Biomechanical Engineering Analysis and Research, Inc., Thousand Oaks, California 91362, USA.
Traffic Inj Prev. 2013;14(7):718-24. doi: 10.1080/15389588.2012.751489.
The objective of this study was a thorough reconsideration, within the framework of Newtonian mechanics and work-energy relationships, of the empirically interpreted relationships employed within the CRASH3 damage analysis algorithm in regards to linearity between barrier equivalent velocity (BEV) or peak collision force magnitude and residual damage depth.
The CRASH3 damage analysis algorithm was considered, first in terms of the cases of collisions that produced no residual damage, in order to properly explain the damage onset speed and crush resistance terms. Under the modeling constraints of the collision partners representing a closed system and the a priori assumption of linearity between BEV or peak collision force magnitude and residual damage depth, the equations for the sole realistic model were derived.
Evaluation of the work-energy relationships for collisions at or below the elastic limit revealed that the BEV or peak collision force magnitude relationships are bifurcated based upon the residual damage depth. Rather than being additive terms from the linear curve fits employed in the CRASH3 damage analysis algorithm, the Campbell b 0 and CRASH3 AL terms represent the maximum values that can be ascribed to the BEV or peak collision force magnitude, respectively, for collisions that produce zero residual damage. Collisions resulting in the production of non-zero residual damage depth already account for the surpassing of the elastic limit during closure and therefore the secondary addition of the elastic limit terms represents a double accounting of the same. This evaluation shows that the current energy absorbed formulation utilized in the CRASH3 damage analysis algorithm extraneously includes terms associated with the A and G stiffness coefficients. This sole realistic model, however, is limited, secondary to reducing the coefficient of restitution to a constant value for all cases in which the residual damage depth is nonzero.
Linearity between BEV or peak collision force magnitude and residual damage depth may be applicable for particular ranges of residual damage depth for any given region of any given vehicle. Within the modeling construct employed by the CRASH3 damage algorithm, the case of uniform and ubiquitous linearity cannot be supported. Considerations regarding the inclusion of internal work recovered and restitution for modeling the separation phase change in velocity magnitude should account for not only the effects present during the evaluation of a vehicle-to-vehicle collision of interest but also to the approach taken for modeling the force-deflection response for each collision partner.
本研究旨在从牛顿力学和功-能关系的角度，对 CRASH3 损伤分析算法中所使用的经验解释关系进行彻底的重新考虑，这些关系涉及到线性关系，即屏障等效速度（BEV）或碰撞力峰值与残余损伤深度之间的关系。
首先，考虑了 CRASH3 损伤分析算法的情况，即没有产生残余损伤的碰撞情况，以便正确解释损伤起始速度和抗压强度项。在碰撞伙伴代表一个封闭系统的建模约束和 BEV 或碰撞力峰值与残余损伤深度之间的线性关系的先验假设下，推导出了唯一现实模型的方程。
对低于弹性极限的碰撞的功-能关系的评估表明，BEV 或碰撞力峰值的关系基于残余损伤深度而分叉。在 CRASH3 损伤分析算法中使用的线性曲线拟合的附加项，而不是 Campbell b0 和 CRASH3 AL 项分别代表了对于产生零残余损伤的碰撞，BEV 或碰撞力峰值的最大可归因值。已经导致产生非零残余损伤深度的碰撞已经在闭合过程中超过了弹性极限，因此，弹性极限项的二次添加代表了相同的双重计算。这种评估表明，当前在 CRASH3 损伤分析算法中使用的能量吸收公式多余地包括与 A 和 G 刚度系数相关的项。然而，这种唯一的现实模型是有限的，其次是将恢复系数降低到所有残余损伤深度非零的情况下的恒定值。
BEV 或碰撞力峰值与残余损伤深度之间的线性关系可能适用于任何给定车辆的任何给定区域的特定残余损伤深度范围。在 CRASH3 损伤算法所采用的建模结构中，不能支持均匀和普遍的线性关系的情况。考虑包括内部功恢复和恢复来模拟速度量级的分离阶段变化，不仅应考虑到在评估感兴趣的车辆对车辆碰撞时的影响，而且还应考虑到为每个碰撞伙伴建模力-变形响应所采用的方法。
