Professor Bechtel's research activities in the Computer Applications of Mechanics Laboratory include the modeling of industrial manufacturing processes, the characterization of industrial and agricultural materials, and the study of fundamental modeling and computational issues in mechanics.
Professor Bechtel's research program applies the theoretical and mathematical subject of continuum mechanics to various practical problems in science and technology. It brings to bear insightful and powerful mathematical and computational methods upon complex, nonlinear, interdisciplinary manufacturing and material characterization problems.
Prof. Bechtel works with industrial and government laboratory partners to employ modeling of industrial and agricultural processes for the purposes of process optimization and design. He has assisted Hoechst Celanese Corporation by discovering the coupled nonlinear integro-differential equations that govern their fiber manufacturing processes, and then developing and validating computer codes that implement these model equations. He is working with researchers in the US Department of Agriculture (USDA) to measure the material properties of pesticide solutions necessary to understand the process of drop formation, and hence control overspray. His research program is an example of how directed research toward technological problems raises the level of science and identifies open and challenging basic science issues. His research has been published in prestigious journals with a wide range of readerships (e.g. ASME J. Appl. Mech., SIAM J. of Applied Math., J. Fluid Mech., J. Rheology, J. Non-Newtonian Fluid. Mech., Physica D, Atomization and Sprays, Polymer, Textile Research J., J. Colloid Interface Sci.). The work on material characterization performed by his student V. Venkataramanan was selected as one of the three winners of the 1996 SIAM Student Paper Prize in a nationwide contest.
To provide quantitatively accurate predictive capability for such clients as the polymer manufacturing industry and the USDA, it is essential to model a wide range of physical mechanisms, dictated by the industrial process. Prof. Bechtel’s research program incorporates expertise in fluid and solid mechanics, heat transfer, solidification, rheology, interfacial behavior, electro-mechanical continuum dynamics, and computational methods. Prof. Bechtel collaborates with, among others, Kurt Koelling in Chemical Engineering and Glenn Daehn in Material Science and Engineering at Ohio State, Greg Forest in the Department of Mathematics at UNC, Chapel Hill, the above-mentioned researchers with the USDA in Wooster, Ohio, and Prof. Karl Jacob in the School of Textile and Fiber Engineering at Georgia Tech.
As representative work: the modeling of fiber spinning has led to the development of a comprehensive perturbation theory for viscoelastic free surface jets, a thermomechanically constrained theory for materials with temperature-dependent density, thin filament equations which include large transverse temperature gradients, and an analysis of the heat transfer in the multifilament quench arrangements of industrial fiber spinning processes. Prof. Bechtel’s research team has developed thermomechanical analytical boundary-value problems for the modeling of industrial melt-spinning processes. These models fundamentally couple the energy equation to the mass, momentum, and constitutive equations; the analysis is necessarily 3-D (2-D if axisymmetric) due to the radial temperature variation that necessarily is present in the cooling fiber. The problem of filament breaks has been correlated with change-of-type in the governing mathematical equations from hyperbolic to mixed hyperbolic-elliptic.
Prof. Bechtel and Forest have produced five generations of a fully integrated code for the spinning and solidification of polyester filaments, currently being used in production facilities for on-line design and optimization of their fiber spinlines. Profs. Bechtel and Jacob have authored a series of papers modeling industrial multi-stage fiber drawing processes.
As an outgrowth of the work for the USDA, Prof. Bechtel has derived the governing equations for the oscillation of viscoelastic free surface jets, and has developed an analysis which inverts these equations to produce dynamic surface tension values and elongational viscosities from jet measurements, in the millisecond time scales necessary for understanding drop formation. In research modeling electromagnetic discharge metal forming work, he has developed a large-deformation, high strain rate theory for electro-magnetic-mechanical continua.
Jointly with Prof. Koelling, Prof. Bechtel has developed and constructed an apparatus which provides state-of-the-art resolution in the on-line measurement of the free surface profile and axial force exiting the die during formation of a liquid filament. The high resolution enables them to accurately compute spatial derivatives through two orders, leading to powerful new inverse techniques for material characterization. In the inverse problem for material characterization of elongational response, the inputs are the free surface and force measurements provided by the rheometer, the flow conditions, and an analytical model for the free surface flow, and the outputs are the constitutive equation for the test fluid, and its surface tension.
RESEARCH AWARDS
1998 Best Proposal Award (with K. Jacob and D. Salem), Materials Division of the National Textile Center, for "Draw-Induced Morphology Development and Fiber Architecture"
2000 College of Engineering Lumley Research Award, The Ohio State University