Johnson K L, Trim M W, Horstemeyer M F, Lee N, Williams L N, Liao J, Rhee H, Prabhu R
J Biomech Eng. 2014 Feb;136(2):021023. doi: 10.1115/1.4026320.
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.
本研究通过有限元模拟，展示了一种仿生固体对弹性、塑性和粘弹性材料的压力和冲量缓解的几何效应。由于采用了仿生几何形状，应力波的缓解以一种非直观的方式变得明显，从而使人类防护装备设计中的潜在实际应用成为可能。在自然界中，有几种环形设计被用于减轻应力波；例如啄木鸟下颚后部围绕头骨延伸至鼻部的舌骨以及公羊的角。本研究在三维有限元分析中评估了在冲击位置具有相同长度和相同初始横截面直径的四种不同几何形状。几何形状复杂度递增的依次为：（1）圆柱体，（2）一端逐渐变细至一点的圆柱体，（3）在二维平面上呈螺旋状的圆柱体，以及（4）在二维平面上逐渐变细并呈螺旋状的圆柱体。结果表明无论材料类型（弹性、塑性和粘弹性）以及输入压力特征如何，与圆柱体相比，逐渐变细的螺旋状几何形状缓解的压力和冲量最大（约98%的缓解率）。由于单轴变形过程以及因其几何形状产生的诱导剪切，样本的锥度有效地减轻了应力波。由于锥度导致横截面积减小，局部单轴应力和剪应力沿样本长度增加。螺旋形状产生了更大的剪应力，有助于减轻应力波，并且在尖端还引起横向位移，使得波反射最小化。尽管仅将纵波作为初始边界条件引入，但仍出现了这种现象。在自然界中，当材料内部或材料之间发生剪切（摩擦）时，通常会产生耗散，这有助于减轻应力波，本研究中逐渐变细和螺旋状的几何形状就说明了这一点。逐渐变细和螺旋形状的组合在压力和冲量方面优化了应力波的缓解；从而为自然界中发现的公羊角设计和啄木鸟舌骨设计提供了见解。
