scholarly journals A Note on the Constitutive Law for Sea Ice

1983 ◽  
Vol 29 (101) ◽  
pp. 191-195
Author(s):  
Ronald B. Smith
Keyword(s):  
Shear Strength ◽  
Sea Ice ◽  
Large Scale ◽  
General Procedure ◽  
Constitutive Law ◽  
Simple Problem ◽  
Flow Rule ◽  
Starting Point

AbstractThe derivation of a constitutive law to describe large-scale sea-ice deformation commonly uses the so-called “flow rule”. This method introduces a mathematically imposed relationship between shear strength and dilatation which is not based on physical postulates. In this note a more general procedure is described which uses the Reiner–Rivlin equation as a starting point. The method is illustrated by deriving a particular constitutive law and applying it to a simple problem of sea ice blown against a shoreline.

scholarly journals A Note on the Constitutive Law for Sea Ice

1983 ◽  
Vol 29 (101) ◽  
pp. 191-195 ◽  
Author(s):  
Ronald B. Smith
Keyword(s):  
Shear Strength ◽  
Sea Ice ◽  
Large Scale ◽  
General Procedure ◽  
Constitutive Law ◽  
Simple Problem ◽  
Flow Rule ◽  
Starting Point

Abstract The derivation of a constitutive law to describe large-scale sea-ice deformation commonly uses the so-called “flow rule”. This method introduces a mathematically imposed relationship between shear strength and dilatation which is not based on physical postulates. In this note a more general procedure is described which uses the Reiner–Rivlin equation as a starting point. The method is illustrated by deriving a particular constitutive law and applying it to a simple problem of sea ice blown against a shoreline.

scholarly journals The Effect Of Rheology On Seasonal Sea-Ice Simulations

1990 ◽  
Vol 14 ◽  
pp. 340
Author(s):  
Bill Ip ◽  
W.D. Hibler ◽  
Greg Flato
Keyword(s):  
Shear Strength ◽  
Sea Ice ◽  
Large Scale ◽  
Arctic Basin ◽  
Velocity Fields ◽  
Ice Thickness ◽  
Flow Rule ◽  
Fram Strait ◽  
Normal Flow ◽  
Different Types

On the seasonal time scales relevant to numerical investigations of climate, the rheology used in large-scale sea ice models significantly affects the ice thickness build-up and ice velocity fields. Plastic rheologies with a normal flow rule have been used to-date in seasonal dynamic thermodynamic simulations. These rheologies have proved useful in simulating discontinuous slip near the coast while still supplying relatively robust velocity fields in the central Arctic Basin. However, as indicated by limited numerical sensitivity studies with different types of elliptical yield curves, the amount of shear strength significantly affects the ice build-up and can possibly cause a stoppage of the ice outflow through Fram Strait. In addition to the shear strength issue, there is also the possibility that non-normal flow rule rheologies, such as the Mohr Coulomb failure criterion used in soil mechanics, may cause somewhat different types of flow patterns, especially in the Fram Strait region. However, to date no seasonal simulations with such non-normal flow rule rheologies have been carried out. In order to investigate the role of different rheologies on the large-scale flow patterns in the Arctic Basin, a more general numerical scheme than that of Hibler (1979) is developed, which allows the simulation of the dynamic thermodynamic behavior of sea ice with a wide variety of different non linear rheologies. Using this numerical scheme, comparative simulations are carried out to seasonal equilibrium with several variations of the Mohr Coulomb rheology and compared to the more standard Elliptical yield curve results. In particular, the main control Mohr Coulomb case is a capped rheology in which the shear strength is taken to be proportional to the compressive stress. In this capped case only shear flow is allowed until a maximum allowable compressive stress is reached. This cap strength is parameterized to be a function of the ice thickness and compactness. For comparison, a simulation with a very large cap strength is also carried out, and an experiment with a similar compressive cap but much lower shear strength. Overall the results are analyzed to determine the sensitivity of the ice build-up to flow rule and shear strength magnitude. In addition special attention is given to the character of the flow and stoppage (if any) through Fram Strait.

scholarly journals The Effect Of Rheology On Seasonal Sea-Ice Simulations

1990 ◽  
Vol 14 ◽  
pp. 340-340
Author(s):  
Bill Ip ◽  
W.D. Hibler ◽  
Greg Flato
Keyword(s):  
Shear Strength ◽  
Sea Ice ◽  
Large Scale ◽  
Arctic Basin ◽  
Velocity Fields ◽  
Ice Thickness ◽  
Flow Rule ◽  
Fram Strait ◽  
Normal Flow ◽  
Different Types

On the seasonal time scales relevant to numerical investigations of climate, the rheology used in large-scale sea ice models significantly affects the ice thickness build-up and ice velocity fields. Plastic rheologies with a normal flow rule have been used to-date in seasonal dynamic thermodynamic simulations. These rheologies have proved useful in simulating discontinuous slip near the coast while still supplying relatively robust velocity fields in the central Arctic Basin. However, as indicated by limited numerical sensitivity studies with different types of elliptical yield curves, the amount of shear strength significantly affects the ice build-up and can possibly cause a stoppage of the ice outflow through Fram Strait. In addition to the shear strength issue, there is also the possibility that non-normal flow rule rheologies, such as the Mohr Coulomb failure criterion used in soil mechanics, may cause somewhat different types of flow patterns, especially in the Fram Strait region. However, to date no seasonal simulations with such non-normal flow rule rheologies have been carried out.In order to investigate the role of different rheologies on the large-scale flow patterns in the Arctic Basin, a more general numerical scheme than that of Hibler (1979) is developed, which allows the simulation of the dynamic thermodynamic behavior of sea ice with a wide variety of different non linear rheologies. Using this numerical scheme, comparative simulations are carried out to seasonal equilibrium with several variations of the Mohr Coulomb rheology and compared to the more standard Elliptical yield curve results. In particular, the main control Mohr Coulomb case is a capped rheology in which the shear strength is taken to be proportional to the compressive stress. In this capped case only shear flow is allowed until a maximum allowable compressive stress is reached. This cap strength is parameterized to be a function of the ice thickness and compactness. For comparison, a simulation with a very large cap strength is also carried out, and an experiment with a similar compressive cap but much lower shear strength. Overall the results are analyzed to determine the sensitivity of the ice build-up to flow rule and shear strength magnitude. In addition special attention is given to the character of the flow and stoppage (if any) through Fram Strait.

scholarly journals Modeling Sea Ice fracture at very high resolution with VP rheologies

2018 ◽  
Author(s):  
Damien Ringeisen ◽  
Nils Hutter ◽  
Martin Losch ◽  
L. Bruno Tremblay
Keyword(s):  
Shear Strength ◽  
High Resolution ◽  
Sea Ice ◽  
Granular Materials ◽  
Yield Curve ◽  
Confining Pressure ◽  
Shear Resistance ◽  
Flow Rule ◽  
Normal Flow ◽  
Strength Parameters

Abstract. Recent high resolution pan-Arctic sea ice simulations show fracture patterns (Linear Kinematic Features – LKFs) that are typical of granular materials but with intersection (fracture) angles wider than those observed from high-resolution satellite images (with a modal value of θ = 20°). In this article, We investigate the mechanism of formation and parameter dependencies of ice fracture in simple numerical bi-axial test on a 8 km x 25 km ice floe at an unprecedented resolution of 25m for two different yield curves: an elliptical (VP) and a Coulombic yield curve both with normal flow rule. In the standardVP model, the simulated angle of fracture is θ = 33.9°, compared to 20° in observations. The dependence of the angle of fracture on the ice shear strength is also contrary to that of typical granular materials with larger angle of fracture for higher shear strength – think of a wet sand castle with steeper walls than a dry sand castle. In this model, the divergence along the fracture lines (or LKFs) is entirely dictated by the ice shear strength used in the model with high shear strength resulting in convergence along LKFs and low shear strength resulting in divergence along LKFs. This is again contrary to typical granular materials where divergence (or dilation) is linked with the orientation of contacts normals that oppose the flow with divergence present for larger shear resistance and convergence for lower shear resistance. Moreover, the angle of fracture depends on the confining pressure in the uni-axial test with more convergence as the confining pressure increases, again contrary to granular material that have an angle of fracture that is independent of the confining pressure. We note that all three behaviors of the VP model are linked with the use of an associative (normal) flow rule. In the Coulombic model, the angle of fracture is smaller (θ = 23.5°), but the solution is unstable when the compressive stresses are too large because of the discontinuity between the straight limbs of the yield curve and the elliptical capping. Our results show that while the VP model gives angles of fracture that are visually correct, the bias in the magnitude of the angle of fracture and the physical dependencies of the angle of fracture on mechanical strength parameters and stress fields couple the sea ice mechanical strength parameters, the sea-ice drift, sea-ice deformation (strain-rate) field in an inconsistent way. We consider this evidence to move away from the elliptical yield curve and associative (normal) flow rule, a deformation law that is not applicable to pressure-sensitive and dilatant granular material such as sea ice.

scholarly journals Analytical Study of an Isotropic Viscoplastic Sea Ice Model in Idealized Configurations

2015 ◽  
Vol 45 (2) ◽  
pp. 331-354 ◽  
Author(s):  
Jérôme Sirven ◽  
Bruno Tremblay
Keyword(s):  
Sea Ice ◽  
Compressive Stress ◽  
Large Scale ◽  
Yield Curve ◽  
Initial Conditions ◽  
Analytic Solutions ◽  
Flow Rule ◽  
Large Area ◽  
Plastic Regime ◽  
Ice Model

AbstractAnalytic solutions of a mechanical sea ice model are computed in idealized configurations. They are then used to study the properties of this model. It classically assumes that the ice behaves at large scale as an isotropic viscoplastic medium. The plastic regime is characterized by a Mohr–Coulomb yield curve. The flow rule corresponds to the one used in granular mediums and depends on a parameter δ that characterizes the expansion properties of the medium. Using simple model configurations, this study first shows that a sliding of the ice along the coast must be permitted; otherwise, the model generally has no solution when the plastic regime is active. This study then shows that the viscous regime is reached only if the stress remains nearly uniform over a large area. For a stress having no particular properties, the plastic regime acts everywhere. In this case, the compressive stress may reach the maximum value allowed by the model close to the coastline. The extension of the domain where the compressive stress is at its maximum depends on δ and the direction of the forcing field. Over this domain, the ice behaves as a fluid material with a small negative viscosity. Last, the authors found that neither the existence of the solution nor its unicity are guaranteed in this stationary model. This result does not imply that the unicity is lost in the transient problem; it suggests that the evolution of sea ice depends not only on the forcing, but also on the initial conditions or history of the system.

scholarly journals Simulating intersection angles between conjugate faults in sea ice with different viscous–plastic rheologies

2019 ◽  
Vol 13 (4) ◽  
pp. 1167-1186 ◽  
Author(s):  
Damien Ringeisen ◽  
Martin Losch ◽  
L. Bruno Tremblay ◽  
Nils Hutter
Keyword(s):  
Shear Strength ◽  
High Resolution ◽  
Sea Ice ◽  
Granular Material ◽  
Yield Curve ◽  
Confining Pressure ◽  
Arctic Sea Ice ◽  
Flow Rule ◽  
Normal Flow ◽  
Loading Test

Abstract. Recent high-resolution pan-Arctic sea ice simulations show fracture patterns (linear kinematic features or LKFs) that are typical of granular materials but with wider fracture angles than those observed in high-resolution satellite images. Motivated by this, ice fracture is investigated in a simple uni-axial loading test using two different viscous–plastic (VP) rheologies: one with an elliptical yield curve and a normal flow rule and one with a Coulombic yield curve and a normal flow rule that applies only to the elliptical cap. With the standard VP rheology, it is not possible to simulate fracture angles smaller than 30∘. Further, the standard VP model is not consistent with the behavior of granular material such as sea ice because (1) the fracture angle increases with ice shear strength; (2) the divergence along the fracture lines (or LKFs) is uniquely defined by the shear strength of the material with divergence for high shear strength and convergent with low shear strength; (3) the angle of fracture depends on the confining pressure with more convergence as the confining pressure increases. This behavior of the VP model is connected to the convexity of the yield curve together with use of a normal flow rule. In the Coulombic model, the angle of fracture is smaller (θ=23∘) and grossly consistent with observations. The solution, however, is unstable when the compressive stress is too large because of non-differentiable corners between the straight limbs of the Coulombic yield curve and the elliptical cap. The results suggest that, although at first sight the large-scale patterns of LKFs simulated with a VP sea ice model appear to be realistic, the elliptical yield curve with a normal flow rule is not consistent with the notion of sea ice as a pressure-sensitive and dilatant granular material.

Adaptive discrete-continuous modeling of evolving discontinuities

2014 ◽  
Vol 31 (7) ◽  
pp. 1305-1320 ◽  
Author(s):  
Annika Sorg ◽  
Manfred Bischoff
Keyword(s):  
Adaptive Mesh Refinement ◽  
Large Scale ◽  
Adaptive Mesh ◽  
Accurate Solution ◽  
Constitutive Law ◽  
Smooth Transition ◽  
Content Type ◽  
Quasicontinuum Method ◽  
Starting Point ◽  
Frictional Materials

Purpose – The purpose of this paper is to develop a method to model entire structures on a large scale, at the same time taking into account localized non-linear phenomena of the discrete microstructure of cohesive-frictional materials. Design/methodology/approach – Finite element (FEM) based continuum methods are generally considered appropriate as long as solutions are smooth. However, when discontinuities like cracks and fragmentation appear and evolve, application of models that take into account (evolving) microstructures may be advantageous. One popular model to simulate behavior of cohesive-frictional materials is the discrete element method (DEM). However, even if the microscale is close to the macroscale, DEMs are computationally expensive and can only be applied to relatively small specimen sizes and time intervals. Hence, a method is desirable that combines efficiency of FEM with accuracy of DEM by adaptively switching from the continuous to the discrete model where necessary. Findings – An existing method which allows smooth transition between discrete and continuous models is the quasicontinuum method, developed in the field of atomistic simulations. It is taken as a starting point and its concepts are extended to applications in structural mechanics in this paper. The kinematics in the method presented herein is obtained from FEM whereas DEM yields the constitutive behavior. With respect to the constitutive law, three levels of resolution – continuous, intermediate and discrete – are introduced. Originality/value – The overall concept combines model adaptation with adaptive mesh refinement with the aim to obtain a most efficient and accurate solution.

scholarly journals Investigation of Salt-Frost Heaving Rules and Mechanical Properties of Chlorite Saline Soil along the Duku Highway under Freezing-Thawing Action

2022 ◽  
Vol 2022 ◽  
pp. 1-12
Author(s):  
Xuebang Huang ◽  
Zizhao Zhang ◽  
Zezhou Guo ◽  
Ruihua Hao ◽  
Qianli Lv ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Shear Strength ◽  
Large Scale ◽  
Saline Soil ◽  
Physical Property ◽  
Freezing Process ◽  
Composition Analysis ◽  
Frost Heaving ◽  
Starting Point ◽  
Strength Tests

Aiming to investigate salt-frost heaving rules and the mechanical properties of natural saline soil along the Duku Highway subjected to multiple freezing-thawing cycles, we collected natural saline soil samples from the alluvial-proluvial plain in front of the Dushanzi Mountain at the starting point of the Duku Highway. Then, we conducted mineral composition analysis tests, essential laboratory physical property measurement, large scale multiple freezing-thawing cyclic salt-frost heaving tests, shear strength tests, and unconfined compressive strength tests on the samples. According to the test results presented, the collected saline soil differed from saline soil in other regions and fell into “chlorite saline soils.” As the number of freezing-thawing cycles increased, the overall salt-frost heaving capacity increased and then decreased in the freezing process but first reduced and then increased in the thawing process. Thus, the salt-frost heaving capacity was cumulative in freezing/thawing cycles. The peak salt-frost heaving capacity reached a maximum after 1 freezing-thawing cycle and then dropped drastically and fluctuated regularly. After 6 freezing-thawing cycles, the displacement deformation and time formed a new equilibrium. After 7 freezing-thawing cycles, the displacement and deformation of the soil no longer appear negative. As the number of freezing-thawing cycles increased, the cohesive force of saline soil first increased and then dropped steadily, the internal friction angle first dropped and then increased steadily, and the unconfined shear strength first increased and then decreased. These research results provided data supporting the prevention and controlling highway saline soil disasters with insightful references for the other projects in this region.

An Elastic-Plastic Constitutive Law for Sea Ice

1975 ◽  
Vol 42 (2) ◽  
pp. 379-384 ◽  
Author(s):  
R. S. Pritchard
Keyword(s):  
Sea Ice ◽  
Plastic Flow ◽  
Yield Criterion ◽  
Material Model ◽  
Careful Consideration ◽  
Constitutive Law ◽  
Elastic Response ◽  
Reference Configuration ◽  
Deformation Tensor ◽  
Flow Rule

The AIDJEX sea ice model is extended by a careful consideration of the deformation measured relative to a reference configuration which changes according to the plastic flow. This approach makes the strain more meaningful than it was previously. The kinematic relations properly allow both finite stretch and rotation. The resulting kinematic relations reflect the feeling that sea ice response is independent of any fixed reference configuration. This formulation has been achieved by writing an incremental kinematic relation using the Finger deformation tensor. A special relation is presented for the case when elastic strain is small, as with sea ice. The elastic response and yield criterion as well as the plastic flow rule remain unchanged from those presently in use. The flow rule is derived by maximizing the rate at which plastic work is done. This approach unifies the development and also helps us to study the material instabilities that occur when the material softens. The material model satisfies the principle of material frame indifference. The model has been subjected to known deformation histories and the response is satisfactory. In many cases the stress history is indistinguishable from that of the previously used elastic-or-plastic model.

Identification of N-Substituted Triazolo-azetidines as Novel Antibacterials using pDualrep2 HTS Platform

2019 ◽  
Vol 22 (5) ◽  
pp. 346-354
Author(s):  
Yan A. Ivanenkov ◽  
Renat S. Yamidanov ◽  
Ilya A. Osterman ◽  
Petr V. Sergiev ◽  
Vladimir A. Aladinskiy ◽  
...  
Keyword(s):  
Antibacterial Activity ◽  
Large Scale ◽  
Underlying Mechanism ◽  
Luciferase Assay ◽  
Reporter System ◽  
E Coli ◽  
Starting Point ◽  
High Concentrations ◽  
Mic Value

Aim and Objective: Antibiotic resistance is a serious constraint to the development of new effective antibacterials. Therefore, the discovery of the new antibacterials remains one of the main challenges in modern medicinal chemistry. This study was undertaken to identify novel molecules with antibacterial activity. Materials and Methods: Using our unique double-reporter system, in-house large-scale HTS campaign was conducted for the identification of antibacterial potency of small-molecule compounds. The construction allows us to visually assess the underlying mechanism of action. After the initial HTS and rescreen procedure, luciferase assay, C14-test, determination of MIC value and PrestoBlue test were carried out. Results: HTS rounds and rescreen campaign have revealed the antibacterial activity of a series of Nsubstituted triazolo-azetidines and their isosteric derivatives that has not been reported previously. Primary hit-molecule demonstrated a MIC value of 12.5 µg/mL against E. coli Δ tolC with signs of translation blockage and no SOS-response. Translation inhibition (26%, luciferase assay) was achieved at high concentrations up to 160 µg/mL, while no activity was found using C14-test. The compound did not demonstrate cytotoxicity in the PrestoBlue assay against a panel of eukaryotic cells. Within a series of direct structural analogues bearing the same or bioisosteric scaffold, compound 2 was found to have an improved antibacterial potency (MIC=6.25 µg/mL) close to Erythromycin (MIC=2.5-5 µg/mL) against the same strain. In contrast to the parent hit, this compound was more active and selective, and provided a robust IP position. Conclusion: N-substituted triazolo-azetidine scaffold may be used as a versatile starting point for the development of novel active and selective antibacterial compounds.

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