 34 (1-2) ◽  
pp. 1-70 ◽  
Author(s):  
S.K. Ghosh ◽  
H. Ramberg
Keyword(s):  
Simple Shear ◽  
Pure Shear

scholarly journals An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Elsiddig Elmukashfi
Keyword(s):  
Crack Propagation ◽  
Viscous Dissipation ◽  
Simple Shear ◽  
Elastic Energy ◽  
Classical Method ◽  
Pure Shear ◽  
Dissipated Energy ◽  
Dynamic Experiments ◽  
Unloading Rate ◽  
Tearing Energy

AbstractA method for determining the critical tearing energy in rubber-like materials is proposed. In this method, the energy required for crack propagation in a rubber-like material is determined by the change of recovered elastic energy which is obtained by deducting the dissipated energy due to different inelastic processes from the total strain energy applied to the system. Hence, the classical method proposed by Rivlin and Thomas using the pure shear tear test is modified using the actual stored elastic energy. The total dissipated energy is evaluated using cyclic pure shear and simple shear dynamic experiments at the critical stretch level. To accurately estimate the total dissipated energy, the unloading rate is determined from the time the crack takes to grow an increment. A carbon-black-filled natural rubber is examined in this study. In cyclic pure shear experiment, the specimens were cyclically loaded under quasi-static loading rate of $$0.01~{\rm {s}}^{-1}$$ 0.01 s - 1 and for different unloading rates, i.e. $$0.01$$ 0.01 , $$0.1$$ 0.1 and $$1.0~{\rm {s}}^{-1}$$ 1.0 s - 1 . The simple shear dynamic experiment is used to obtain the total dissipated energy at higher frequencies, i.e. $$0.5$$ 0.5 -$$18~{\rm {Hz}}$$ 18 Hz which corresponds to unloading rates $$0.46$$ 0.46 -$$16.41~{\rm {s}}^{-1}$$ 16.41 s - 1 , using the similarities between simple and pure shear deformation. The relationship between dissipated energy and unloading stretch rate is found to follow a power-law such that cyclic pure shear and simple shear dynamic experiments yield similar result. At lower unloading rates (i.e. $${\dot{\lambda }}_{\rm {U}} < 1.0~{\rm {s}}^{-1}$$ λ ˙ U < 1.0 s - 1 ), Mullins effect dominates and the viscous dissipation is minor, whereas at higher unloading rates, viscous dissipation becomes significant. At the crack propagation unloading rate $$125.2~{\rm {s}}^{-1}$$ 125.2 s - 1 , the viscous dissipation is significant such that the amount of dissipated energy increases approximately by $$125.4\%$$ 125.4 % from the lowest unloading rate. The critical tearing energy is obtained to be $$7.04~{\rm {kJ}}/{\rm {m}}^{2}$$ 7.04 kJ / m 2 using classical method and $$5.12~{\rm {kJ}}/{\rm {m}}^{2}$$ 5.12 kJ / m 2 using the proposed method. Hence, the classical method overestimates the critical tearing energy by approximately $$37.5\%$$ 37.5 % .

scholarly journals Crystal rotations and alignment in spatially varying magma flows: Two-dimensional examples of common subvolcanic flow geometries

2021 ◽  
Author(s):  
Rémi Vachon ◽  
Mohsen Bazargan ◽  
Christoph F Hieronymus ◽  
Erika Ronchin ◽  
Bjarne Almqvist
Keyword(s):  
Shear Flow ◽  
Magma Chamber ◽  
Simple Shear ◽  
Thermal Convection ◽  
Pure Shear ◽  
Simple Shear Flow ◽  
Two Dimensional ◽  
Crystal Orientations ◽  
Volcanic Plumbing System ◽  
Spatially Varying

Summary Elongate inclusions immersed in a viscous fluid generally rotate at a rate that is different from the local angular velocity of the flow. Often, a net alignment of the inclusions develops, and the resulting shape preferred orientation (SPO) of the particle ensemble can then be used as a strain marker that allows reconstruction of the fluid’s velocity field. Much of the previous work on the dynamics of flow-induced particle rotations has focused on spatially homogeneous flows with large-scale tectonic deformations as the main application. Recently, the theory has been extended to spatially varying flows, such as magma with embedded crystals moving through a volcanic plumbing system. Additionally, an evolution equation has been introduced for the probability density function (PDF) of crystal orientations. Here, we apply this new theory to a number of simple, two-dimensional flow geometries commonly encountered in magmatic intrusions, such as flow from a dyke into a reservoir or from a reservoir into a dyke, flow inside an inflating or deflating reservoir, flow in a dyke with a sharp bend, and thermal convection in a magma chamber. The main purpose is to provide a guide for interpreting field observations and for setting up more complex flow models with embedded crystals. As a general rule, we find that a larger aspect ratio of the embedded crystals causes a more coherent alignment of the crystals, while it has only a minor effect on the geometry of the alignment pattern. Due to various perturbations in the crystal rotation equations that are expected in natural systems, we show that the time-periodic behavior found in idealized systems is probably short-lived in nature, and the crystal alignment is well described by the time-averaged solution. We also confirm some earlier findings. For example, near channel walls, fluid flow often follows the bounding surface and the resulting simple shear flow causes preferred crystal orientations that are approximately parallel to the boundary. Where pure shear deformation dominates, there is a tendency for crystals to orient themselves in the direction of the greatest tensile strain rate. Where flow impinges on a boundary, for example in an inflating magma chamber or as part of a thermal convection pattern, the stretching component of pure shear aligns with the boundary, and the crystals orient themselves in that direction. In the field, this local pattern may be difficult to distinguish from a boundary-parallel simple shear flow. Pure shear also dominates along the walls of a deflating magma chamber and in places where the flow turns away from the reservoir walls, but in these locations, the preferred crystal orientation is perpendicular to the wall. Overall, we find that our calculated patterns of crystal orientations agree well with results from analogue experiments where similar geometries are available.

Vibrational energy distribution in plate excited with random white noise

2021 ◽  
Vol 263 (6) ◽  
pp. 965-969
Author(s):  
Tyrode Victor ◽  
Nicolas Totaro ◽  
Laurent Maxit ◽  
Alain Le Bot
Keyword(s):  
Boundary Conditions ◽  
Energy Distribution ◽  
White Noise ◽  
Numerical Simulations ◽  
Ray Tracing ◽  
Energy Analysis ◽  
Vibrational Energy ◽  
Statistical Energy Analysis ◽  
Vibrational Energy Distribution ◽  
Tracing Method

In Statistical Energy Analysis (SEA) and more generally in all statistical theories of sound and vibration, the establishment of diffuse field in subsystems is one of the most important assumption. Diffuse field is a special state of vibration for which the vibrational energy is homogeneously and isotropically distributed. For subsystems excited with a random white noise, the vibration tends to become diffuse when the number of modes is large and the damping sufficiently light. However even under these conditions, the so-called coherent backscattering enhancement (CBE) observed for certain symmetric subsystems may impede diffusivity. In this study, CBE is observed numerically and experimentally for various geometries of subsystem. Also, it is shown that asymmetric boundary conditions leads to reduce or even vanish the CBE. Theoretical and numerical simulations with the ray tracing method are provided to support the discussion.

Postbuckling mechanics in slender steel plates under pure shear: A focus on boundary conditions and load path

2021 ◽  
Vol 169 ◽  
pp. 108448
Author(s):  
Peter Y. Wang ◽  
Parfait M. Masungi ◽  
Maria E.M. Garlock ◽  
Spencer E. Quiel
Keyword(s):  
Boundary Conditions ◽  
Pure Shear ◽  
Steel Plates ◽  
Load Path

scholarly journals Coupled ice sheet–climate modeling under glacial and pre-industrial boundary conditions

2014 ◽  
Vol 10 (5) ◽  
pp. 1817-1836 ◽  
Author(s):  
F. A. Ziemen ◽  
C. B. Rodehacke ◽  
U. Mikolajewicz
Keyword(s):  
Boundary Conditions ◽  
General Circulation ◽  
Climate Modeling ◽  
Ice Sheets ◽  
Ice Sheet ◽  
General Circulation Models ◽  
Quasi Equilibrium ◽  
Ice Streams ◽  
Ice Stream ◽  
First Results

Abstract. In the standard Paleoclimate Modelling Intercomparison Project (PMIP) experiments, the Last Glacial Maximum (LGM) is modeled in quasi-equilibrium with atmosphere–ocean–vegetation general circulation models (AOVGCMs) with prescribed ice sheets. This can lead to inconsistencies between the modeled climate and ice sheets. One way to avoid this problem would be to model the ice sheets explicitly. Here, we present the first results from coupled ice sheet–climate simulations for the pre-industrial times and the LGM. Our setup consists of the AOVGCM ECHAM5/MPIOM/LPJ bidirectionally coupled with the Parallel Ice Sheet Model (PISM) covering the Northern Hemisphere. The results of the pre-industrial and LGM simulations agree reasonably well with reconstructions and observations. This shows that the model system adequately represents large, non-linear climate perturbations. A large part of the drainage of the ice sheets occurs in ice streams. Most modeled ice stream systems show recurring surges as internal oscillations. The Hudson Strait Ice Stream surges with an ice volume equivalent to about 5 m sea level and a recurrence interval of about 7000 yr. This is in agreement with basic expectations for Heinrich events. Under LGM boundary conditions, different ice sheet configurations imply different locations of deep water formation.

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