Abstract The response characteristics of large-scale structures subjected to impact loading can in principle be determined by scaled experiments. Unfortunately, scaling suffers from scale effects and for impact mechanics, the non-scalability of strain rate and strain hardening can diminish the effectiveness of scaled trials. To resolve this difficulty, a new scaling method has recently appeared in the open literature called finite similitude. The theory is founded on the metaphysical concept of space scaling, where the idea is that by expanding or contracting space, changes in the governing mechanics can be assessed. In this paper the finite-similitude theory is further developed, where it is demonstrated how the constraints imposed by dimensional analysis can be broken. A new form of similarity is introduced but at the cost of requiring two scaled experiments at distinct scales. It is shown however, how the theory is able to combine the information from the two scaled trials to predict outcomes that can be markedly superior to what can be achieved with experiments at a single scale. All scale dependencies are accounted by the theory and consequently the new formulation attempts to capture scale effects, so provides a more realistic approach to scaled experimentation. Unlike dimensional analysis, the new first-order finite similitude theory can simultaneously target two independent physical properties of common dimension (e.g. initial-yield stress and linear strain hardening). The advantage offered by this feature is demonstrated analytically and numerically in the paper with a focus on axisymmetrical tube buckling and energy absorption. The analytical model serves to expound the theory and the numerical highlights its capabilities and the kinds of accuracy achievable with the new approach.

中文翻译：

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nn 尺度冲击力学的有限相似法

摘要 大型结构在冲击载荷作用下的响应特性，原则上可以通过比例试验来确定。不幸的是，缩放会受到缩放效应的影响，对于冲击力学，应变率和应变硬化的不可缩放性会降低缩放试验的有效性。为了解决这个难题，最近在公开文献中出现了一种新的缩放方法，称为有限相似。该理论建立在空间缩放的形而上学概念之上，其思想是通过扩大或收缩空间，可以评估控制力学的变化。在本文中，有限相似理论得到进一步发展，展示了如何打破量纲分析强加的约束。引入了一种新形式的相似性，但代价是需要在不同尺度上进行两次缩放实验。然而，它显示了该理论如何能够结合来自两个规模试验的信息来预测结果，这些结果可以显着优于单一规模的实验所能实现的结果。所有规模依赖性都由理论解释，因此新公式试图捕捉规模效应，因此为规模化实验提供了更现实的方法。与尺寸分析不同，新的一阶有限相似理论可以同时针对共同尺寸的两个独立物理属性（例如初始屈服应力和线性应变硬化）。该特征提供的优势在论文中以分析和数值方式进行了论证，重点是轴对称管屈曲和能量吸收。分析模型用于阐述理论，而数值则突出了它的能力和新方法可实现的精度类型。