Suggestion of the DLV dimensionless number system to represent the scaled behavior of structures under impact loads

TL;DR

The paper introduces the DLV dimensionless number system, based on Density, Length, and Velocity, to effectively represent and analyze the scaled impact behavior of structures, addressing material and velocity effects.

Contribution

It proposes a new DLV dimensionless number system derived via Buckingham Pi theorem, enabling clear physical interpretation and addressing non-scaling problems in impact analysis.

Findings

The DLV system includes 15 dimensionless numbers with clear physical significance.

It can directly match response equations of dynamic impact problems.

The system effectively addresses non-scaling issues across different materials and strain rates.

Abstract

A group of dimensionless numbers, termed DLV (Density-Length-Velocity) system, is put forward to represent the scaled behavior of structures under impact loads. It is obtained by means of the Buckingham Pi theorem with an alternative basis. The distinct features of this group of dimensionless numbers are that it relates physical quantities of the impacted structure with essential basis of the Density, the Length and the Velocity, and thus it can represent the scaled influence of material property, geometry characteristic and velocity on the behavior of structures. The newly 15 proposed dimensionless numbers reflect three advantages. (1) The intuitively clear physical significance of these dimensionless numbers, such as the ratios of force intensity, force, moment of inertia to the corresponding dynamic quantities, the Johnson's damage number Dn and Zhao's response number Rn etc. are naturally included. (2) The property of direct matching the dimensionless expression of response equations of dynamic problems with these dimensionless numbers through simple equation analysis; (3) The ability of addressing non-scaling problems for different materials and strain-rate-sensitive as well as the VSG (initial impact Velocity-dynamic flow Stress-impact mass G) system. Four classical impact models are used to verify the direct matching property and the non-scaling addressing ability of the DLV system by equation analysis. The results show that the proposed dimensionless number system is simple, clear and efficient, and we suggest using it to represent the scaled behavior of structures under impact loads.