On the potential of computational methods and numerical simulation in ice mechanics

Transcription

1 IOP Conference Series: Materials Science and Engineering On the potential of computational methods and numerical simulation in ice mechanics To cite this article: Pål G Bergan et al 2010 IOP Conf. Ser.: Mater. Sci. Eng View the article online for updates and enhancements. Related content - A Node Placement Method with high quality for mesh generation Yufeng Nie, Weiwei Zhang, Ying Liu et al. - Bird impact at aircraft structure Damage analysis using Coupled Euler Lagrangian Approach I Smojver and D Ivancevic - A unified enrichment scheme for fracture problems Safdar Abbas and Thomas-Peter Fries Recent citations - Analysis of the mechanical behavior of thin ice layers on structures including radial cracking and de-icing Hannah Sommerwerk and Peter Horst - Peridynamic simulation of brittle-ice crushed by a vertical structure Minghao Liu et al - Simulation of ice crushing experiments with cohesive surface methodology Juha Kuutti et al This content was downloaded from IP address on 21/08/2018 at 23:53

2 On the potential of computational methods and numerical simulation in ice mechanics Pål G. Bergan 1, Gus Cammaert 2, Geir Skeie 2 and Venkatapathi Tharigopula 2 1 NTNU, Trondheim, Norway and Department of Ocean Systems Engineering, KAIST, Daejeon, Korea 2 DNV Research and Innovation, Høvik, Norway PBergan@kaist.edu Abstract. This paper deals with the challenge of developing better methods and tools for analysing interaction between sea ice and structures and, in particular, to be able to calculate ice loads on these structures. Ice loads have traditionally been estimated using empirical data and engineering judgment. However, it is believed that computational mechanics and advanced computer simulations of ice-structure interaction can play an important role in developing safer and more efficient structures, especially for irregular structural configurations. The paper explains the complexity of ice as a material in computational mechanics terms. Some key words here are large displacements and deformations, multi-body contact mechanics, instabilities, multi-phase materials, inelasticity, time dependency and creep, thermal effects, fracture and crushing, and multi-scale effects. The paper points towards the use of advanced methods like ALE formulations, mesh-less methods, particle methods, XFEM, and multi-domain formulations in order to deal with these challenges. Some examples involving numerical simulation of interaction and loads between level sea ice and offshore structures are presented. It is concluded that computational mechanics may prove to become a very useful tool for analysing structures in ice; however, much research is still needed to achieve satisfactory reliability and versatility of these methods. 1. Introduction The use of advanced computational mechanics and computer methods for simulation of the behaviour of ice and the interaction between ice and structures is a rather new discipline. The traditional approaches for solving such problems have primarily been based on empirical methods, field and laboratory measurements, and on engineering judgement. Today there is a strong interest for finding new and better methods for simulating ice behaviour and the interaction between sea ice and structures; the reason for this may be found in increasing oil and gas activities in arctic regions and the growing interest for regular ship transport through the North-East and North-West arctic sea passages owing to the reduction of ice coverage and thickness under the influence of climate change. In short one may say that there are considerable industrial and economical interests associated with finding better methods for safe design of ships and offshore platforms that are exposed to sea ice. Ice mechanics is not only a matter of understanding how the ice itself behaves; what happens to the ice is in fact of lesser interest in an industrial perspective. What really is of importance is to be able to model the ice behaviour and, on that basis, to be able to analyse and estimate the c 2010 Published under licence by Ltd 1

3 ice loads and effects on the structure including the full static and dynamic interaction between these two media. In fact, there is also a third material that is important in this context, and that is the sea water on which the lower density sea ice is floating. Simulation of the hydrostatic and to some extent the hydrodynamic, interaction of breaking ice sheets, ice floes and ice ridges in contact with fixed or floating structures represent challenges for computational mechanics of formidable complexity and magnitude. The complexity of ice mechanics modelling is staggering. Ice is a material whose properties depend on salinity, temperature, age, and history. The material can be linear, inelastic and visco-plastic; in fact, it can be regenerative through re-crystallization. In its failure modes it can be plastic, crushing with multi-fracturing, and it can behave in brittle fracture. The overall behaviour is also scale-dependent; this is a fact that makes it a challenge to transfer laboratory test results to real scale situations. The interaction with the structure depends, in addition to the mechanical properties themselves, on structural size and geometric shape, special features such as ridges, and on the relative velocity between the structure and the ice. Ice breaking and accumulation of ice next to the structure are parts of this complex contact problem. The paper presents an overview of the current state of the art in ice mechanics. Reference is made to computational mechanics methods that have been tested and described in the literature. Comments are made regarding strengths and short comings of these different methods. In particular the cases of breaking of level sea ice against cylindrical structures and the interaction between such structures and ice ridges are discussed. Further, the paper points to areas in which further research is obviously needed in order to make the methods more reliable and suitable for practical use and in design. Important research topics for the future are also suggested. 2. Some important applications Climate changes that have taken place during recent years have lead to shrinking of the ice caps in the Arctic as well as in the Antarctic. At the same time the mid-winter ice cover has become thinner. The reduction of the extent of the summer sea ice is opening for use of sea routes like the North-East Passage and North-West Passage by commercial ships, potentially reducing the time of sea transport between Europe and Asia with more than a week. However, sea transports in arctic regions present many perils to the ships as well to crew, passengers, cargo and the environment. The requirement for safety must consequently be the primary consideration. Ships that are sailing in ice infested waters have to be designed and operated according to strict ice notations or class requirements. The current rules span from ships that can operate in lightly ice covered water to polar class and ice breaker class vessels that can break multi-year ice of more than a meter thickness and perform repeated ramming of ice ridges. Although current rules are prescriptive in their nature there is a need for calculating the effect of particular aspects of ice conditions and ice breaking operations. The combined bending, breaking and clearing sea ice from a ship is a most difficult mechanical problem to calculate. A particular threat is collision between a ship and an iceberg; this is well known from the Titanic and more recent accidents like the polar cruise ship M/V Explorer hitting an iceberg and capsizing in It is believed that about 25 percent of the World s total oil and gas reserves may be located in the Arctic; the race for locating and exploiting these reserves is already on. It may seem as a contradiction, but the fact that the ice cap is seemingly retracting increases the need for better understanding of the interaction between ice and offshore structures; the reason being that less ice opens up for exploration and industrial activities. There are a host of important and interesting problems associated with ice interaction with fixed or floating structures. Typically the design of such structures has to be based on encountering the most severe conditions in terms of ice thickness and strength, particular ice features like rubble and ridges, and strong currents. Advanced analysis methods may not only help in estimating the actual forces acting locally and globally on the structure, but may also 2

4 (a) (b) Figure 1. Left: 1(a) Ice breaker and cargo ship in sea ice. Right: 1(b) Drill platform encountering ice floe. be of great help in developing structural geometries that can minimize these forces through geometry and shape optimization. Ice forces on multi-leg structures, for example, are difficult to quantify because of the interaction between the legs, and inevitably the designer has to rely on expensive and somewhat unreliable model tests. Sloped structures with multiple transitions are also very difficult to analyse using current methods. Another important and interesting problem is interaction between scouring icebergs or ice ridges and oil and gas pipelines located on or under the sea bed. It may today be possible to simulate how floating icebergs may scrape into the seabed and thereby pose a severe threat to such pipelines. A particular problem receiving attention recently is icing; that is, accumulation of a coating of ice on structures such as ships and offshore platforms due to freezing of humidity in the air or sea spray from waves. Icing not only represents a practical problem in relation to human access and performance of equipment on deck; it can be a very serious threat to the safety and stability of a ship simply because of the added ice weight above the sea surface. Understanding and modelling of the mechanisms that generate water vapour and spray as well as dealing with the following accumulated icing on an object represent a tall order. It seems clear that the industrial and commercial interests for better understanding of how sea ice interacts with structures are considerable; better analysis methods and tools and stronger focus on safety should be prerequisites for allowing for strongly increased commercial activities in the Arctic. Universities and research institutions should be in the forefront of developing such methods. 3. Mechanical properties of ice and various forms of ice Ice is undoubtedly one of the most complex materials that exists, both in terms of rheological characterization as well as possible geometric shapes and form. In simplified terms one may characterize the mechanical behaviour of ice and ice formations in interaction with structures as representing multi-phase problem: structure, ice and water inelasticity geometric instabilities phase transitions 3

5 time dependency and creep large displacements and deformations thermal effects fracture and crushing multi-body contact mechanics multi-scale effects Temperature and loading rates are the two most important properties defining the state of ice as a material. The parameters are related to the type of ice defined by grain size, orientation and also the size and shape of the voids. Ice is considered to be polycrystalline and behaves in principle like metals with both ductile and brittle behaviour. The transition from a ductile to a brittle response is determined by temperature, grain size and loading rates. Two aspects differentiate and complicate the treatment of ice as compared with the engineering approach to metals; the grain size is relatively large and secondly, ice exists close to its freezing temperature. Void spaces due to the presence of brine or air from the freezing process, also complicate material behaviour. Figure 2. Some main failure modes of level ice sheets. It is important to note that ice may fail in many different modes such as Crushing at contact Local and large scale brittle and inelastic fracture Bending Buckling and instabilities Splitting Spalling Short and long term creep It is worth noting that these failure modes normally do not appear separately but rather in combination. The most likely failure modes depend on the material properties, geometric features of the ice and the structure, as well as boundary conditions such as boundary constraints and ice motion. As an example, the picture may be as follows: (1) crushing and spalling dominate failure in a local, confined contact zone; (2) bending, buckling, inelastic cracking, and off-set of broken off pieces may be appearing in an intermediate zone; and, (3) long brittle cracks appear farther away. 4

6 It is also necessary to take into consideration that ice on sea may appear in many different forms such as First year and multi-year level ice sheets Ice floes Rafted sheets Ice ridges Chaotic ice rubble Variation in ice masses from small ice blocks to icebergs of several million tonnes A more systematic and extensive characterization of ice actions may be found in Løset [1]. It is not difficult to understand that building realistic computer models and carrying out simulations of ice-structure interaction represent a formidable challenge. Ice, and especially sea ice, appears in so many forms, many of which have yet not been fully studied. It is therefore evident that computer analysis at the present stage of development has to concentrate on some simplified cases which are of importance for gaining more insight and possibly also to provide rather crude estimate of forces and their effects. Beyond this, safe design has to account for the uncertainties that exist through use of probabilistic models and conservative safety factors. 4. Discretization techniques and analysis A number of different physical processes related to sea ice were addressed by the diverse applications described in Section 2. A particularly important problem is ice-structure interaction and in this respect ice, and especially sea ice, represents particular challenges to numerical treatment, Løset et al. [1]: Large scale ice features, the mechanical properties of ice, the structural geometry and ice failure modes all affect the global and local ice pressures important for design decisions. A number of numerical approaches have been used to address different topics related to icestructure interaction. Many of them are based on the continuum concept, thus considering ice as a continuous medium. The finite element method, Belytschko et al. [2], has proved to be a versatile tool in solving a variety of problems of importance for engineering. The gain in computational power, the development of new algorithms, high robustness and increase in efficiency have all contributed in extending the realm of engineering processes that can be simulated by the method. The finite element method is dominating the field of solid and structural mechanics and in particular when it comes to nonlinear simulations. Thus, it is only natural to explore finite element analysis in ice structure interaction problems as well. When level ice interacts with a sloping structure the ice sheet may fail by forming radial cracks. The cracks propagate in the radial direction until circumferential cracks form and the ice sheet reaches its ultimate capacity. In the study of the onset of circumferential flexural cracks in an ice cover. A simple plate or wedge shaped beam model resting on an elastic foundation constitutes a first approach. This problem is depicted in Figure 4. The model may be extended to include dynamic effects and also the dynamic interaction with the sea in a hydroelastic simulation. This has been studied by Lubbad et al. [3] using Comsol Multiphysics, an equation-based finite element toolbox. The interaction of level ice against a structure is complex in the post-failure regime but important to model in order to establish ultimate capacities and gain insight in the complex interacting dynamic effects. When ice moves against a strong and stiff structure the ice may fail by a series of different failure modes; fracturing, crushing, spalling and fragmentation are fundamental failure modes in many interacting scenarios, Gürtner [4]. The ultimate loading 5

7 Figure 3. Isogeometric analysis of an ice sheet acting on a conical structure, radial bending moment. transferred depends on post-failure behaviour where the interaction of fragmented ice, ice, water and structure are important mechanisms. The multi-fracture simulation has been addressed using cohesive zone elements within an explicit finite element procedure. The fragmentation or break-up into new ice-blocks are included and their dynamic interaction is included in the analysis, Gürtner [4] and also Konuk et al. [5]. For low load levels the ice act as an elastic or visco-elastic material. Depending on grain-size, temperature, loading and strain-rate, the ice may behave like a plastic or visco-plastic material. It is noted that this type of model experience no scale effects which is inherent in ice failure behaviour, Bažant [6]. The governing equations of the finite element method have to be expressed in a particular kinematic description of the continuum. In solid mechanics Lagrangian motion is extensively used while the Eulerian description is normally preferred in fluid flow problems. In Lagrangian motion the underlying mesh gets distorted while in the Eulerian frame the underlying mesh is constant. A mixture of the two, the Arbitrary Lagrangian Eulerian (ALE) description, combines the best of both methods and allow for easy boundary tracking without significant mesh distortion. Independent combination of Eulerian and Lagrangian applications, denoted Coupled- Eulerian Lagrangian (CEL) technology, is another technique to avoid severe mesh distortion. However, such formulation results in immersed boundary conditions with less accurate resolution of the boundary layer. These methods have been applied for the study of ice gouging or ice scouring. A fully coupled Arbitrary Lagrangian Eulerian approach will normally be necessary in order to take account of the large deformations involved in modelling of ice ridge - soil - pipeline interactions. The ALE method has been used by Kenny et al. [7] to study extreme loading events for a buried pipeline. Abdalla et al. [8] used the CEL approach in the Abaqus computer program to explore extended numerical approaches to scouring in order to shed some light on the uncertainties regarding pipeline burial depth. Ship-ship collision and ship grounding have been studied using explicit finite element calculations; the motivation for this has been to better understand the dynamics of these scenarios and enhance the crashworthiness of new designs. The external, large scale dynamic behaviour of colliding ships interacting with the surrounding water as well as structural dynamics 6

8 including large geometric distortion, material fracture and crack propagation, have been included in some of the analyses. Collisions in the Arctic include the possibility of encountering icebergs; this does not only bring with it safety issues related of a damaged ship, but also the possibility of leakage of oil with enormous consequences for the fragile environment. Reliable modelling of failure with transient dynamics, extensive contact, large deformation and material failure of the structure as well as the iceberg does indeed represent a formidable challenge. Issues of this type have been addressed in recent studies by Liu et al. [9], using explicit finite element modelling. In problems with a large number of interacting particles, or objects, some version of the Discrete Element Method, Cundall and Strack [10], may be used. The methods look at a large collection of interacting rigid bodies of simple or complex shapes. The method implements efficient procedures for treatment of extensive contact where the success relies on efficient neighbour element search algorithms. The method has proved to be efficient in the study of granular materials, powder flow and rock mechanics. The problem of ice pile-up in front of an inclined structure has also been studied in a number of publications by Paavilainen et al. [11] using a combination of finite element cohesive zone modelling and discrete element methods. The continuous model is treated using finite elements while the broken ice is converted into discrete elements. The ice pile-up including extensive contact is handled by a discrete element procedure. Ice ridge shear performance has been simulated using combined FEM-DEM in Polojärvi and Tuhkuri [12]. Discrete elements have been used to model the ice blocks in the keel of the ridge. Similar situations where multiple ice objects may interact with sea water and a marine structure are encountered in ice management and ice breaking problems. The dynamics of multi-media interaction and failure effects are indeed very complicated. This type of problem may lend itself to using mesh-less methods such as the Particle Finite Element Method (see Oñate et al. [13]). A main objective of this method is to enable fully coupled simulations involving fluids with a free surface, solids and structures. Classical mesh-based methods such as finite differences, finite volumes and finite elements are difficult to apply to multi-physics problems with fluids, solids and contacts because they intrinsically will suffer from severe distortion of the background mesh. In mesh-less methods the topology of the numerical scheme is part of the solution process. A number of interesting methods exists within the class of mesh-less and particle like methods; the Smoothed Particle Hydrodynamics initially suggested by Lucy [14] and Ginold and Monaghan [15], the Discrete Element Method by Cundall and Strack [10], the element free Galerkin method proposed by Belytschko et al. [16], and Particle Finite Element Method (see Oñate et al. [13]). Further, extensions to the finite element method, like the extended Finite Element Method by Belytschko and Black [17], have been introduced to combine the best from FEM and meshless methods. XFEM includes special functions to enhance the FEM approximations in the treatment of both weak and strong discontinuities. These new discretization schemes may prove to be of importance in handling the different fracture and cracking problems encountered when ice interacts with marine installations in Arctic regions. Some initial, current studies using the extended finite element method for simulating level ice interacting with a sloping structure are presented in Section Numerical study of Ice-structure interaction Numerical simulations of ice-structure interaction using the extended finite element method are carried out to predict some of the failure modes of ice. Two cases were investigated: one is focused on an ice sheet interacting with a rigid cylindrical structure (2D model, Figure 4), and the second case is an ice sheet interacting with a rigid cone structure (3D model, Figure 5). The ice is treated as an isotropic, nonlinear material capable of cracking, and the interaction between the 7

9 ice sheet and structure is modelled with a contact formulation based on finite sliding. The main ingredients of the constitutive model used in this work are isotropic elasticity, crack detection using maximum principal stress and a crack model based on the fracture energy approach by Hilleborg et al. [18]. Numerical simulations are performed using non-linear finite element code Figure 4. Ice sheet-rigid cylindrical structure interaction, failure mode: cracks.! (a) Buckling (b) Crushing and radial cracks Figure 5. Predicted failure modes in ice-rigid cone structure interaction. Abaqus/standard. In 2D case, the cylinder is modelled as a rigid structure, and the ice sheet is discretized using a four node plane stress elements with three degrees of freedom at each node (Figure 4). In 3D case, the cone is modelled as a rigid structure and the ice sheet is discretized with 8 node solid elements with three degrees of freedom. In both the cases, the ice sheet was moved into contact with the rigid structure by prescribing displacement in the width direction at the outer edge of the ice sheet. The boundary condition of the outer edge was such that the ice sheet was kept in the horizontal direction and the remaining edges were free. The geometry of the model was taken from the doctoral thesis of Sand [19]. The constitutive model based on the traction-separation cohesive behaviour was adopted to model the mechanical behaviour of ice. The available traction-separation model in Abaqus [20] assumes initially linear elastic 8

10 behaviour followed by the initiation and evolution of damage. The linear elastic behaviour of ice was defined using the Young s modulus E = 6000 MPa and Poisson s ratio ν = 0.3. The fracture mechanism consists of two ingredients: a damage initiation criterion and a damage evolution law. The damage initiation was specified by using the maximum principal stress criterion, in which maximum principal stress was set to 0.5 MPa. Energy based damage evolution law was used with fracture energy given as 40 N/m, independent of the fracture mode. An early indication of XFEM methodology is that it may be able to predict some of the failure modes such as crushing and radial cracks (as mentioned in Section 3) in ice sheets as seen in Figures 5 and 6. However, a detailed check of the methodology is necessary. The advantage of XFEM is that simulation can be carried out on simple meshes without mesh alignment or refinement near the discontinuities. Moreover, no mass will be removed from the simulation during the propagation of discontinuities or cracks. However, there are some issues still remain with respect to numerical handling of crushed ice after fracture. 6. Conclusion Ice mechanics is still a relatively new discipline in an early stage of development. Simulation of situations involving interaction between sea ice, structure and water represent a formidable challenge because of the intrinsic complexity of the problem. It seems clear that the traditional finite element and finite difference methods are not capable of dealing realistically with such problems whereas some more recently developed numerical simulation methods like meshless and particle methods bear promise. Moreover, complex cracking, crushing and contact mechanisms may be dealt with techniques like the XFEM method. However, much work is still needed in order to gain more experience with these techniques and to be able to model the full complexity of the ice-structure interaction problems. Acknowledgments The pioneering work by ice mechanics researchers referenced herein has been of great importance for the current studies and will also prove to be invaluable for developing more reliable simulation techniques in the future. In particular the authors would like to thank the Arctic Technology research group headed by Professor Løset at NTNU in Trondheim for their energetic research efforts and kind cooperation. References [1] Løset S, Shkhinek K and Høyland V 1998 Ice Physics and Mechanics (NTNU) [2] Belytschko T, Liu W K and Moran B 2000 Nonlinear Finite Elements for Continua and Structures (John Wiley & Sons, Ltd.) [3] Lubbad R, Moe G and Løset S 2008 Proceedings of 19th IAHR International Symposium on Ice [4] Gürtner A 2009 Experimental and numerical investigations of ice-structure interaction Ph.D. thesis Norwegian University of Science and Technology, Faculty of Engineering Science and Technology, Department of Civil and Transport Engineering URL [5] Konuk I, Gürtner A and Yu S 2009 Proceedings of the 20th International Conference on Port and Ocean Engineering under Arctic Conditions vol 2 ed Fransson L [6] Bažant Z P 2008 The Mechanics of Solids: History and Evolution (A Festschrift in Honor of Arnold Kerr) ed Santare M and Chajes M (University of Delaware Press) pp URL [7] Kenny S, Barrett J, Phillips R and Popescu R 2007 Proceedings of The Seventeenth 2007 International Offshore and Polar Engineering Conference, ISOPE 2007 [8] Abdalla B, Pike K, Eltaher A and Jukes P 2009 (Osaka, Japan) pp ISSN arctic pipelines;eulerian;ice scour;lagrangian;limit state;local buckling; URL [9] Liu Z, Amdahl J and Løset S 2009 Proceedings of the 20th International Conference on Port and Ocean Engineering under Arctic Conditions vol 1 ed Fransson L 9

11 [10] Cundall P and Strack O 1979 Geotechnique ISSN granular assemblies;photoelastic analysis; [11] Paavilainen J, Tuhkuri J and Polojärvi A 2009 Proceedings of the 20th International Conference on Port and Ocean Engineering under Arctic Conditions vol 2 ed Fransson L [12] Polojärvi A and Tuhkuri J 2009 Proceedings of the 20th International Conference on Port and Ocean Engineering under Arctic Conditions vol 2 ed Fransson L [13] Oñate E, Idelsohn S, Pin F D and Aubry R 2004 International Journal of Computational Methods [14] Lucy L 1977 The Astronomical Journal [15] Gingold R A and Monaghan J J 1977 Monthly Notices of the Royal Astronomical Society [16] Belytschko T, Lu Y and Gu L 1994 International Journal for Numerical Methods in Engineering ISSN element free GAlerkin method;moving least squares interpolants;volumetric locking;weight functions; [17] Belytschko T and Black T 1999 International Journal for Numerical Methods in Engineering [18] Hilleborg A, Modeer M and Petersson P E 1976 Cement and Concrete Research [19] Sand B 2008 Nonlinear finite element simulation of ice forces on offshore structures Ph.D. thesis Lule University of Technology 2008:39, ISSN: [20] Abaqus analysis user manual 2009 Modelling discontinuities as an enriched feature using the extended finite element method, Dassault Systems 10