Geometric effects on stress wave propagation
AbstractThe 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 realworld 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 crosssectional 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 crosssectional 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. Author(s): K.L. Johnson, M.W. Trim, M.F. Horstemeyer, N. Lee, L.N. Williams, J. Liao, H. Rhee, R. Prabhu 

MethodologyFig. 1 depicts the four geometries that were studied along with the load and prescribed boundary conditions. The total length and crosssectional diameters at the starting end were maintained among the four geometries. The ratio of the large and smallend diameters was also consistent for the tapered geometries. The finite element program ABAQUS/Explicit v6.11 [14], a stress wave dynamics code, was used as the numerical model in this study. To demonstrate material independence, material properties for three different materials were used. The materials are metal (AM30 magnesium denoting a common plastic material), polymer (Polycarbonate denoting a common viscoelastic material), and ceramic (Silicon Carbide (SiC) denoting a common elastic material) were investigated. Postprocessing of data was performed using ABAQUS/CAE v6.11 [14]. Pressure and von Mises contour plots were generated when the wave front was at distance 1/3L, 2/3L, and L. Pressure and displacement response histories were generated at a distance of 0.1 m away from the free end to avoid edge effects. The distance corresponded to a rotation of 180 degrees from the free end on the spiraled geometries. The pressure histories were created by averaging the respective output of each node lying on the crosssection at the specified offset from the free end.  
Material ModelABAQUS/Explicit v6.11: Abaqus/Explicit is a finite element analysis software application that employs explicit integration scheme to solve highly nonlinear transient dynamic and quasistatic analyses. 

Input DataNone 

ResultsFig. 2 show the pressure contour plots for the cylinder, tapered cylinder, spiral, and tapered spiral using AM30 material properties when the wave front is at distance 1/3L, 2/3L, and L. Fig. 2 shows indeed that the tapered cylinder geometry induced greater hydrostatic and shear stresses as the dynamic wave propagated towards the smaller end of the bar. The following conclusions can be made regarding this study:


Acknowledgments
 
ReferencesK. L. Johnson, M. W. Trim, M. F. Horstemeyer, N. Lee, L. N. Williams, J. Liao, H. Rhee, and R. Prabhu, “Geometric Effects on Stress Wave Propagation,” J. Biomech. Eng., vol. 136, no. 2, pp. 021023–021023, Feb. 2014. 