Polymeric foam cores are widely used as core materials in sandwich panels subject to blast loads, where high strain rates of the order of 4000 /s are observed. Unlike metallic foams polymeric foams exhibit transversely isotropic response when tested in a laboratory setting. More specifically, they exhibit different hardening along the foam thickness than that in a direction transverse to the thickness. Furthermore, polymeric foams harden differently in tension and compression. In this thesis we adopt ideas from the constitutive model developed by Hoo Fatt et al. cite{hoofatt2}, which captures strain hardening, transverse isotropy and distinguishes the response in tension and in compression, to include isotropic strain rate hardening in our constitutive model. A one dimensional prototype of the model is used to aid in the physical explanation of various variables, and the model is generalized to three dimensions. The material model is implemented as a VUMAT (user defined) subroutine in the commercial finite element software ABAQUS Explicit. We show that the model works robustly in uniaxial deformations as well as in sandwich problems using the test data available in the literature. We provide values of the 39 material parameters for H45, H60, H80, H100, H130 and H200 foams. The constitutive relation is utilized in an optimization problem in which the surrogate optimizer is utilized to minimize the backface deflection of a blast loaded clamped sandwich plate of a fixed mass. The core in the optimized sandwich structure has a stratified configuration (not functionally graded) and has 24% less maximum back face deflection as compared to that in which the six core layers vary from highest density to lowest density or vice a versa. For a sandwich panel subject to a blast load, when the strain rate hardening effect are neglected, we observed a 12% reduction in the predicted peak deflection from that when strain rate effects are considered. It is counter intuitive and needs further investigation. / Master of Science / Sandwich panels are widely used in high performance structures requiring high stiffness, low weight and the ability to withstand blasts. Sandwich panels consist of several layers, and it is possible to vary the material and thickness of each layer to arrive at a sandwich panel design which performs optimally. In this thesis, we numerically find an optimum sandwich panel design so that it deflects the least when exposed to a given blast. The problem is studied using ABAQUS Explicit and the Surrogate Optimization solver built into MATLAB. The outer layers of the sandwich panel are made of a highly stiff material and their thicknesses are fixed. The remaining six inner layers are allowed to be any of six different H45, H60, H80, H100, H130, H200 Divinycell polymeric foams and are allowed to vary in thickness. In order to draw a fair comparison between the designs, we constrain the total mass of the sandwich panel to be 1 kg. In our quest to find the best sandwich panel design, we develop and implement, in ABAQUS Explicit, a custom mathematical model which captures the complex behavior of the polymeric foams. Experimental data in the literature and other techniques were utilized to check that this mathematical model accurately predicts the physical response of polymeric foams in different scenarios. The reader is given all of the theory and physical constants needed to use this mathematical model for the six foams. The optimal sandwich panel deflects 24% less than a baseline design, and it is found that the material properties of the six foams do not vary gradually as they did in the baseline designs.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/113534 |
| Date | 26 January 2023 |
| Creators | Kim, Dong Ho |
| Contributors | Engineering Science and Mechanics, Batra, Romesh C., Stremler, Mark A., Domann, John P. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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