Analytical and Numerical Investigation of Energy Absorption in Graded Aluminum Open Cell Foam under Low Velocity Impact Loading

Subject Areas : Mechanics of Solids

S Davari ¹ , Seyed Ali Galehdari ² , Amir Atrian ³

1 - Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2 -
3 -

Received: 2023-05-25 Accepted : 2023-08-27 Published : 2024-09-21

Keywords: Open cell foam, Optimization, Specific energy absorption, Low velocity impact, Graded structure,

Abstract :

Given the significance of energy absorption in various industries, light shock absorbers such as structures made of metal foam have been considered. In this study, analytical equation of plateau stress is presented for an open cell foam based on the Gibson-Ashby model, which follows elastic perfectly plastic behavior. For comparison of acquired analytical equations, the problem for a cell and then for three cells that make up an aluminum open cell foam is simulated in ABAQUS/CAE. Using the stress strain diagram, plateau stress and densification strain equations, the specific energy absorbed of the open cell metal foam is extracted. The capacity of absorb energy for an aluminum open cell foam with three cell is obtained once using analytical equations and again by using numerical simulation in ABAQUS/CAE. Numerical results retain an acceptable accordance with analytical equations with less than 3% occurred error for absorbed energy. To ensure the accuracy of numerical simulation, the results of simulating are compared with the results of the simulation of the same foam in a reference whose accuracy is verified by the experiment. Based on the results, the effective cross-sectional area of the foam with Gibson-Ashby cell does not follow the cross-sectional that is used for the calculation of plateau stress in adsorbent structures. Then tow equations are extracted to calculate the effective cross-sectional area and the transfer force. Applying sequential quadratic programming method (SQP) and genetic algorithm (GA), to design a graded metal foam with high specific Energy absorption.

References:

S. A. Galehdari, "Analytical, experimental and numerical study of a graded honeycomb structure under in-plane impact," International Journal of Crashworthiness, vol. 20, pp. 1-15, 2015.
[2] L. Gibson, "Biomechanics of cellular solids," Journal of Biomechanics, vol. 38, pp. 372-378, 2004.
[3] L. J. Gibson, "Cellular Solids," Elmsford: Pergmon Press, pp. 175-231, 1988.
[4] Q. Sawei, "Research Progress on Simulation Modeling of Metal Foams," Rare Metal Materials and Engineering, pp. 2670-2676, 2015.
[5] R. Stone, "Strength and Stiffness of Cellular Foamed Materials," The University of Arizona, pp. 82-93, 1997.
[6] K. Kremer, "Metal Foams for Improved Crash Energy Absorption in Passengers Equipment," Center for Manufacturing and Advanced Materials, pp. 1-31, 2004.
[7] P.K.Pinnoji, "Impact dynamics of metal foam shells for motorcycle helmets: Experiments & numerical modeling," International Journal of Impact Engineering, vol. 37, no. 3, pp. 274-284, 2009.
[8] P. Moreira, "Numerical Simulation of Impact Loading on Open-Cell Aluminum Foams," Mechanisms and Machine Science, 2014.
[9] C. Li, "Compressive behavior and energy absorption capacity of unconstrained and constrained open-cell aluminum foams," Advanced Composites, vol. 29, pp. 1-4, 2020.
[10] J. Ramírez, "Numerical modeling and simulation of uniaxial ompression of aluminum foams using FEM and 3D-CT images," Procedia Materials Science, pp. 227-231, 2014.
[11] M. A. Hasan, "An Improved Model for FE Modeling and Simulation of Closed Cell Al-Alloy Foams," Advances in Materials Science and Engineering,, pp. 1-12, 2010.
[12] V. Goga, " Phenomenological Material Model of Foam Solids," Journal of Echanical Engineering, pp. 1-11, 2016.
[13] J. Bin, "Effect of pore size and relative density on the mechanical properties of open cell aluminum foams," Scripta Materialia, pp. 169-172, 2007.
[14] S. Kaoua, "Numerical modelling of open-cell metal foam with Kelvin cell," Computational & Applied Mathematics, vol. 35, no. 3, pp. 977-985, 2016.
[15] F. Branca, "Modeling of the Mechanical Behavior of Metallic Foams: Damage Effects at Finite Strains," Mechanics of Advanced Materials and Structures, vol. 16, no. 2, pp. 110-119, 2009.
[16] S. Lopatnikov, "High-velocity plate impact of metal foams," International Journal of Impact Engineering, vol. 30, no. 4, pp. 421-445, 2004.
[17] T. Mukai, "Dynamic Compressive Behavior of An Ultralightweight Magnesium Foam," Scripta Materialia, vol. 41, no. 4, pp. 365-371, 1999.
[18] W. Zhihua, "Effect of Cell Size on the Dynamic Compressive Properties of Aluminum Alloy Foams," Transactions of Nonferrous Metals Society of China, vol. 16, no. 2, pp. 351-356, 2006.
[19] S. Davari, "Design and Analysis of Graded Open-cell Aluminum Foam Shock Absorber for Helicopter Seats During Emergency Landing Conditions," Journal of Stress Analysis, vol. 4, pp. 1-11, 2020.
[20] B. H. M. Ashby , 2000. , "Metal Foams: A Design Guide," Boston: Hutterworth, pp. 1-50, 2000.
[21] J. Hughes, "Metallic Materials Properties Development and Standardization (MMPDS)," Federal Aviation Administration, pp. 258-293, 2003.
[22] S. A. Galehdari, "Design and analysis of a graded honeycomb shock absorber for a helicopter seat during a crash condition," Journal of Crashworthiness, vol. 21, pp. 231-241, 2016.
[23] "https://bioaktive-kollagenpeptide.de/wirkungen-knochen," pp. 44-53, 2018.