Geometric Effects on Stress Wave Propagation

Abstract

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.

Microstructure and mechanical properties of sheep horn

“…The impact surface of the horn sheath is wide and thick seen from the cross section. The tapered and spiral horn sheath can attenuate the shocks to protect the skull and brain from reflection (Johnson et al, ). The inner core is hollow and contains multiple compartments which have the characteristics of lightness and stable mechanical properties.…”

Bioinspired designs for shock absorption, based upon nacre and Bouligand structures

“…But the presence of voids on the side portions allows for some movement. At the same time, the irregular geometry allows for multiple reflection of stress waves within the specimens, similar to the phenomenon observed in the hyoid structure of a woodpecker's head [35]. This is not possible in the reference model, which provides a smooth, straight path for the propagation of any stress waves that are generated during the dynamic impact event.…”

How the geometry and mechanics of bighorn sheep horns mitigate the effects of impact and reduce the head injury criterion

“…It was previously suggested that horn tip oscillations intentionally directed into side-to-side (medial-lateral) motion may be one mechanism of energy dissipation. Additionally, geometry has been shown to affect dynamic wave propagation in other curved structures (Johnson et al, 2014). For example, the woodpecker's curved hyoid bone absorbs impact energy during pecking and has been used for bioinspired design of impact mitigation structures (Lee et al, 2016).…”