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Research Papers

Geometric Effects on Stress Wave Propagation

[+] Author and Article Information
K. L. Johnson, M. F. Horstemeyer

Department of Mechanical Engineering,
Center for Advanced Vehicular Systems (CAVS),
Mississippi State University,
Mississippi State, MS 39762

M. W. Trim

Naval Surface Warfare Center,
9500 MacArthur Blvd,
Bethesda, MD 20817

N. Lee

Center for Advanced Vehicular Systems (CAVS),
200 Research Blvd,
Mississippi State, MS 39762;
Agriculture and Biological Engineering,
Mississippi State University,
Mississippi State, MS 39762

L. N. Williams, J. Liao

Agriculture and Biological Engineering,
Mississippi State University,
Mississippi State, MS 39762

H. Rhee

Center for Advanced Vehicular Systems (CAVS),
200 Research Blvd,
Mississippi State, MS 39762

R. Prabhu

Center for Advanced Vehicular Systems (CAVS),
Agriculture and Biological Engineering,
200 Research Blvd,
Mississippi State, MS 39762

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received September 5, 2013; final manuscript received December 13, 2013; accepted manuscript posted December 24, 2013; published online February 5, 2014. Editor: Beth Winkelstein.

J Biomech Eng 136(2), 021023 (Feb 05, 2014) (12 pages) Paper No: BIO-13-1412; doi: 10.1115/1.4026320 History: Received September 05, 2013; Revised December 13, 2013; Accepted December 24, 2013

The present study, through finite element simulations, shows the geometric effects of a bioinspired solid on pressure and impulse mitigation for an elastic, plastic, and viscoelastic material. Because of the bioinspired geometries, stress wave mitigation became apparent in a nonintuitive manner such that potential real-world applications in human protective gear designs are realizable. In nature, there are several toroidal designs that are employed for mitigating stress waves; examples include the hyoid bone on the back of a woodpecker's jaw that extends around the skull to its nose and a ram's horn. This study evaluates four different geometries with the same length and same initial cross-sectional diameter at the impact location in three-dimensional finite element analyses. The geometries in increasing complexity were the following: (1) a round cylinder, (2) a round cylinder that was tapered to a point, (3) a round cylinder that was spiraled in a two dimensional plane, and (4) a round cylinder that was tapered and spiraled in a two-dimensional plane. The results show that the tapered spiral geometry mitigated the greatest amount of pressure and impulse (approximately 98% mitigation) when compared to the cylinder regardless of material type (elastic, plastic, and viscoelastic) and regardless of input pressure signature. The specimen taper effectively mitigated the stress wave as a result of uniaxial deformational processes and an induced shear that arose from its geometry. Due to the decreasing cross-sectional area arising from the taper, the local uniaxial and shear stresses increased along the specimen length. The spiral induced even greater shear stresses that help mitigate the stress wave and also induced transverse displacements at the tip such that minimal wave reflections occurred. This phenomenon arose although only longitudinal waves were introduced as the initial boundary condition (BC). In nature, when shearing occurs within or between materials (friction), dissipation usually results helping the mitigation of the stress wave and is illustrated in this study with the taper and spiral geometries. The combined taper and spiral optimized stress wave mitigation in terms of the pressure and impulse; thus providing insight into the ram's horn design and woodpecker hyoid designs found in nature.

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References

Figures

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Fig. 5

Pressure contour plots in silicon carbide

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Fig. 4

Pressure contour plots in polycarbonate

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Fig. 3

Pressure contour plots in AM30

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Fig. 2

Fixed end loading conditions under (a) increasing ramped pressure pulse, (b) decreasing ramped pressure pulse, (c) step pressure pulse, (d) consecutive increasing and decreasing pressure pulse. The peak amplitude was set as 130 MPa. Loading times vary to ensure consistent impulse is applied to the free end.

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Fig. 1

Schematic representation of the four finite element meshes illustrating the four different geometric configurations with the same length (and the same bar diameter where the pressure was applied) used in the analysis

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Fig. 6

Von Mises contour plots in AM30

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Fig. 7

Von Mises contour plots in polycarbonate

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Fig. 8

Von Mises contour plots in silicon carbide

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Fig. 9

Maximum shear stress in AM30 under (a) increasing ramped pressure pulse, (b) decreasing ramped pressure pulse, (c) step pressure pulse, (d) consecutive increasing and decreasing pressure pulse

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Fig. 10

Maximum shear stress in polycarbonate under (a) increasing ramped pressure pulse, (b) decreasing ramped pressure pulse, (c) step pressure pulse, (d) consecutive increasing and decreasing pressure pulse

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Fig. 11

Maximum shear stress in SiC under (a) increasing ramped pressure pulse, (b) decreasing ramped pressure pulse, (c) step pressure pulse, (d) consecutive increasing and decreasing pressure pulse

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Fig. 12

Free-end transverse displacement response and in AM30 under (a) increasing ramped pressure pulse, (b) decreasing ramped pressure pulse, (c) step pressure pulse, (d) consecutive increasing and decreasing pressure pulse

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Fig. 13

Free-end transverse displacement response and in polycarbonate under (a) increasing ramped pressure pulse, (b) decreasing ramped pressure pulse, (c) step pressure pulse, (d) consecutive increasing and decreasing pressure pulse

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Fig. 14

Free-end transverse displacement response and in silicon carbide under (a) increasing ramped pressure pulse, (b) decreasing ramped pressure pulse, (c) step pressure pulse, (d) consecutive increasing and decreasing pressure pulse

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Fig. 18

Normalized strain energy at loading location (Initial) and 0.1 m from free end (Final) under (a) increasing ramped pressure pulse, (b) decreasing ramped pressure pulse, (c) step pressure pulse, (d) consecutive increasing and decreasing pressure pulse

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Fig. 19

Normalized impulse in AM30 under consecutive increasing and decreasing pressure pulse with average mesh sizes of (a) 9509 and (b) 3816 elements

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Fig. 15

Normalized impulse in AM30 under (a) increasing ramped pressure pulse, (b) decreasing ramped pressure pulse, (c) step pressure pulse, (d) consecutive increasing and decreasing pressure pulse

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Fig. 16

Normalized impulse in polycarbonate under (a) increasing ramped pressure pulse, (b) decreasing ramped pressure pulse, (c) step pressure pulse, (d) consecutive increasing and decreasing pressure pulse

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Fig. 17

Normalized impulse in SiC under (a) increasing ramped pressure pulse, (b) decreasing ramped pressure pulse, (c) step pressure pulse, (d) consecutive increasing and decreasing pressure pulse

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