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The design of structural and functional materials for specialized applications is experiencing significant growth fueled by rapid advancements in materials synthesis, characterization, and manufacturing, as well as by sophisticated computational materials modeling frameworks that span a wide spectrum of length and time scales in the mesoscale between atomistic and homogenized continuum approaches. This is leading towards a systems-based design methodology that will replace traditional empirical approaches, embracing the principles of the Materials Genome Initiative. However, there are several gaps in this framework as it relates to advanced structural materials development: (1) limited availability and access to high-fidelity experimental and computational datasets, (2) lack of co-design of experiments and simulation aimed at computational model validation, (3) lack of on-demand access to verified and validated codes for simulation and for experimental analyses, and (4) limited opportunities for workforce training and educational outreach. These shortcomings stifle major innovations in structural materials design. This paper describes plans for a community-driven research initiative that addresses current gaps based on best-practice recommendations of leaders in mesoscale modeling, experimentation, and cyberinfrastructure obtained at an NSF-sponsored workshop dedicated to this topic and subsequent discussions. The proposal is to create a hub for "Mesoscale Experimentation and Simulation co-Operation (h-MESO)---that will (I) provide curation and sharing of models, data, and codes, (II) foster co-design of experiments for model validation with systematic uncertainty quantification, and (III) provide a platform for education and workforce development. h-MESO will engage experimental and computational experts in mesoscale mechanics and plasticity, along with mathematicians and computer scientists with expertise in algorithms, data science, machine learning, and large-scale cyberinfrastructure initiatives. 

A path-independent measure in order parameter space is introduced such that, when integrated along any closed contour in a three-dimensional nematic phase, it yields the topological charge of any line defects encircled by the contour. A related measure, when integrated over either closed or open surfaces, reduces to known results for the charge associated with point defects (hedgehogs) or Skyrmions. We further define a tensor density, the disclination density tensor $\mathbf{D}$, from which the location of a disclination line can be determined. This tensor density has a dyadic decomposition near the line into its tangent and its rotation vector, allowing a convenient determination of both. The tensor $\mathbf{D}$may be non-zero in special configurations in which there are no defects (double-splay or double-twist configurations), and its behaviour there is provided. The special cases of Skyrmions and hedgehog defects are also examined, including the computation of their topological charge from $\mathbf{D}$.