Browsing by Author "Higgs, C. Fred III"

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    A finite element model for magnetohydrodynamic squeeze-film flows
    (AIP Publishing LLC, 2018) Wagner, Jordan R.; Higgs, C. Fred III
    A computational model is developed to analyze magnetohydrodynamic (MHD) squeeze-film flows featuring an electrically conducting fluid subjected to imposed magnetic and electric fields. The model is based on the so-called MHD Reynolds equation for squeeze-films—an extension of the classical hydrodynamic Reynolds equation. A complete derivation of the MHD Reynolds equation is performed by applying thin-film and quasi-steady assumptions to the Maxwell/Navier-Stokes system coupled by the Lorentz force. The resulting equation is a two-dimensional and variable-coefficient Poisson equation for pressure, which reduces to the purely hydrodynamic form in the limit of vanishing Hartmann number. A geometric calculus formulation facilitates the reduction of the mathematical system into two dimensions, which is a challenge in standard vector calculus due to the cross product. The model permits realistic geometrical representations of the constraining squeeze-surfaces, and we demonstrate the use of a multi-variate Weierstrass-Mandelbrot fractal to numerically generate scale-invariant surface roughness profiles. Ultimately, the governing equation is solved with the Galerkin finite element method. Several numerical examples are conducted to highlight some of the model’s capabilities. MHD forces—as well as the roughness, geometry, and topology of the squeeze surfaces—are shown to significantly influence flow characteristics.
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    Heterogeneous material mapping methods for patient-specific finite element models of pelvic trabecular bone: A convergence study
    (Elsevier, 2021) Babazadeh Naseri, Ata; Dunbar, Nicholas J.; Baines, Andrew J.; Akin, John E.; Higgs, C. Fred III; Fregly, Benjamin J.
    Patient-specific finite element (FE) models of bone require the assignment of heterogeneous material properties extracted from the subject's computed tomography (CT) images. Though node-based (NB) and element-based (EB) material mapping methods (MMMs) have been proposed, the sensitivity and convergence of FE models to MMM for varying mesh sizes are not well understood. In this work, CT-derived and synthetic bone material data were used to evaluate the effect of MMM on results from FE analyses. Pelvic trabecular bone data was extracted from CT images of six subjects, while synthetic data were created to resemble trabecular bone properties. The numerical convergence of FE bone models using different MMMs were evaluated for strain energy, von-Mises stress, and strain. NB and EB MMMs both demonstrated good convergence regarding total strain energy, with the EB method having a slight edge over the NB. However, at the local level (e.g., maximum stress and strain), FE results were sensitive to the field type, MMM, and the FE mesh size. The EB method exhibited superior performance in finer meshes relative to the voxel size. The NB method converged better than did the EB method for coarser meshes. These findings may lead to higher-fidelity patient-specific FE bone models.
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    Spreading Process Maps for Powder-Bed Additive Manufacturing Derived from Physics Model-Based Machine Learning
    (MDPI, 2019) Desai, Prathamesh S.; Higgs, C. Fred III
    The powder bed additive manufacturing (AM) process is comprised of two repetitive steps—spreading of powder and selective fusing or binding the spread layer. The spreading step consists of a rolling and sliding spreader which imposes a shear flow and normal stress on an AM powder between itself and an additively manufactured substrate. Improper spreading can result in parts with a rough exterior and porous interior. Thus it is necessary to develop predictive capabilities for this spreading step. A rheometry-calibrated model based on the polydispersed discrete element method (DEM) and validated for single layer spreading was applied to study the relationship between spreader speeds and spread layer properties of an industrial grade Ti-6Al-4V powder. The spread layer properties used to quantify spreadability of the AM powder, i.e., the ease with which an AM powder spreads under a set of load conditions, include mass of powder retained in the sampling region after spreading, spread throughput, roughness of the spread layer and porosity of the spread layer. Since the physics-based DEM simulations are computationally expensive, physics model-based machine learning, in the form of a feed forward, back propagation neural network, was employed to interpolate between the highly nonlinear results obtained by running modest numbers of DEM simulations. The minimum accuracy of the trained neural network was 96%. A spreading process map was generated to concisely present the relationship between spreader speeds and spreadability parameters.