Ratna Kumar Annabattula

Abstract: We present a phase field formulation for fracture in functionally graded materials (FGMs). The model builds upon homogenization theory and accounts for the spatial variation of elastic and fracture properties. Several paradigmatic case studies are addressed to demonstrate the potential of the proposed modelling framework. Specifically, we (i) gain insight into the crack growth resistance of FGMs by conducting numerical experiments over a wide range of material gradation profiles and orientations, (ii) accurately reproduce the crack trajectories observed in graded photodegradable copolymers and glass-filled epoxy FGMs, (iii) benchmark our predictions with results from alternative numerical methodologies, and (iv) model complex crack paths and failure in three dimensional functionally graded solids. The suitability of phase field fracture methods in capturing the crack deflections intrinsic to crack tip mode-mixity due to material gradients is demonstrated. Material gradient profiles that prevent unstable fracture and enhance crack growth resistance are identified: this provides the foundation for the design of fracture resistant FGMs. The finite element code developed can be downloaded from www.empaneda.com/codes .

Abstract: Among the international fusion solid breeder blanket community, there exists steady progress on the experimental, phenomenological, and numerical characterizations of the pebble bed effective thermo physical and mechanical properties, and of thermomechanic state of the bed under prototypical operating conditions. This paper summarizes recent achievements in pebble bed thermomechanics that were carried out by members of the IEA Fusion Nuclear Technology Subtask I Solid Breeding Blanket. A major goal is on developing predictive capability while identifying a pre-conditioned equilibrium stress state that would warrant pebble bed integrity during operations. The paper reviews and synthesizes existing computational modeling approaches for pebble bed thermomechanics prediction, and differentiating points of convergence/divergence among existing approaches. The progress toward modeling benchmark is also discussed. These advancements have led to a framework to help navigate future research.

Abstract: Highly ordered two-dimensional self-organized nanochannel networks as well as free-standing nanomembranes are produced on rigid substrates by means of III-V semiconductor compressively strained layers grown on top of an etchant-sensitive material. The releasing process is controlled by regularly spaced pits obtained from photolithography and a subsequent wet chemical etching. By tuning basic film parameters such as strain and thickness, one obtains periodic arrays of two-dimensional nanochannel networks with symmetries defined by the shape and periodicity of the photolithographic starting pits. Such nanochannel networks with a submicroscale lateral feature size exhibit a surprising flexibility with respect to the crystal lattice symmetry, retaining the original film crystalline quality as confirmed by X-ray grazing-incidence diffraction (GID) measurements. Finite element modeling helps in understanding the particular process of the cross-nanochannel formation.

Abstract: The micromechanical behavior of an assembly of binary and polydisperse spherical pebbles is studied using discrete element method (DEM) accounting for microscopic interactions between individual pebbles. A in-house DEM code has been used to simulate the assemblies consisting of different pebble diameters and the results of the simulations are compared with that of mono-size pebble assemblies. The effect of relative radii and volume fraction of the pebbles on the macroscopic stress–strain response is discussed. Furthermore, the effect of packing factor and coefficient of friction on the overall stress–strain behavior of the system is studied in detail. The shear (tangential) stiffness between the particles is also another influencing parameter. For a very small shear stiffness the system shows a strong dependence on the packing factor while a pebble material dependent shear stiffness shows a rather moderate dependence on the packing factor. For a similar packing factor, the mono-size assembly shows a stiff behavior during loading compared to binary assembly. However, the simulations do not show a significant difference between the two behaviors in contrast to the observations made in the experiments. The discrepancy can be attributed to (i) probable difference in packing factors for mono-size and binary assemblies in the experiments, (ii) arbitrary friction coefficient in the current model and (iii) the tangential interaction (constant shear stiffness) implemented in the present model which needs further modification as a function of the load history on the pebbles. Evolution of other micromechanical characteristics such as coordination number, contact force distribution and stored elastic energy of individual pebbles as a function of external load and system parameters is presented which can be used to estimate important macroscopic properties such as overall thermal conductivity and crushing resistance of the pebble beds.

Abstract: In this work, we propose an adaptive phase field method (PFM) to simulate quasi-static brittle fracture problems. The phase field equations are solved using the scaled boundary finite element method (SBFEM). The adaptive refinement strategy is based on an error indicator evaluated directly from the solutions of the SBFEM without any need for stress recovery techniques. Quadtree meshes are adapted to perform mesh refinement. The polygons with hanging nodes in the quadtree decomposition are treated as n − sided polygons within the framework of the SBFEM and do not require any special treatment in contrast to the conventional finite element method. Several benchmark problems are used to demonstrate the robustness and the efficacy of the proposed technique. The adaptive refinement strategy reduces the mesh burden when adopting the PFM to model fracture. Numerical results show an improvement in the computational efficiency in terms of the number of elements required in the standard PFM without compromising the accuracy of the solution.

Abstract: Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Abstract: We developed two-step solution-phase reactions to form hybrid materials of Mn3O4 nanoparticles on reduced graphene oxide (RGO) sheets for lithium ion battery applications. Mn3O4 nanoparticles grown selectively on RGO sheets over free particle growth in solution allowed for the electrically insulating Mn3O4 nanoparticles wired up to a current collector through the underlying conducting graphene network. The Mn3O4 nanoparticles formed on RGO show a high specific capacity up to ~900mAh/g near its theoretical capacity with good rate capability and cycling stability, owing to the intimate interactions between the graphene substrates and the Mn3O4 nanoparticles grown atop. The Mn3O4/RGO hybrid could be a promising candidate material for high-capacity, low-cost, and environmentally friendly anode for lithium ion batteries. Our growth-on-graphene approach should offer a new technique for design and synthesis of battery electrodes based on highly insulating materials.

Abstract: To study the operational behaviour of λ-terms, we will use the denotational (mathematical) approach. A denotational semantics for a language is based on the choice of a space of semantics values, or denotations, where terms are to be interpreted. Choosing a space with nice mathematical properties can help in proving the semantic properties of terms, since to this aim standard mathematical techniques can be used.

Abstract: The English-language dictionary defines wrinkles as "small furrows, ridges, or creases on a normally smooth surface, caused by crumpling, folding, or shrinking". In this paper we review the scientific aspects of wrinkling and the related phenomenon of buckling. Specifically, we discuss how and why wrinkles/buckles form in various materials. We also describe several examples from everyday life, which demonstrate that wrinkling or buckling is indeed a commonplace phenomenon that spans a multitude of length scales. We will emphasize that wrinkling is not always a frustrating feature (e.g., wrinkles in human skin), as it can help to assemble new structures, understand important physical phenomena, and even assist in characterizing chief material properties.