On the mechanical dynamic similitude of solid continuum

Abstract

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.