ABSTRACT. Calving mechanisms are still poorly understood and stress states in the vicinity of ice-shelf fronts are insufficiently known for the development of physically motivated calving laws that match observations. A calving model requires the knowledge of maximum tensile stresses. These stresses depend on different simulation approaches and material models. Therefore, this study compares results of a two-dimensional (2-D) continuum approach using finite elements with results of a onedimensional (1-D) beam model elaborated in Reeh (1968). A purely viscous model, as well as a viscoelastic Maxwell model, is applied for the 2-D case. The maximum tensile stress usually appears at the top surface of an ice shelf. Its location and magnitude are predominantly influenced by the thickness of the ice shelf and the height of the freeboard, the traction-free part at the ice front. More precisely, doubling the thickness leads to twice the stress maximum, while doubling the freeboard, based on changes of the ice density, results in an increase of the stress maximum by 61%. Poisson's ratio controls the evolution of the maximum stress with time. The viscosity and Young's modulus define the characteristic time of the Maxwell model and thus the time to reach the maximum principal stress.

To understand the dynamics of ice shelves, a knowledge of their internal and basal structure is very important. As the capacity to perform local surveys is limited, remote sensing provides an opportunity to obtain the relevant information. We must prove, however, that the relevant information can be obtained from remote sensing of the surface. That is the aim of this study. The Jelbart Ice Shelf, Antarctica, exhibits a variety of surface structures appearing as stripe-like features in radar imagery. We performed an airborne geophysical survey across these features and compared the results to TerraSAR-X imagery. We find that the stripe-like structures indicate surface troughs coinciding with the location of basal channels and crevasse-like features, revealed by radio-echo sounding. HH and VV polarizations do not show different magnitude. In surface troughs, the local accumulation rate is larger than at the flat surface. Viscoelastic modelling is used to gain an understanding of the surface undulations and their origin. The surface displacement, computed with a Maxwell model, matches the observed surface reasonably well. Our simulations show that the surface troughs develop over decadal to centennial timescales.

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 <i>K</i>_<i>I</i> at the crack tip. Ice, for this purpose, is treated as a compressible solid and the consequences of this choice in comparison to the predominant incompressible approaches is discussed. The computed stress intensity factors <i>K</i>_<i>I</i> for dry and water filled cracks are compared with critical values <i>K</i>_<i>I</i>c from measurements that can be found in literature

This work presents a continuum mechanics approach to model fracturing processes in brittle materials that are subjected to rapidly applied high-temperature gradients. Such a type of loading typically occurs when a solid is exposed to an intense high-energy particle beam that deposits a large amount of energy into a small sample volume. Given the rapid energy deposition leading to a fast temperature increase, dynamic effects have to be considered. Our existing phase field model for dynamic fracture is thus extended in a way that allows modelling of thermally induced fracture. A finite element scheme is employed to solve the governing partial differential equations numerically. Finally, the functionality of our model is illustrated by two examples.

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 K I 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 K I for dry and water filled cracks are compared to critical values K Ic from measurements that can be found in literature.

Metallic materials often exhibit a complex microstructure with varying material properties in the different phases. Of major importance in mechanical engineering is the evolution of the austenitic and martensitic phases in steel. The martensitic transformation can be induced by heat treatment or by plastic surface deformation at low temperatures. A two dimensional elastic phase field model for martensitic transformations considering several martensitic orientation variants to simulate the phase change at the surface is introduced in [1]. However here, only one martensitic orientation variant is considered for the sake of simplicity. The separation potential is temperature dependent. Therefore, the coefficients of the Landau polynomial are identified by results of molecular dynamics (MD) simulations for pure iron [2]. The resulting separation potential is applied to analyse the mean interface velocity with respect to temperature and load. The interface velocity is computed by use of the dissipative part to the configurational forces balance as suggested in [3]. The model is implemented in the finite element code FEAP using standard 4-node elements with bi-linear shape functions. A phase field model is used to determine the solution of the martensitic transformation (MT). In this model, two allotropes are of interest: the body cubic centered (bcc, ϕ = 1) martensitic, and the face cubic centered (fcc, ϕ = 0) austentic phase. The model relies on minimisation of the total free energy F [1] :

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Previous studies on the sensitivity of cracks in ice shelves with different boundary conditions, stress states and density profiles revealed the need for further analyses. As the transfer of boundary conditions from dynamic ice flow simulations to the linear elastic fracture analyses proved to be a critical point in previous studies, a new approach to relate viscous and elastic material behaviour is proposed. The numerical simulations are conducted using Finite Elements utilizing the concept of configurational forces. To show the applicability of the approach, a 2-dimensional plane stress geometry with volume loads due to the ice shelf flow is analyzed. The resulting crack path is compared to available crack paths from satellite images. In a first approach, ice can be regarded as a visco-elastic material represented by a Maxwell element that consists of a linear elastic spring and a nonlinear dashpot. For this material the stress can be written as σ v = σ e = σ with the elastic stress σ e and the viscous stress σ v . Under steady state conditions and the absence of volume forces, the equilibrium condition yields(1)For a given horizontal ice flow field with the velocities v(x, y) in the plane of the shelf, the viscous surface stress σ v can be evaluated using Glen's flow law [1] yielding, σ v = Bd 1−n n (trD1 + D), with the effective strain rate d = 1 2 tr(D 2 ), the strain rate tensor D and the material parameters B ≈ 7 · 10 7 Pa s 1 3 and n = 3. If we now understand the divergence of the viscous surface stress as a negative viscous volume force f v = − div σ v , Eqn. (1) can be rewritten asInstead of using stress or equivalent displacement boundary conditions, which are difficult to determine, the ice shelf is loaded by viscous volume forces yielding a stress field in the unfractured ice shelf that represents the viscous stresses.