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Register a new userMechanical Analyses using Discrete Harmonic Expansions of Grain-Based Field Data
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A methodology for computing expansion basis functions using discrete harmonic modes is presented. The discrete harmonic modes are determined grain-by-grain for virtual polycrystals for which finite element meshes are available. The expansion weights associated with representing field variables over grain domains are determined by exploiting the orthogonality of the harmonic modes. The methodology is demonstrated with the representation of the axial stress distributions during tensile loading of a polycrystalline sample. An open source code, MechMonics, is available to researchers wishing to use the methodology to analyze data.
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The application of harmonic expansions to estimate intra-grain stress distributions from grain-averaged stress data is presented that extends the capabilities of the open source code, MechMonics. The method is based on using an optimization algorithm to determine the harmonic expansion weights that reduce the violation of equilibrium while maintaining prescribed grain-averages. The method is demonstrated using synthetic data generated for uniaxial extension of a virtual polycrystal with the mechMet code.
Computing the grain boundary (GB) counterparts to bulk phase diagrams represents an emerging research direction with potentially broad impacts. Using a classical embrittlement model system Ga-doped Al, this study demonstrates the feasibility of computing temperature- and composition-dependent GB diagrams to represent not only equilibrium thermodynamic and structural characters, but also mechanical properties. Specifically, hybrid Monte Carlo and molecular dynamics (MC/MD) simulations are used to obtain the equilibrium GB structure as a function of temperature and composition. Simulated GB structures are validated by aberration-corrected scanning transmission electron microscopy. Subsequently, MD tensile tests are performed on the simulated equilibrium GB structures. GB diagrams are computed for not only GB adsorption and disorder, but also interfacial structural and chemical widths, MD ultimate strength, and tensile toughness. A model is established to forecast the ductile-to-brittle transition. This study establishes a new paradigm to compute a spectrum of GB diagrams to enable the investigation of the unique GB composition-structure-property relationship.
Volume shrinkage, grain growth, and their interaction are major events occurring during free sintering of ceramics. A high temperature sintering dilatometry curve is influenced by these both phenomena. It is shown that the continuum theory of sintering can be utilized in the format enabling the extraction of the maximum amount of information on the densification and grain growth kinetics based on a simple dilatometry test. We present here the capability of such a fast approach (Dilatometry based Grain growth Assessment DGA) utilized for the modeling of sintering and grain growth of zirconia.
Compressed sensing has become a widely accepted paradigm to construct high dimensional cluster expansion models used for statistical mechanical studies of atomic configuration in complex multicomponent crystalline materials. However, strict sampling requirements necessary to obtain minimal coherence measurements for compressed sensing to guarantee accurate estimation of model parameters are difficult and in some cases impossible to satisfy due to the inability of physical systems to access certain configurations. Nevertheless, the dependence of energy on atomic configuration can still be adequately learned without these strict requirements by using compressed sensing by way of coherent measurements using redundant function sets known as frames. We develop a particular frame constructed from the union of all occupancy-based cluster expansion basis sets. We illustrate how using this highly redundant frame yields sparse expansions of the configuration energy of complex oxide materials that are competitive and often surpass the prediction accuracy and sparsity of models obtained from standard cluster expansions.
Geometric compatibility constraints dictate the mechanical response of soft systems that can be utilized for the design of mechanical metamaterials such as the negative Poisson ratio Miura-ori origami crease pattern. We examine the broad family of crease patterns composed of unit cells with four generic parallelogram faces, expanding upon the family of Morph patterns, and characterize the familys low-energy modes via a permutation symmetry between vertices. We map these modes to the resulting strains and curvatures at the intercellular level where the same symmetries elucidate a geometric relationship between the strains of the systems rigid planar mode and the curvatures of its semi-rigid bend mode. Our formalism for the analysis of low-energy modes generalizes to arbitrary numbers of quadrilateral---not necessarily parallelogram---faces where symmetries may play an important role in the design of origami metamaterials.
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