Optimal Blast-Resistant Sandwich Structures with Transversely Isotropic, Elasto-plastic Polymeric Foams as Cores

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Virginia Tech


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.



Plasticity, composites, finite element method, optimization