scholarly journals Ice shelf rift propagation: stability, three dimensional effects, and the role of marginal weakening

2019 ◽  
Author(s):  
Bradley Paul Lipovsky
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Ice Shelf ◽  
Linear Elastic ◽  
Partial Contact ◽  
Rift Propagation ◽  
Elastic Fracture ◽  
Shelf Margins ◽  
Determining Factor

Abstract. Understanding the processes that govern ice shelf extent are of fundamental importance to improved estimates of future sea level rise. In present-day Antarctica, ice shelf extent is most commonly determined by the propagation of through-cutting fractures called ice shelf rifts. Here, I present the first three-dimensional analysis of ice shelf rift propagation. I present a linear elastic fracture mechanical (LEFM) description of rift propagation. The model predicts that rifts may be stabilized when buoyant flexure results in contact at the tops of the near-tip rift walls. This stabilizing tendency may be overcome, however, by processes that act in the ice shelf margins. In particular, both marginal weakening and the advection of rifts into an ice tongue are shown to be processes that may trigger rift propagation. Marginal shear stress is shown to be the determining factor that governs these types of rift instability. I furthermore show that rift stability is closely related to the transition from uniaxial to biaxial extension known as the compressive arch. Although the partial contact of rift walls is fundamentally a three-dimensional process, I demonstrate that it may be parameterized within more numerically efficient two-dimensional calculations. This study provides a step towards a description of calving physics that is based in fracture mechanics.

scholarly journals Ice shelf rift propagation: stability, three-dimensional effects, and the role of marginal weakening

2020 ◽  
Vol 14 (5) ◽  
pp. 1673-1683
Author(s):  
Bradley Paul Lipovsky
Keyword(s):  
Three Dimensional ◽  
Tangential Displacement ◽  
Ice Shelf ◽  
Linear Elastic ◽  
Partial Contact ◽  
Rift Propagation ◽  
Iceberg Calving ◽  
Elastic Fracture ◽  
Shelf Margins

Abstract. Understanding the processes that govern ice shelf extent is important to improving estimates of future sea-level rise. In present-day Antarctica, ice shelf extent is most commonly determined by the propagation of through-cutting fractures called ice shelf rifts. Here, I present the first three-dimensional analysis of ice shelf rift propagation. I model rifts using the assumptions of linear elastic fracture mechanics (LEFM). The model predicts that rifts may be stabilized (i.e., stop propagating) when buoyant flexure results in the partial contact of rift walls. This stabilizing tendency may be overcome, however, by processes that act in the ice shelf margins. In particular, loss of marginal strength, modeled as a transition from zero tangential displacement to zero tangential shear stress, is shown to favor rift propagation. Rift propagation may also be triggered if a rift is carried with the ice flow (i.e., advected) out of an embayment and into a floating ice tongue. I show that rift stability is closely related to the transition from uniaxial to biaxial extension known as the compressive arch. Although the partial contact of rift walls is fundamentally a three-dimensional process, I demonstrate that it may be parameterized within more numerically efficient two-dimensional calculations. This study constitutes a step towards a first-principle description of iceberg calving due to ice shelf rift propagation.

On the Correspondence between Two- and Three-Dimensional Elastic Solutions of Crack Problems

2016 ◽  
Vol 713 ◽  
pp. 18-21 ◽  
Author(s):  
Andrei G. Kotousov ◽  
Zhuang He ◽  
Aditya Khanna
Keyword(s):  
Scale Effects ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Governing Equations ◽  
Singular Stress ◽  
Linear Elastic ◽  
Crack Problems ◽  
Elastic Fracture ◽  
Stress States

The classical two-dimensional solutions of the theory of elasticity provide a framework of Linear Elastic Fracture Mechanics. However, these solutions, in fact, are approximations despite that the corresponding governing equations of the plane theories of elasticity are solved exactly. This paper aims to elucidate the main differences between the approximate (two-dimensional) and exact (three-dimensional) elastic solutions of crack problems. The latter demonstrates many interesting features, which cannot be analysed within the plane theories of elasticity. These features include the presence of scale effects of deterministic nature, the existence of new singular stress states and fracture modes. Furthermore, the deformation and stress fields near the tip of the crack is essentially three-dimensional and do not follow plane stress or plane strain simplifications. Moreover, in certain situations the two-dimensional solutions can provide misleading results; and several characteristic examples are outlined in this paper.

The Role of Three Dimension Computerized Imaging in Hand Surgery

1987 ◽  
Vol 12 (3) ◽  
pp. 349-352
Author(s):  
J. ENGEL ◽  
M. SALAI ◽  
B. YAFFE ◽  
R. TADMOR
Keyword(s):  
Three Dimensional ◽  
Hand Surgery ◽  
New Technique ◽  
Silicone Implants ◽  
Three Dimension ◽  
Two Dimensional ◽  
Radiological Imaging ◽  
Preliminary Results ◽  
Dimensional Picture

Three-dimensional computerized imaging is a new modality of radiological imaging. This new technique transforms the two-dimensional slices of bi-plane CT into a three-dimensional picture by a computer’s monitor adjusted to the system. This system enables the physician to rotate the angle of viewing of the desired region to any desired angle. Moreover, this system can delete certain features of different densities from the picture, such as silicone implants, thus improving visualization. Our preliminary results using this technique are presented. The advantages, pitfalls, and suggested future applications of this new technique in hand surgery are discussed.

Role of divalent cation (Ba) substitution in the Li+ ion conductor LiTi2(PO4)3: a molecular dynamics study

2020 ◽  
Vol 22 (26) ◽  
pp. 14471-14479
Author(s):  
Kartik Sau ◽  
Tamio Ikeshoji ◽  
Supriya Roy
Keyword(s):  
Molecular Dynamics ◽  
Divalent Cation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Ion Diffusion ◽  
Ion Conductor ◽  
Li Ion ◽  
Ba Substitution

Influence of Ba2+ ordering on cationic diffusion: (a) three-dimensional low Li+ ion diffusion using randomly substituted Ba2+, and (b) two-dimensional layered type high Li+ ion diffusion using specifically ordered substitution of Ba2+.

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

The Role of Three-Dimension Computerized Imaging in Hand Surgery

1992 ◽  
Vol 17 (6) ◽  
pp. 702-702
Author(s):  
J. Engel ◽  
M. Salai ◽  
B. Yaffe ◽  
R. Tadmor
Keyword(s):  
Three Dimensional ◽  
Hand Surgery ◽  
New Technique ◽  
Silicone Implants ◽  
Three Dimension ◽  
Two Dimensional ◽  
Radiological Imaging ◽  
Preliminary Results ◽  
Dimensional Picture

Three-dimensional computerized imaging is a new modality of radiological imaging. This new technique transforms the two-dimensional slices of bi-plane CT into a three-dimensional picture by a computer's monitor adjusted to the system. This system enables the physician to rotate the angle of viewing of the desired region to any desired angle. Moreover, this system can delete certain features of different densities from the picture, such as silicone implants, thus improving visualization. Our preliminary results using this technique are presented. The advantages, pitfalls, and suggested future applications of this new technique in hand surgery are discussed.

scholarly journals Evaluation of the criticality of cracks in ice shelves using finite element simulations

2012 ◽  
Vol 6 (5) ◽  
pp. 973-984 ◽  
Author(s):  
C. Plate ◽  
R. Müller ◽  
A. Humbert ◽  
D. Gross
Keyword(s):  
Stress Intensity ◽  
Configurational Forces ◽  
Intensity Factors ◽  
Physical Processes ◽  
Ice Shelf ◽  
Critical Crack ◽  
Ice Shelves ◽  
Various Boundary Conditions ◽  
Linear Elastic ◽  
Elastic Fracture

Abstract. The ongoing disintegration of large ice shelf parts in Antarctica raise the need for a better understanding of the physical processes that trigger critical crack growth in ice shelves. Finite elements in combination with configurational forces facilitate the analysis of single surface fractures in ice under various boundary conditions and material parameters. The principles of linear elastic fracture mechanics are applied to show the strong influence of different depth dependent functions for the density and the Young's modulus on the stress intensity factor KI at the crack tip. Ice, for this purpose, is treated as an elastically compressible solid and the consequences of this choice in comparison to the predominant incompressible approaches are discussed. The computed stress intensity factors KI for dry and water filled cracks are compared to critical values KIc from measurements that can be found in literature.

scholarly journals Parallel computations in nonlinear solid mechanics using adaptive finite element and meshless methods

2016 ◽  
Vol 33 (4) ◽  
pp. 1161-1191 ◽  
Author(s):  
Zahur Ullah ◽  
Will Coombs ◽  
C Augarde
Keyword(s):  
Finite Element ◽  
Parallel Algorithms ◽  
Meshless Method ◽  
Three Dimensional ◽  
Meshless Methods ◽  
Basis Functions ◽  
Two Dimensional ◽  
Content Type ◽  
Linear Elastic ◽  
Geometrical Nonlinearities

Purpose – A variety of meshless methods have been developed in the last 20 years with an intention to solve practical engineering problems, but are limited to small academic problems due to associated high computational cost as compared to the standard finite element methods (FEM). The purpose of this paper is to develop an efficient and accurate algorithms based on meshless methods for the solution of problems involving both material and geometrical nonlinearities. Design/methodology/approach – A parallel two-dimensional linear elastic computer code is presented for a maximum entropy basis functions based meshless method. The two-dimensional algorithm is subsequently extended to three-dimensional adaptive nonlinear and three-dimensional parallel nonlinear adaptively coupled finite element, meshless method cases. The Prandtl-Reuss constitutive model is used to model elasto-plasticity and total Lagrangian formulations are used to model finite deformation. Furthermore, Zienkiewicz and Zhu and Chung and Belytschko error estimation procedure are used in the FE and meshless regions of the problem domain, respectively. The message passing interface library and open-source software packages, METIS and MUltifrontal Massively Parallel Solver are used for the high performance computation. Findings – Numerical examples are given to demonstrate the correct implementation and performance of the parallel algorithms. The agreement between the numerical and analytical results in the case of linear elastic example is excellent. For the nonlinear problems load-displacement curve are compared with the reference FEM and found in a very good agreement. As compared to the FEM, no volumetric locking was observed in the case of meshless method. Furthermore, it is shown that increasing the number of processors up to a given number improve the performance of parallel algorithms in term of simulation time, speedup and efficiency. Originality/value – Problems involving both material and geometrical nonlinearities are of practical importance in many engineering applications, e.g. geomechanics, metal forming and biomechanics. A family of parallel algorithms has been developed in this paper for these problems using adaptively coupled finite element, meshless method (based on maximum entropy basis functions) for distributed memory computer architectures.

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