Geometric Effects on Stress Wave Propagation
Johnson, K. L., Trim, W., Williams, L. N., Liao, J., Horstemeyer, M., & Prabhu, R. (2013). Geometric Effects on Stress Wave Propagation. ASME Journal of Biomechanical Engineering. New York, NY: ASME. 2(136), 021023. DOI:10.1115/1.4026320.
Background: The present study, through finite element simulations, shows the geometric effects of a bio-inspired solid on pressure and impulse mitigation for an elastic, plastic, and viscoelastic material. Because of the bio-inspired geometries, shock wave mitigation became apparent in a non-intuitive 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 shock 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. Method: 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. Result: 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 shock 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 shock 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). Conclusions: In nature, when shearing occurs within or between materials (friction), dissipation usually results helping the mitigation of the shock wave and is illustrated in this study with the taper and spiral geometries. The combined taper and spiral optimized shock mitigation in terms of the pressure and impulse, thus providing insight into the ram\'s horn design and woodpecker hyoid designs found in nature. Keywords: guided wave propagation, elastic wave interaction and reflection, finite element analysis, dispersion in waveguides, shock wave mitigation, bio-inspired design, geometric effects.