Research Papers

Improvement of Stiffness and Energy Absorption by Harnessing Hierarchical Interlocking in Brittle Polymer Blocks

[+] Author and Article Information
Muhammed Imam

Department of Mechanical Engineering-Engineering Mechanics,
Michigan Technological University
Houghton, MI 49931
e-mail: mimam@mtu.edu

Julien Meaud

G.W.W. School of Mechanical Engineering,
Georgia Institute of Technology,
Atlanta, GA 30332
e-mail: julien.meaud@me.gatech.edu

Susanta Ghosh

Department of Mechanical Engineering-Engineering Mechanics,
Michigan Technological University,
Houghton, MI 49931
e-mail: susantag@mtu.edu

Trisha Sain

Department of Mechanical Engineering-Engineering Mechanics,
Michigan Technological University,
Houghton, MI 49931
e-mail: tsain@mtu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received October 5, 2018; final manuscript received January 4, 2019; published online March 5, 2019. Assoc. Editor: Junlan Wang.

J. Appl. Mech 86(5), 051007 (Mar 05, 2019) (11 pages) Paper No: JAM-18-1557; doi: 10.1115/1.4042567 History: Received October 05, 2018; Accepted January 04, 2019

The objective of the present work is to investigate the possibility of improving both stiffness and energy absorption in interlocking, architectured, brittle polymer blocks through hierarchical design. The interlocking mechanism allows load transfer between two different material blocks by means of contact at the mating surfaces. The contacting surfaces further act as weak interfaces that allow the polymer blocks to fail gradually under different loading conditions. Such controlled failure enhances the energy absorption of the polymer blocks but with a penalty in stiffness. Incorporating hierarchy in the form of another degree of interlocking at the weak interfaces improves stress transfer between contacting material blocks; thereby, improvement in terms of stiffness and energy absorption can be achieved. In the present work, the effects of hierarchy on the mechanical responses of a single interlocking geometry have been investigated systematically using finite element analysis (FEA) and results are validated with experiments. From finite element (FE) predictions and experiments, presence of two competing failure mechanisms have been observed in the interlock: the pullout of the interlock and brittle fracture of the polymer blocks. It is observed that the hierarchical interface improves the stiffness by restricting sliding between the contacting surfaces. However, such restriction can lead to premature fracture of the polymer blocks that eventually reduces energy absorption of the interlocking mechanism during pullout deformation. It is concluded that the combination of stiffness and energy absorption is optimal when fracture of the polymer blocks is delayed by allowing sufficient sliding at the interfaces.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Barthelat, F., 2015, “Architectured Materials in Engineering and Biology: Fabrication, Structure, Mechanics and Performance,” Int. Mater. Rev., 60(8), pp. 413–430. [CrossRef]
Ashby, M. F., 2005, “Hybrids to Fill Holes in Material Property Space,” Philos. Mag., 85(26–27), pp. 3235–3257. [CrossRef]
Ashby, M., and Bréchet, Y., 2003, “Designing Hybrid Materials,” Acta Mater., 51(19), pp. 5801–5821. [CrossRef]
Gibson, L. J., and Ashby, M. F., 1999, Cellular Solids: Structure and Properties, Cambridge University Press, Cambridge.
Zheng, X., Lee, H., Weisgraber, T. H., Shusteff, M., DeOtte, J., Duoss, E. B., Kuntz, J. D., Biener, M. M., Ge, Q., Jackson, J. A., Kucheyev, S. O., Fang, N. X., and Spadaccini, C. M., 2014, “Ultralight, Ultrastiff Mechanical Metamaterials,” Science, 344(6190), pp. 1373–1377. [CrossRef] [PubMed]
Li, M.-Z., Stephani, G., and Kang, K.-J., 2011, “New Cellular Metals With Enhanced Energy Absorption: Wire-Woven Bulk Kagome (wbk)-Metal Hollow Sphere (mhs) Hybrids,” Adv. Eng. Mater., 13(1–2), pp. 33–37. [CrossRef]
Bückmann, T., Stenger, N., Kadic, M., Kaschke, J., Frölich, A., Kennerknecht, T., Eberl, C., Thiel, M., and Wegener, M., 2012, “Tailored 3d Mechanical Metamaterials Made by Dip-in Direct-Laser-Writing Optical Lithography,” Adv. Mater., 24(20), pp. 2710–2714. [CrossRef] [PubMed]
Martin, A., Kadic, M., Schittny, R., Bückmann, T., and Wegener, M., 2012, “Phonon Band Structures of Three-Dimensional Pentamode Metamaterials,” Phys. Rev. B: Condens. Matter Mater. Phys., 86(15), p. 155116. [CrossRef]
Bertoldi, K., Reis, P. M., Willshaw, S., and Mullin, T., 2010, “Negative Poisson’s Ratio Behavior Induced by an Elastic Instability,” Adv. Mater., 22(3), pp. 361–366. [CrossRef] [PubMed]
Li, D., Ma, J., Dong, L., and Lakes, R. S., 2017, “Three-Dimensional Stiff Cellular Structures With Negative Poisson’s Ratio,” Phys. Status Solidi B, 254(12), 1600785. [CrossRef]
Valdevit, L., Pantano, A., Stone, H. A., and Evans, A. G., 2006, “Optimal Active Cooling Performance of Metallic Sandwich Panels With Prismatic Cores,” Int. J. Heat Mass Transf., 49(21–22), pp. 3819–3830. [CrossRef]
Valentin, J. E., Badylak, J. S., McCabe, G. P., and Badylak, S. F., 2006, “Extracellular Matrix Bioscaffolds for Orthopaedic Applications: A Comparative Histologic Study,” J. Bone Joint Surg. Am., 88(12), pp. 2673–2686. [CrossRef] [PubMed]
Bai, H., Walsh, F., Gludovatz, B., Delattre, B., Huang, C., Chen, Y., Tomsia, A. P., and Ritchie, R. O., 2016, “Bioinspired Hydroxyapatite/Poly (Methyl Methacrylate) Composite With a Nacre-Mimetic Architecture by a Bidirectional Freezing Method,” Adv. Mater., 28(1), pp. 50–56. [CrossRef] [PubMed]
Launey, M. E., Munch, E., Alsem, D. H., Saiz, E., Tomsia, A. P., and R. O. Ritchie, 2009, “A Novel Biomimetic Approach to the Design of High-Performance Ceramic–Metal Composites,” J. R. Soc. Interface, 7(46), rsif20090331.
Mirkhalaf, M., Dastjerdi, A. K., and Barthelat, F., 2014, “Overcoming the Brittleness of Glass Through Bio-Inspiration and Micro-Architecture,” Nat. Commun., 5, pp. 3166. [CrossRef] [PubMed]
Chen, L., Ballarini, R., Kahn, H., and Heuer, A., 2007, “Bioinspired Micro-Composite Structure,” J. Mater. Res., 22(1), pp. 124–131. [CrossRef]
Dimas, L. S., Bratzel, G. H., Eylon, I., and Buehler, M. J., 2013, “Tough Composites Inspired by Mineralized Natural Materials: Computation, 3D Printing, and Testing,” Adv. Funct. Mater., 23(36), pp. 4629–4638. [CrossRef]
Valadez-Gonzalez, A., Cervantes-Uc, J., Olayo, R., and Herrera-Franco, P., 1999, “Effect of Fiber Surface Treatment on the Fiber–Matrix Bond Strength of Natural Fiber Reinforced Composites,” Compos. Part B, 30(3), pp. 309–320. [CrossRef]
Anand, K., and Ramamurthy, K., 2000, “Development and Performance Evaluation of Interlocking-Block Masonry,” J. Arch. Eng., 6(2), pp. 45–51. [CrossRef]
Corbett, M., Sharos, P. A., Hardiman, M., and McCarthy, C. T., 2017, “Numerical Design and Multi-Objective Optimisation of Novel Adhesively Bonded Joints Employing Interlocking Surface Morphology,” Int. J. Adhes. Adhes., 78, pp. 111–120. [CrossRef]
Allen, E. G., 2007, “Understanding Ammonoid Sutures: New Insight Into the Dynamic Evolution of Paleozoic Suture Morpholog,” Cephalopods Present and Past: New Insights and Fresh Perspectives, Springer, Dordrecht, pp. 159–180.
Achrai, B., and Wagner, H. D., 2013, “Micro-Structure and Mechanical Properties of the Turtle Carapace as a Biological Composite Shield,” Acta Biomater., 9(4), pp. 5890–5902. [CrossRef] [PubMed]
Song, J., Reichert, S., Kallai, I., Gazit, D., Wund, M., Boyce, M. C., and Ortiz, C., 2010, “Quantitative Microstructural Studies of the Armor of the Marine Threespine Stickleback (Gasterosteus aculeatus),” J. Struct. Biol., 171(3), pp. 318–331. [CrossRef] [PubMed]
Malik, I., Mirkhalaf, M., and Barthelat, F., 2017, “Bio-Inspired “jigsaw-like” Interlocking Sutures: Modeling, Optimization, 3D Printing and Testing,” J. Mech. Phys. Solids, 102, pp. 224–238. [CrossRef]
Malik, I. A., and Barthelat, F., 2018, “Bioinspired Sutured Materials for Strength and Toughness: Pullout Mechanisms and Geometric Enrichments,” Int. J. Solids Struct., 138, pp. 118–133. [CrossRef]
Mirkhalaf, M., and Barthelat, F., 2017, “Design, 3d Printing and Testing of Architectured Materials With Bistable Interlocks,” Extreme Mech. Lett., 11, pp. 1–7. [CrossRef]
Mirkhalaf, M., Zhou, T., and Barthelat, F., 2018, “Simultaneous Improvements of Strength and Toughness in Topologically Interlocked Ceramics,” Proc. Natl. Acad. Sci. U.S.A., 15, pp. 9128–9133. [CrossRef]
Dyskin, A. V., Estrin, Y., Kanel-Belov, A. J., and Pasternak, E., 2003, “Topological Interlocking of Platonic Solids: A Way to New Materials and Structures,” Philos. Mag. Lett., 83(3), pp. 197–203. [CrossRef]
Khandelwal, S., Siegmund, T., Cipra, R., and Bolton, J., 2012, “Transverse Loading of Cellular Topologically Interlocked Materials,” Int. J. Solids Struct., 49(18), pp. 2394–2403. [CrossRef]
Wegst, U. G., Bai, H., Saiz, E., Tomsia, A. P., and Ritchie, R. O., 2015, “Bioinspired Structural Materials,” Nat. Mater. 14(1), pp. 23–36. [CrossRef] [PubMed]
Mueller, J., Raney, J. R., Shea, K., and Lewis, J. A., 2018, “Architected Lattices With High Stiffness and Toughness Via Multicore–Shell 3D Printing,” Adv. Mater., 30(12), 1705001. [CrossRef]
Li, T., Chen, Y., and Wang, L., 2018, “Enhanced Fracture Toughness in Architected Interpenetrating Phase Composites by 3D Printing,” Compos. Sci. Technol., 67, pp. 251–259. [CrossRef]
Zhang, Z., Zhang, Y.-W., and Gao, H., 2010, “On Optimal Hierarchy of Load-Bearing Biological Materials,” Proc. R. Soc. Lond. B: Biol. Sci., 278(1705), rspb20101093.
Thorpe, C. T., and Screen, H. R., 2016, “Tendon Structure and Composition,” Metabolic Influences on Risk for Tendon Disorders, Springer, Cham, pp. 3–10.
Yao, H., and Gao, H., 2006, “Mechanics of Robust and Releasable Adhesion in Biology: Bottom–Up Designed Hierarchical Structures of Gecko,” J. Mech. Phys. Solids, 54(6), pp. 1120–1146. [CrossRef]
Li, Y., Ortiz, C., and Boyce, M. C., 2011, “Stiffness and Strength of Suture Joints in Nature,” Phys. Rev. E: Stat. Nonlinear Soft Matter Phys., 84(6), 062904. [CrossRef]
Lin, E., Li, Y., Weaver, J. C., Ortiz, C., and Boyce, M. C., 2014, “Tunability and Enhancement of Mechanical Behavior With Additively Manufactured Bio-Inspired Hierarchical Suture Interfaces,” J. Mater. Res., 29(17), pp. 1867–1875. [CrossRef]
Liu, L., Jiang, Y., Boyce, M., Ortiz, C., Baur, J., Song, J., and Li, Y., 2017, “The Effects of Morphological Irregularity on the Mechanical Behavior of Interdigitated Biological Sutures Under Tension,” J. Biomech., 58, pp. 71–78. [CrossRef] [PubMed]
Dassault Systèmes, 2017, “Abaqus/Explicit,” Research License.
Hooputra, H., Gese, H., Dell, H., and Werner, H., 2004, “A Comprehensive Failure Model for Crashworthiness Simulation of Aluminium Extrusions,” Int. J. Crashworthiness, 9(5), pp. 449–464. [CrossRef]
Dorogoy, A., Rittel, D., and Brill, A., 2010, “A Study of Inclined Impact in Polymethylmethacrylate Plates,” Int. J. Impact Eng., 37(3), pp. 285–294. [CrossRef]
Stansbury, J. W., and Idacavage, M. J., 2016, “3d Printing With Polymers: Challenges Among Expanding Options and Opportunities,” Dent. Mater., 32(1), pp. 54–64. [CrossRef] [PubMed]
Wong, K. V., and Hernandez, A., 2012, “A Review of Additive Manufacturing,” ISRN Mech. Eng., 2012, pp. 1–10. [CrossRef]


Grahic Jump Location
Fig. 1

Overview of the design of interlocking tabs; schematic representation of a single interlocking tab containing (a) one level of hierarchy and (b) two levels of hierarchy (zooming the top part only)

Grahic Jump Location
Fig. 2

(a) A typical finite element mesh for N = 1 hierarchy (θ = 35 deg and D0/W = 0.50) and (b) zoomed view of the interlock

Grahic Jump Location
Fig. 3

Uniaxial tensile testing on the 3D printed specimens

Grahic Jump Location
Fig. 4

Normalized force–displacement curves of one level of hierarchy specimens (35 deg interlock): experiments and FEA results

Grahic Jump Location
Fig. 5

(a) Pullout response prediction using FEA, (b) pullout response from experiment, (c) normalized stiffness comparison between FEA and experiment, (d) energy absorption comparison between FEA and experiment, considering interlocking angle as a variable. Error bars represent the range of the experimental measurements. (e) Comparison between FEA and experiment when θ = 30 deg.

Grahic Jump Location
Fig. 6

Von Mises stress (MPa) plot: (a) at effective strain 0.27 for θ = 25 deg, (b) at effective strain 0.21 for θ = 30 deg, showing the failure of the interlock. (c) Equivalent plastic strain at effective strain 0.21 for θ = 30 deg, before the failure of the interlock.

Grahic Jump Location
Fig. 7

One level of hierarchical specimen (θ = 30 deg) demonstrating brittle fracture

Grahic Jump Location
Fig. 8

(a) Pullout curves from FEA, (b) pullout curves from experiments, (c) normalized stiffness comparison between FEA and experiment, (d) energy absorption comparison between FEA and experiment, considering relative width as a variable. Error bars represent the range of the experimental measurements. (e) Comparison between FEA and experiment for D0/W = 0.33.

Grahic Jump Location
Fig. 9

X directional strain (LE11) plot for θ = 30 deg and D0/W = (a) 0.33, (b) 0.50, and (c) 0.87

Grahic Jump Location
Fig. 10

Effects of w1/D1 on (a) pullout response, (b) energy absorption versus normalized stiffness map (FEM results)

Grahic Jump Location
Fig. 11

Von Mises stress (MPa) plot at global strain (a) 0.10, (b) 0.11, and (c) 0.14

Grahic Jump Location
Fig. 12

Effects of D1/D0 on (a) pullout response and (b) energy absorption versus normalized stiffness map (FEM results)

Grahic Jump Location
Fig. 13

(a) Effects of w2/D0 on pullout response and (b) energy absorption versus normalized stiffness map (FEM results)

Grahic Jump Location
Fig. 14

(a) Virgin and fractured N = 2 hierarchical specimen. (b) Experimental pullout curves for N = 2 hierarchical specimen. Comparison between N = 1 and N = 2 in terms of (c) stiffness and (d) energy absorption. Error bars represent SD of the experimental measurements. (e) Energy absorption versus normalized stiffness plot to show the comparison between FE and experiment.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In