Publications (64)83.21 Total impact
- [Show abstract] [Hide abstract] ABSTRACT: Thermodynamic growth or melt and mechanical redistribution due to lead opening or ridge formation shape the thickness distribution of the Arctic ice cover and impact the overall strength of pack ice. Specifically, the deformation and strength of ice are not isotropic but vary with the thickness and lead orientation. To reflect these facts, we develop an anisotropic, elastic-decohesive constitutive model for sea ice together with a model to describe an oriented, ice thickness distribution. The tight connection between the mechanical response and the thickness distribution is an improvement over a previous model that only depended on the average ice thickness. The model describes mechanical responses anisotropically in both the elastic and failure regimes. In the elastic regime, the constitutive relation implicitly reflects strong and weak directions of the pack ice depending on the distribution of thin ice (including open water) and thicker ice (e.g., multi-year ice or ridges). In the failure regime, the model predicts both failure initiation and the lead orientation. Evolution from initial failure to complete failure when traction-free crack surfaces are formed is also modeled. Crack or lead width is determined during the evolution. Various examples of failure surfaces are presented to describe the behavior of modeled ice when the thickness distribution varies. The model predictions are also illustrated and compared with previous modeling efforts by examining regions of ice under idealized loading. Copyright © 2015 John Wiley & Sons, Ltd.
- [Show abstract] [Hide abstract] ABSTRACT: The material-point method models continua by following a set of unconnected material points throughout the deformation of a body. This set of points provides a Lagrangian description of the material and geometry. Information from the material points is projected onto a background grid where equations of motion are solved. The grid solution is then used to update the material points. This paper describes how to use this method to solve quasi-static problems. The resulting discrete equations are a coupled set of nonlinear equations that are then solved with a Jacobian-free, Newton–Krylov algorithm. The technique is illustrated by examining two problems. The first problem simulates a compact tension test and includes a model of material failure. The second problem computes effective, macroscopic properties of a polycrystalline thin film. Copyright © 2015 John Wiley & Sons, Ltd.
- [Show abstract] [Hide abstract] ABSTRACT: A three-dimensional constitutive model for joints is described that incorporates nonlinear elasticity based on volumetric elastic strain, and plasticity for both compaction and shear with emphasis on compaction. The formulation is general in the sense that alternative specific functional forms and evolution equations can be easily incorporated. A corresponding numerical structure based on finite elements is provided so that a joint width can vary from a fraction of an element size to a width that occupies several elements. The latter case is particularly appropriate for modeling a fault, which is considered simply to be a joint with large width. For small joint widths, the requisite equilibrium and kinematic requirements within an element are satisfied numerically. The result is that if the constitutive equation for either the joint or the rock is changed, the numerical framework remains unchanged. A unique aspect of the general formulation is the capability to handle either pre-existing gaps or the formation of gaps. Representative stress-strain plots are given to illustrate both the features of the model and the effects of changes in values of material parameters.
- [Show abstract] [Hide abstract] ABSTRACT: Damage in the form of cracks is predicted to assess the susceptibility of a tunnel to failure due to a blast. The material-point method is used in conjunction with a decohesive failure model as the basis for the numerical simulations. The assumption of a cylindrical charge as the source for the blast allows the restriction of plane strain and two-dimensional analyses. In the simulation, a further restriction of a single pressure pulse is used as the source of stress waves that are reflected and refracted after reaching the free surface of the tunnel wall. Three critical zones of significant cracking in the vicinity of a tunnel are identified as potential contributors to tunnel failure. Copyright © 2014 John Wiley & Sons, Ltd.
- [Show abstract] [Hide abstract] ABSTRACT: Electrodeposited thin films in MEMS devices often show fiber texture resulting in transverse isotropic, effective elastic properties. It is of interest to predict these elastic properties since they play a role in device performance. In addition to predicting effective material properties of the devices, we quantify the uncertainty in our predictions of these material properties for use in downstream simulations aimed at studies of performance, lifetime, or reliability. In this paper, we estimate the numerical value of the effective in-plane Young's modulus of thin nickel polycrystalline films using numerical simulation. We also examine the variability and sensitivity of the in-plane Young's modulus due to uncertainties in microstructure geometry, crystallographic texture, and numerical values of single-crystal elastic constants. The importance of accurate characterization of the texture is shown, as is the sensitivity of the effective in-plane Young's modulus to single-crystal elastic moduli. [2013-0118]
- [Show abstract] [Hide abstract] ABSTRACT: This study examines the well-posedness of the initial-value problems that arise in common models of sea ice. The model equations describe the balance of linear momentum combined with simplified thermodynamics represented by two continuity equations for effective ice thickness and ice concentration. The constitutive model for sea ice is given by two possible variants of the viscous-plastic model: the viscous-plastic model with pressure replacement and the viscous-plastic model with pressure replacement plus a tensile cutoff. The authors identify regimes of well- and ill-posedness for both models in one and two space dimensions. In one space dimension, the study finds that the viscous-plastic model and viscous-plastic model with pressure replacement behave similarly: there is ill-posedness when the divergent flow rate is larger than a minimum value. On the other hand, the viscous-plastic model with pressure replacement plus a tensile cutoff is ill-posed for all divergent flows. In two space dimensions the analysis is inconclusive for the viscous-plastic model with pressure replacement, but with the tensile cutoff the problem is ill-posed for certain divergent flows. The authors also discuss energy bounds and the difference between ill-posedness and stability of a solution. The study shows by examples that boundedness of solutions does not imply well-posedness and that it is possible for well-posed problems to have unstable solutions. The analysis shows that previous arguments in the literature, which state that a bound on the energy in sea ice models provides control over ill-posedness, are flawed.
Article: Decohesion with refreezing[Show abstract] [Hide abstract] ABSTRACT: In a previous paper, an elastic-decohesive model was developed for sea ice. Unlike previous models, orientation and displacement discontinuity associated with lead opening are specifically predicted. However, over the course of a season a specific lead may open and close several times with significant implications related to ice production and heat flux. The focus of this paper is to indicate, in a generic manner, how the formation of new ice by freezing within a lead and the recovery of tensile strength by the freezing of ridges can be accommodated easily within the decohesive structure. A sample simulation is provided to show the implications of these additional terms on ice production over several cycles of lead opening and closing.
- [Show abstract] [Hide abstract] ABSTRACT: This paper argues for a new constitutive model, an elastic–decohesive model for sea ice. The model is motivated by examining satellite observations of the Arctic processed to show ice deformation in the form of divergence, shear and vorticity. The model is implemented numerically in the material-point method and used to predict motion and deformation of sea ice by simulating a region of the Beaufort Sea. The model is able to capture the qualitative and statistical behavior of localized deformation seen in the observations.
- [Show abstract] [Hide abstract] ABSTRACT: Tunnels and other structures are often embedded underground within a media of jointed rock. If the tunnel is subjected to the resulting wave of an explosive blast in proximity, it is of interest to determine the blast properties, as well as the material and geometrical factors which identify a parameter space where the integrity of the structure may be compromised. The constitutive framework within the Material Point Method (MPM) [1,2] is extended to model joints as existing cracks. Results are presented investigating the effect of gap closure, and of impulse and energy transmission around embedded structures such as tunnels.[4pt]  Schreyer, H.L., 2007, ``Modelling surface orientation and stress at failure of concrete and geological materials'', J. for Numerical and Analytical Methods in Geomechanics, Vol 31, pp 141-171. [0pt]  Sulsky, D., Schreyer, H., Peterson, K., Kwok, R., and Coon, M., 2007, ``Using the material-point method to model sea ice dynamics'', J. Geophys. Res., Vol 112:CO2S90, doi:10.1029/2005JC00329
- [Show abstract] [Hide abstract] ABSTRACT: The material-point method is used to examine numerically the macroscopic stress-strain response of a granular sample under compression. The simulations reproduce experimental observations of the large stiffening that occurs as the granular bed becomes packed. We also show the network of force chains that forms and how the character of contacts between grains changes for large deformations. Finally, we examine the probability distribution of forces and observe exponential distributions above the mean with a small peak at the mean for small deformations, and a transition to a larger peak at larger deformations.
- [Show abstract] [Hide abstract] ABSTRACT: Sea ice in the Arctic plays an important role in the Earth’s climate and has been an early indicator of global warming. Remote sensing data, particularly synthetic aperture radar (SAR) imagery of Arctic regions, can help us understand the complex processes controlling sea ice dynamics and thermodynamics. The RADARSAT Geophysical Processor System (RGPS) was developed by the Polar Remote Sensing Group at the Jet Propulsion Laboratory (JPL) to extract sea ice motion data from SAR imagery. A set of points initially forming a regular grid is tracked providing displacements at each point over time. If the set of points in the original configuration is viewed as the vertices of square cells then the motion of the points determines the deformation of the cells. With this interpretation, grid quantities such as divergence, shear, and vorticity can be approximated using the nodal displacements. In this work an alternative approach for evaluating the deformation of sea ice from these data is proposed that uses the deformation gradient and a kinematic crack algorithm. With this approach, the deformation in a cell is assumed to be due solely to a displacement discontinuity caused by a crack. Then a minimization approach is used to find the crack dimension and orientation for each cell that best fits the nodal displacements. The kinematic crack algorithm is illustrated using RGPS data for a period of 16 days in February and March of 2004 for a region in the Beaufort Sea lying between Banks Island in the East and Point Barrow in the West.
- [Show abstract] [Hide abstract] ABSTRACT: Ideally, a verification and validation scheme should be able to evaluate and incorporate lower dimensional features (e.g., discontinuities) contained within a bulk simulation even when not directly observed or represented by model variables. Nonetheless, lower dimensional features are often ignored. Conversely, models that resolve such features and the associated physics well, yet imprecisely are penalized by traditional validation schemes. This can lead to (perceived or real) poor model performance and predictability and can become deleterious in model improvements when observations are sparse, fuzzy, or irregular. We present novel algorithms and a general framework for using information from available satellite data through fuzzy verification that efficiently and effectively remedy the known problems mentioned above. As a proof of concept, we use a sea-ice model with remotely sensed observations of leads in a one-step initialization cycle. Using the new scheme in a sixteen day simulation experiment introduces model skill (against persistence) several days earlier than in the control run, improves the overall model skill and delays its drop off at later stages of the simulation. Although sea-ice models are currently a weak link in climate models, the appropriate choice of data to use, and the fuzzy verification and evaluation of a system’s skill in reproducing lower dimensional features are important beyond the initial application to sea ice. Our strategy and framework for fuzzy verification, selective use of information, and feature extraction could be extended globally and to other disciplines. It can be incorporated in and complement existing verification and validation schemes, increasing their computational efficiency and the information they use. It can be used for model development and improvements, upscaling/downscaling models, and for modeling processes not directly represented by model variables or direct observations. Finally, if successful, it can also be used for scale selection in models and for selecting models for specific applications, e.g., component models of ensemble forecasting. The potential and requirements to extend this scheme to different applications, and to both empirical and statistical multivariate and full cycle model validation schemes are discussed.
Article: Physically-based data assimilation[Show abstract] [Hide abstract] ABSTRACT: Ideally, a validation and assimilation scheme should maintain the physical principles embodied in the model and be able to evaluate and assimilate lower dimensional features (e.g., discontinuities) contained within a bulk simulation, even when these features are not directly observed or represented by model variables. We present such a scheme and suggest its potential to resolve or alleviate some outstanding problems that stem from making and applying required, yet often non-physical, assumptions and procedures in common operational data assimilation. As proof of concept, we use a sea-ice model with remotely sensed observations of leads in a one-step assimilation cycle. Using the new scheme in a sixteen day simulation experiment introduces model skill (against persistence) several days earlier than in the control run, improves the overall model skill and delays its drop off at later stages of the simulation. The potential and requirements to extend this scheme to different applications, and to both empirical and statistical multivariate and full cycle data assimilation schemes, are discussed.
- [Show abstract] [Hide abstract] ABSTRACT: Novel metrics designed to evaluate the skill of geophysical models in simulating discontinuities and linear features are introduced and tested using a sea-ice model and remotely sensed observations of leads. The metrics are formulated as frequency-based indices of agreement, thus maintaining the simplicity desired in model development and operational applications, while remedying known shortcomings of common existing skill metrics. User-selectable spatial scales and features of significance allow for the general use of the metrics in variable applications, scales, and observation types.
- [Show abstract] [Hide abstract] ABSTRACT: Recently, a decohesive model  has been developed with special attributes appropriate for modeling the initiation of failure for quasibrittle materials such as concrete and ice. In particular, the model provides a prediction for the orientation of the plane of failure that varies smoothly with the state of stress at failure and is in agreement with experimental data including splitting under uniaxial compression. This model has been used successfully with a smeared-crack algorithm in the material point method (MPM) with one recent application being that of large-scale lead (crack) formation in Arctic ice [2,3]. A limitation of the method is that cracks are represented only weakly in the sense that neither the crack path nor displacement discontinuity is continuous. However, in addition to computational simplicity, there are other important advantages of the model and the computational scheme. These advantages include: (1) a method involving rotation for choosing one orientation over another when the model predicts two orientations for planes of material failure, and (2) the capability to handle simultaneously two or more cracks with different orientations at a single material point.
- [Show abstract] [Hide abstract] ABSTRACT: Our team has developed a new sea ice model which accounts for lead formation and deformation explicitly. This model will account directly for the evolution of that part of the mass balance resulting from the mechanical redistribution of ice in leads. We show results from our first simulation of the Beaufort Sea for 28 days 52-70 (February/March) in 2004. The numerical simulation was done using the material-point method with an elastic- decohesive constitutive model for sea ice. In the simulation, land is represented by material points that are treated as rigid and a no slip boundary condition is used between land and ice. Observed displacements from the RGPS data are used to prescribe the motion along the portion of the computational region that intersects the ocean, also. The simulation was forced with 6 hour NCEP winds on a 10 km grid. Earlier simulations on a smaller region of the Beaufort Sea showed that for these 16-day simulations some initialization of the ice conditions is required to reproduce the observed deformations in detail. Not surprisingly, the ice is too strong and does not deform appropriately in 16 days if we start from a homogeneous state of intact ice. Thus, we use RGPS observations from day 53.6-54.7 to determine the location and extent of some of the larger existing leads and use these observations to initialize a simulation that begins on day 54 and runs through day 70. The leads in the simulation can be compared visually with the leads from RGPS. Observations and simulations are not exactly the same. Nevertheless, we can see that reasonable looking lead patterns are produced in the simulation. This first simulation with the elastic-decohesive model shows great potential for reproducing observed pack ice dynamics.
- [Show abstract] [Hide abstract] ABSTRACT: 1] This paper revisits the Arctic Ice Dynamics Joint Experiment (AIDJEX) assumptions about pack ice behavior with an eye to modeling sea ice dynamics. The AIDJEX assumptions were that (1) enough leads were present in a 100 km by 100 km region to make the ice isotropic on that scale; (2) the ice had no tensile strength; and (3) the ice behavior could be approximated by an isotropic yield surface. These assumptions were made during the development of the AIDJEX model in the 1970s, and are now found inadequate. The assumptions were made in part because of insufficient large-scale (10 km) deformation and stress data, and in part because of computer capability limitations. Upon reviewing deformation and stress data, it is clear that a model including deformation on discontinuities and an anisotropic failure surface with tension would better describe the behavior of pack ice. A model based on these assumptions is needed to represent the deformation and stress in pack ice on scales from 10 to 100 km, and would need to explicitly resolve discontinuities. Such a model would require a different class of metrics to validate discontinuities against observations.
- [Show abstract] [Hide abstract] ABSTRACT: 1] The material-point method (MPM) is a numerical method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The material points provide a Lagrangian description of the ice that models convection naturally. Thus properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected material points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best methods for sea ice dynamics.
- [Show abstract] [Hide abstract] ABSTRACT: In recent years, the availability of large volumes of recorded ice motion derived from high-resolution SAR data has provided an amazingly detailed look at the deformation of the ice cover. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. These remarkable data put us in a position to begin detailed evaluation of current coupled mechanical and thermodynamic models of sea ice. This presentation will describe the material-point method (MPM) for solving these model equations. MPM is a numerical method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The material points provide a Lagrangian description of the ice that models convection naturally. Thus, properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected material points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best methods for sea ice dynamics. Simulations will also be presented for an area of the Beaufort Sea, where predictions can be validated against satellite observations of the Arctic.
Article: Kinematics of Strong Discontinuities[Show abstract] [Hide abstract] ABSTRACT: Synthetic Aperature Radar (SAR) provides a detailed view of the Arctic ice cover. When processed with the RADARSAT Geophysical Processor System (RGPS), it provides estimates of sea ice motion and deformation over large regions of the Arctic for extended periods of time. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. The RGPS deformation products are based on the assumption that the displacement and velocity are smooth functions of the spatial coordinates. However, if the dominant deformation of multiyear ice results from the opening, closing and shearing of leads, then the displacement and velocity can be discontinuous. This presentation discusses the kinematics associated with strong discontinuities that describe possible jumps in displacement or velocity. Ice motion from SAR data are analyzed using this framework. It is assumed that RGPS cells deform due to the presence of a lead. The lead orientation is calculated to optimally account for the observed deformation. It is shown that almost all observed deformation can be represented by lead opening and shearing. The procedure used to reprocess motion data to account for leads will be described and applied to regions of the Beaufort Sea. The procedure not only provides a new view of ice deformation, it can be used to obtain information about the presence of leads for initialization and/or validation of numerical simulations.
University of New Mexico
Albuquerque, New Mexico, United States
- • Department of Mathematics & Statistics
- • Department of Mechanical Engineering
University of California, Los AngelesLos Ángeles, California, United States