Modeling of a compact functionally graded cellular structure: a finite element study for medium and high strain rates
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Modeling of a compact functionally graded cellular structure: a finite element study for medium and high strain rates Muhammad Ali • Sun-il Kim • Tessa Matthews
Received: 25 February 2013 / Accepted: 17 October 2013 / Published online: 29 October 2013 Ó Springer Science+Business Media Dordrecht 2013
Abstract The work discussed here is a continuation of study performed previously (Ali et al. in Int J Adv Eng Softw 39:95–106, 2008), in which we presented a detailed analysis of quasi-static and low dynamic response (up to strain rates of 1,200 s-1) for a compact functionally graded cellular structure found in a banana peel. In this paper, we focus on the in-plane response of the graded structure under medium and high velocity impacts (strain rates ranging from 2,400 to 12,416 s-1). A theoretical model developed earlier (Ali et al. in Int J Adv Eng Softw 39:95–106, 2008) for predicting the static, quasi-static, and low dynamic response of the graded structure is modified to take into account high dynamic effects. Different critical energy absorbing characteristics, e.g., deformation modes, collapsing mechanism, crushing stress, locking strain, total energy absorbed, etc. are discussed. The output of the high strain analytical model is
M. Ali (&) Department of Mechanical Engineering, Russ College of Engineering and Technology, Ohio University, Athens, OH, USA e-mail: [email protected] S. Kim University of Alabama Huntsville, Huntsville, AL, USA e-mail: [email protected] T. Matthews United States Patent and Trademark Office (USPTO), Washington, DC, USA e-mail: [email protected]
compared with finite element simulations. The results show that the analytical model aligns well with finite element output for high dynamic cases. Keywords Graded structure Honeycomb Crushing stress Impact Deformation mode Strain rate List of symbols GHS Graded honeycomb structure Y Vertical loading direction m Mass of impacting plate m0 Mass of the crushed portion of GHS A0 Cross-sectional area of GHS C Stress wave speed rsc Quasi-static crushing stress rdc Dynamic crushing stress ry Yield strength of honeycomb cell wall material c Length of horizontal cell wall l Length of inclined cell wall d Honeycomb cell wall thickness b Depth of honeycomb cell wall D Displacement t Time vi Instantaneous velocity Ei Instantaneous energy q Cellular density of GHS qS Density of cell wall material t Poisson’s ratio of cell wall material Young’s modulus E
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Angle of inclined cell walls with normal Densification or locking strain Strain rate
1 Introduction Extensive work has been done in investigating the characteristics of energy absorbing structures and materials. One of the primary characteristics of energy absorbing structures and materials is their ability to convert kinetic energy into a different energy form, most often at the cost of the structure’s permanent deformation. For example, a channel with increasing cross-sectional area along the flow direction converts kinetic energy of fluid into pressure
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