In-plane and out-of plane failure of an ice sheet using peridynamics

When dealing with ice structure interaction modeling, such as designs for offshore structures/icebreakers or predicting ice cover's bearing capacity for transportation, it is essential to determine the most important failure modes of ice. Structural properties, ice material properties, ice-structure interaction processes, and ice sheet geometries have significant effect on failure modes. In this paper two most frequently observed failure modes are studied; splitting failure mode for in-plane failure of finite ice sheet and out-of-plane failure of semi-infinite ice sheet. Peridynamic theory was used to determine the load necessary for in-plane failure of a finite ice sheet. Moreover, the relationship between radial crack initiation load and measured out-of-plane failure load for a semi-infinite ice sheet is established. To achieve this, two peridynamic models are developed. First model is a 2 dimensional bond based peridynamic model of a plate with initial crack used for the in-plane case. Second model is based on a Mindlin plate resting on a Winkler elastic foundation formulation for out-of-plane case. Numerical results obtained using peridynamics are compared against experimental results and a good agreement between the two approaches is obtained confirming capability of peridynamics for predicting in-plane and out-of-plane failure of ice sheets

Peridynamic model for a Mindlin plate resting on a Winkler elastic foundation

In this study, a peridynamic model is presented for a Mindlin plate resting on a Winkler elastic foundation. In order to achievestatic and quasi-static loading conditions, direct solution of the peridynamic equations are utilised by directly assigning inertia terms to zero rather than using widely adapted Adaptive Dynamic Relaxationapproach. The formulation is verified by comparing againsta finite elementsolutionfor transverse loading conditionwithout considering damageand comparing against a previous study for pure bending of a Mindlin plate with a central crack made of PMMA material havingnegligibly small elastic foundation stiffness. Finally, the fracture behaviour of a pre-cracked Minlin platerested on a Winkler foundation subjected to transverse loadingrepresenting a floating ice floe interacting with sloping structures. Similar fracture patternsobserved in field observations weresuccessfully captured by peridynamics

Family member search algorithms for peridynamic analysis

Peridynamic equation of motion is usually solved numerically by using meshless approaches, Family search process is one of the most time consuming parts of a peridynamic analysis. Especially for problems which require continuous update of family members inside the hurizoli of a material point, the time spent to search for family members becomes crucial. Hence, efficient algorithms are required to reduce the computational time. In this study, various family member search algorithms suitable for peridynamic simulations are presented including brute-force search, region partitioning and tree data structures. By considering problem cases for different number of material points, computational time between different algorithms is compared and the most efficient algorithm is determined

Dynamic propagation of a macrocrack interacting with parallel small cracks

In this study, the effect of small cracks on the dynamic propagation of a macrocrack is investigated by using a new continuum mechanics formulation, peridynamics. Various combinations of small cracks with different number, location and density are considered. Depending on the location, density and number of small cracks, the propagation speed of macrocrack differs. Some combinations of small cracks slows down the propagation of a macrocrack by 34%. Presented results show that this analysis can be useful for the design of new microstructurally toughened materials

Ice-structure interactions by using peridynamics

Despite of its advantages, utilization of the Arctic region for sailing brings new challenges due to its harsh environment. Therefore, ship structures must be designed to withstand ice loads in case of a collision between a ship and ice takes place. Moreover, ice-structure interactions are also important concern for the oil & gas platforms in the Arctic. Although experimental studies can give invaluable information about ice-structure interactions, full scale tests are very costly to perform. Therefore, computer simulations can be a good alternative. Ice-structure interaction modelling is a very challenging process since ice material response depends on many different factors including applied-stress, strain-rate, temperature, grain-size, salinity, porosity and confining pressure. In this study, a state-of-the-art technique, peridynamics is utilized for ice-structure interaction modelling. Peridynamics is a non-classical (non-local) continuum mechanics formulation which is very suitable for failure analysis of materials due its mathematical structure. Cracks can occur naturally in the formulation and there is no need to impose any external crack growth law

Uticaj različitih nivoa ishrane na karakteristike rasta i teksturu mesa dužičaste pastrmke (oncorhynchus mykiss wal.)

Eksperiment je realizovan u laboratoriji za akvakulturu Poljoprivrednog fakulteta Univerziteta u Banjoj Luci. Ukupno je naseljeno 100 jedinki u 5 eksperimentalnih grupa, prosječne individualne mase 91.091.37 g, totalne dužine tijela 20.080.10 cm i dužine tijela do račve repnog peraja 19.370.10 cm (MSEM). Cilj rada je bio praćenje efekata različitih nivoa ishrane na karakteristike rasta i teksturu (tvrdoću) mesa dužičaste pastrmke (Oncorhynchus mykiss). Dužičasta pastrmka u svim eksperimentalnim grupama hranjena je istom hranom, sa različitim nivoima ishrane: 20% (G-20) i 10% manje (G-10) u odnosu na standardni nivo ishrane, standardni nivo ishrane (G100) (preporuka proizvođača hrane), 10% (G+10) i 20% više (G+20) u odnosu na standardni nivo ishrane. Statistički značajna razlika sredina (p<0.05) mase i dužine tijela između posmatranih eksperimentalnih grupa javlja se u drugom periodu. Najmanja potrebna sila (kg) za presijecanje mesa dužičaste pastrmke konstatovana je na početku eksperimenta kod jedinki prosječne mase oko 90 g. Najtvrđe meso je kod riba iz eksperimentalnih grupa G+10 i G-10. Između posmatranih eksperimentalnih grupa konstatovana je statistički značajna razlika sredina (p<0.05) potrebne sile za presijecanje mesa

A Kirchhoff plate formulation in a state-based peridynamic framework

In recent years, there has been rapid progress on peridynamics. It has been applied to many different material systems, used for coupled field analysis and is suitable for multi-scale analysis. This study mainly focuses on peridynamic analysis for plate-type structures. For this purpose, a new peridynamic Kirchhoff plate is developed. The new formulation is computationally efficient by having only one degree of freedom for each material point. Moreover, it is based on the state-based peridynamic formulation, which does not impose any limitation on material constants. After presenting how to impose simply supported and clamped boundary conditions in this new formulation, several numerical studies are considered to demonstrate the accuracy and capability of the proposed formulation

Beam and plate formulations in peridynamic framework

Every object in the world has a 3-Dimensional geometrical shape. Therefore, it is usually possible to model structures in a 3-Dimensional fashion although this approach can be computationally expensive. In order to reduce computational time, the 3-Dimensional geometry can be simplified as a beam, plate or shell type of structure depending on the geometry and loading. This simplification should also be accurately reflected in the formulation which is used for the analysis. In this presentation, such simplifications in the form of beam and plate formulations within peridynamic framework will be presented. The equations of motion are obtained by utilizing Euler-Lagrange equations. Moreover, it is possible to implement such formulations in finite element framework which can bring significant computational efficiency for the numerical solution process. The accuracy of the formulations is validated by considering various benchmark problems subjected to different loading and displacement/rotation boundary conditions

Peridynamic modelling of fracture in polycrystalline ice

In this study, a peridynamic material model for a polycrystalline ice is utilised to investigate its fracture behaviour under dynamic loading condition. First, the material model was validated by considering a single grain, double grains and polycrystalline structure under tension loading condition. Peridynamic results are compared against finite element analysis results without allowing failure. After validating the material model, dynamic analysis of a polycrystalline ice material with two pre-existing cracks under tension loading is performed by considering weak and strong grain boundaries with respect to grain interiors. Numerical results show that the effect of microstructure is significant for weak grain boundaries. On the other hand, for strong grain boundaries, the effect of microstructure is insignificant. The evaluated results have demonstrated that peridynamics can be a very good alternative numerical tool for fracture analysis of polycrystalline ice material

Multi-scale modelling of ice-structure interactions

The present investigation has been devoted to the modeling of the ice-structure interactions by using the state-of-the-art technique, peridynamics. Peridynamics is a new continuum mechanics formulation originally developed at Sandia National Laboratories, USA and very suitable for failure analysis of structures due to its mathematical structure. Structures can vary from thin-walled structures such as ship hulls or airplane fuselage to bridges and wind-turbines. Furthermore by using peridynamics structural failure can be observed as compressive, tensile, bending or buckling failure and materials can be classified as elastic, viscoelastic or plastic.;Peridynamic equation is in integro-differential equation form rather than a partial differential equation as in the classical continuum mechanics which allows the continuous usage of these equations without specially treating the discontinuities. Although relatively new, it is successfully verified and utilized for modelling both metallic and composite structures. Hence, it is an excellent candidate to investigate complex problems such as the ice-structure interaction modelling. Furthermore, in a general sense, it may bring a new dimension to the analysis of marine structures especially in the area of arctic engineering.;Furthermore, peridynamic solver was developed including 2D and 3D geometry definitions together with peridynamic mesh. Several different solvers were implemented, such as explicit solver, adaptive dynamic relaxation and direct solver. In order to reduce the computational time, several family search algorithms (such as brute-force search, region partitioning algorithm, K-d tree and R-tree algorithms) were tested and implemented together with parallelization of most time consuming parts of code. Finally, several numerical studies were considered in order to demonstrate ice-structure interaction via peridynamic analysis.;Where those numerical studies range from 2D and 3D Bond Based peridynamic models used for analysis of ice splitting loads for in-plane failure and impact analysis between cylindrical (offshore structures) and conical (ship's bow) rigid bodies and ice sheet. Furthermore advanced peridynamic model for Mindlin plate resting on Winkler foundation was developed in order to test for out-of-plane failure of an ice sheet.The present investigation has been devoted to the modeling of the ice-structure interactions by using the state-of-the-art technique, peridynamics. Peridynamics is a new continuum mechanics formulation originally developed at Sandia National Laboratories, USA and very suitable for failure analysis of structures due to its mathematical structure. Structures can vary from thin-walled structures such as ship hulls or airplane fuselage to bridges and wind-turbines. Furthermore by using peridynamics structural failure can be observed as compressive, tensile, bending or buckling failure and materials can be classified as elastic, viscoelastic or plastic.;Peridynamic equation is in integro-differential equation form rather than a partial differential equation as in the classical continuum mechanics which allows the continuous usage of these equations without specially treating the discontinuities. Although relatively new, it is successfully verified and utilized for modelling both metallic and composite structures. Hence, it is an excellent candidate to investigate complex problems such as the ice-structure interaction modelling. Furthermore, in a general sense, it may bring a new dimension to the analysis of marine structures especially in the area of arctic engineering.;Furthermore, peridynamic solver was developed including 2D and 3D geometry definitions together with peridynamic mesh. Several different solvers were implemented, such as explicit solver, adaptive dynamic relaxation and direct solver. In order to reduce the computational time, several family search algorithms (such as brute-force search, region partitioning algorithm, K-d tree and R-tree algorithms) were tested and implemented together with parallelization of most time consuming parts of code. Finally, several numerical studies were considered in order to demonstrate ice-structure interaction via peridynamic analysis.;Where those numerical studies range from 2D and 3D Bond Based peridynamic models used for analysis of ice splitting loads for in-plane failure and impact analysis between cylindrical (offshore structures) and conical (ship's bow) rigid bodies and ice sheet. Furthermore advanced peridynamic model for Mindlin plate resting on Winkler foundation was developed in order to test for out-of-plane failure of an ice sheet