3 resultados para Fully-Implicit Method

em CaltechTHESIS


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Inspired by key experimental and analytical results regarding Shape Memory Alloys (SMAs), we propose a modelling framework to explore the interplay between martensitic phase transformations and plastic slip in polycrystalline materials, with an eye towards computational efficiency. The resulting framework uses a convexified potential for the internal energy density to capture the stored energy associated with transformation at the meso-scale, and introduces kinetic potentials to govern the evolution of transformation and plastic slip. The framework is novel in the way it treats plasticity on par with transformation.

We implement the framework in the setting of anti-plane shear, using a staggered implicit/explict update: we first use a Fast-Fourier Transform (FFT) solver based on an Augmented Lagrangian formulation to implicitly solve for the full-field displacements of a simulated polycrystal, then explicitly update the volume fraction of martensite and plastic slip using their respective stick-slip type kinetic laws. We observe that, even in this simple setting with an idealized material comprising four martensitic variants and four slip systems, the model recovers a rich variety of SMA type behaviors. We use this model to gain insight into the isothermal behavior of stress-stabilized martensite, looking at the effects of the relative plastic yield strength, the memory of deformation history under non-proportional loading, and several others.

We extend the framework to the generalized 3-D setting, for which the convexified potential is a lower bound on the actual internal energy, and show that the fully implicit discrete time formulation of the framework is governed by a variational principle for mechanical equilibrium. We further propose an extension of the method to finite deformations via an exponential mapping. We implement the generalized framework using an existing Optimal Transport Mesh-free (OTM) solver. We then model the $\alpha$--$\gamma$ and $\alpha$--$\varepsilon$ transformations in pure iron, with an initial attempt in the latter to account for twinning in the parent phase. We demonstrate the scalability of the framework to large scale computing by simulating Taylor impact experiments, observing nearly linear (ideal) speed-up through 256 MPI tasks. Finally, we present preliminary results of a simulated Split-Hopkinson Pressure Bar (SHPB) experiment using the $\alpha$--$\varepsilon$ model.

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The quasicontinuum (QC) method was introduced to coarse-grain crystalline atomic ensembles in order to bridge the scales from individual atoms to the micro- and mesoscales. Though many QC formulations have been proposed with varying characteristics and capabilities, a crucial cornerstone of all QC techniques is the concept of summation rules, which attempt to efficiently approximate the total Hamiltonian of a crystalline atomic ensemble by a weighted sum over a small subset of atoms. In this work we propose a novel, fully-nonlocal, energy-based formulation of the QC method with support for legacy and new summation rules through a general energy-sampling scheme. Our formulation does not conceptually differentiate between atomistic and coarse-grained regions and thus allows for seamless bridging without domain-coupling interfaces. Within this structure, we introduce a new class of summation rules which leverage the affine kinematics of this QC formulation to most accurately integrate thermodynamic quantities of interest. By comparing this new class of summation rules to commonly-employed rules through analysis of energy and spurious force errors, we find that the new rules produce no residual or spurious force artifacts in the large-element limit under arbitrary affine deformation, while allowing us to seamlessly bridge to full atomistics. We verify that the new summation rules exhibit significantly smaller force artifacts and energy approximation errors than all comparable previous summation rules through a comprehensive suite of examples with spatially non-uniform QC discretizations in two and three dimensions. Due to the unique structure of these summation rules, we also use the new formulation to study scenarios with large regions of free surface, a class of problems previously out of reach of the QC method. Lastly, we present the key components of a high-performance, distributed-memory realization of the new method, including a novel algorithm for supporting unparalleled levels of deformation. Overall, this new formulation and implementation allows us to efficiently perform simulations containing an unprecedented number of degrees of freedom with low approximation error.

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We carried out quantum mechanics (QM) studies aimed at improving the performance of hydrogen fuel cells. This led to predictions of improved materials, some of which were subsequently validated with experiments by our collaborators.

In part I, the challenge was to find a replacement for the Pt cathode that would lead to improved performance for the Oxygen Reduction Reaction (ORR) while remaining stable under operational conditions and decreasing cost. Our design strategy was to find an alloy with composition Pt3M that would lead to surface segregation such that the top layer would be pure Pt, with the second and subsequent layers richer in M. Under operating conditions we expect the surface to have significant O and/or OH chemisorbed on the surface, and hence we searched for M that would remain segregated under these conditions. Using QM we examined surface segregation for 28 Pt3M alloys, where M is a transition metal. We found that only Pt3Os and Pt3Ir showed significant surface segregation when O and OH are chemisorbed on the catalyst surfaces. This result indicates that Pt3Os and Pt3Ir favor formation of a Pt-skin surface layer structure that would resist the acidic electrolyte corrosion during fuel cell operation environments. We chose to focus on Os because the phase diagram for Pt-Ir indicated that Pt-Ir could not form a homogeneous alloy at lower temperature. To determine the performance for ORR, we used QM to examine all intermediates, reaction pathways, and reaction barriers involved in the processes for which protons from the anode reactions react with O2 to form H2O. These QM calculations used our Poisson-Boltzmann implicit solvation model include the effects of the solvent (water with dielectric constant 78 with pH 7 at 298K). We found that the rate determination step (RDS) was the Oad hydration reaction (Oad + H2Oad -> OHad + OHad) in both cases, but that the barrier for pure Pt of 0.50 eV is reduced to 0.48 eV for Pt3Os, which at 80 degrees C would increase the rate by 218%. We collaborated with the Pu-Wei Wu’s group to carry out experiments, where we found that the dealloying process-treated Pt2Os catalyst showed two-fold higher activity at 25 degrees C than pure Pt and that the alloy had 272% improved stability, validating our theoretical predictions.

We also carried out similar QM studies followed by experimental validation for the Os/Pt core-shell catalyst fabricated by the underpotential deposition (UPD) method. The QM results indicated that the RDS for ORR is a compromise between the OOH formation step (0.37 eV for Pt, 0.23 eV for Pt2ML/Os core-shell) and H2O formation steps (0.32 eV for Pt, 0.22 eV for Pt2ML/Os core-shell). We found that Pt2ML/Os has the highest activity (compared to pure Pt and to the Pt3Os alloy) because the 0.37 eV barrier decreases to 0.23 eV. To understand what aspects of the core shell structure lead to this improved performance, we considered the effect on ORR of compressing the alloy slab to the dimensions of pure Pt. However this had little effect, with the same RDS barrier 0.37 eV. This shows that the ligand effect (the electronic structure modification resulting from the Os substrate) plays a more important role than the strain effect, and is responsible for the improved activity of the core- shell catalyst. Experimental materials characterization proves the core-shell feature of our catalyst. The electrochemical experiment for Pt2ML/Os/C showed 3.5 to 5 times better ORR activity at 0.9V (vs. NHE) in 0.1M HClO4 solution at 25 degrees C as compared to those of commercially available Pt/C. The excellent correlation between experimental half potential and the OH binding energies and RDS barriers validate the feasibility of predicting catalyst activity using QM calculation and a simple Langmuir–Hinshelwood model.

In part II, we used QM calculations to study methane stream reforming on a Ni-alloy catalyst surfaces for solid oxide fuel cell (SOFC) application. SOFC has wide fuel adaptability but the coking and sulfur poisoning will reduce its stability. Experimental results suggested that the Ni4Fe alloy improves both its activity and stability compared to pure Ni. To understand the atomistic origin of this, we carried out QM calculations on surface segregation and found that the most stable configuration for Ni4Fe has a Fe atom distribution of (0%, 50%, 25%, 25%, 0%) starting at the bottom layer. We calculated that the binding of C atoms on the Ni4Fe surface is 142.9 Kcal/mol, which is about 10 Kcal/mol weaker compared to the pure Ni surface. This weaker C binding energy is expected to make coke formation less favorable, explaining why Ni4Fe has better coking resistance. This result confirms the experimental observation. The reaction energy barriers for CHx decomposition and C binding on various alloy surface, Ni4X (X=Fe, Co, Mn, and Mo), showed Ni4Fe, Ni4Co, and Fe4Mn all have better coking resistance than pure Ni, but that only Ni4Fe and Fe4Mn have (slightly) improved activity compared to pure Ni.

In part III, we used QM to examine the proton transport in doped perovskite-ceramics. Here we used a 2x2x2 supercell of perovskite with composition Ba8X7M1(OH)1O23 where X=Ce or Zr and M=Y, Gd, or Dy. Thus in each case a 4+ X is replace by a 3+ M plus a proton on one O. Here we predicted the barriers for proton diffusion allowing both includes intra-octahedron and inter-octahedra proton transfer. Without any restriction, we only observed the inter-octahedra proton transfer with similar energy barrier as previous computational work but 0.2 eV higher than experimental result for Y doped zirconate. For one restriction in our calculations is that the Odonor-Oacceptor atoms were kept at fixed distances, we found that the barrier difference between cerates/zirconates with various dopants are only 0.02~0.03 eV. To fully address performance one would need to examine proton transfer at grain boundaries, which will require larger scale ReaxFF reactive dynamics for systems with millions of atoms. The QM calculations used here will be used to train the ReaxFF force field.