Elastomer Modeling
The elastomer modeling project started in September, 1994, in cooperation with scientists at the Thomas Lord Research Center, Lord Corporation. Lord Corporation, based in Cary, NC, produces many products with rubber--like (elastomer) components. Many of these products are used as vibration control devices, such as engine mounts for buses and airplanes. Thus models which accurately predict the dynamic mechanical behavior of elastomers could be used to aid engineers in the design of components. Many models have been developed which predict the behavior of rubber under static conditions. While these models can do an excellent job of fitting static data for lightly filled (non-hysteretic) samples, they do not include damping or hysteresis terms that are necessary for dynamic models or for highly filled samples. The goal of this project has been to develop more general models that encompass the nonlinear constitutive laws, damping, and hysteresis which are common to elastomers.
Two deformations have been studied thus far: a rod in simple extension, and a block in simple shear. Using nonlinear partial differential equation models for lightly filled (non-hysteretic) materials, good results have been achieved using inverse problem methodoligies with dynamic data to identify material dependent parameters. Integral equations have been developed as a model of hysteresis. Inverse methodologies with quasi-static data for a rod in extension have been used to validate this model. Most recently, hysteresis has been incorporated in the dynamic model, yielding satisfactory results for highly filled elastomers.
This project involves a wide variety of scientific skills. Theoretical results regarding existence and uniqueness of solutions, as well as convergence of approximation schemes, have been developed. Numerical techinques have been used to solve the partial differential equation systems within the paramter identification, which is itself a numerical optimization problem. Finally, engineering methods have been used to develop and perform experiments which will lead to the best results in the identification problem. Project members are: H. T. Banks, Gabriella Pinter and Laura K. Potter of the CRSC, along with Mike Gaitens, and Lynn Yanyo of Lord Corporation.
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