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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.
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
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 compu
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 sinteri
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
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 cr