Dynamic similitude has proven to be a valuable tool, which is widely adopted in fluid mechanics. However, even with the ever-growing interest in dynamic similitude in solid mechanics, there is still no unified scaling law applicable to any given solid structure or system, and this has prevented the broad adoption of similitude in the field. Here we develop a unified similitude model for solid mechanics using the momentum and the energy conservation. The model allows for the use of different materials in both elastic and plastic regimes. Never reported dimensionless numbers are derived for the first time in this article, and this set of numbers is sufficient for strictly accurate dynamic similitude of any solid structure. Very different case studies are considered, and the perfect agreement seen in compared results confirms the accuracy of the developed scaling model. The exactness of the dimensionless numbers is also confirmed through analytical solutions. The model allows for the scaling of strain rate and, for the first time, the scaling of the strain state between the full-scale structure and its scaled replica.

动态相似性已被证明是一种有价值的工具，在流体力学中被广泛采用。但是，即使对固体力学中动态相似性的兴趣日益增长，对于任何给定的固体结构或系统，仍然没有统一的缩放定律，这阻碍了相似性在该领域的广泛采用。在这里，我们使用动量和能量守恒为固体力学建立统一的模拟模型。该模型允许在弹性和塑性状态下使用不同的材料。本文从未首次导出未报告的无量纲数字，而这组数字足以满足任何实体结构的严格精确的动态相似要求。考虑了非常不同的案例研究，在比较结果中看到的完美一致性证实了开发的缩放模型的准确性。无量纲数的准确性也通过分析解决方案得到了证实。该模型允许缩放应变率，并且首次允许缩放全尺寸结构及其缩放副本之间的应变状态。