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

Abstract

Highlights(1) The DLV dimensionless number system to represent structural impact is proposed.(2) Two well-known numbers, the damage number and the response number, are naturally included in DLV dimensionless numbers.(3) The property of directly matching the dimensionless expression of the response equations is verified through simple equation analysis of four impact models.(4) The ability of addressing non-scalability as well as the VSG system is confirmed. 3 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 Π 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 and Zhao's response number etc. are naturally included. (2) The property of directly 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 directly 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.

Material similarity of scaled models

“…For impact mechanics with strain hardening and strain-rate sensitive materials, recent researchers have developed several effective similarity systems [11,19,[21][22][23][24] to derive scaling factors. As a more concise, clear and effective system, the density-lengthvelocity (DLV) dimensional analysis system [23] was expressed as the seven main…”

“…Similar studies in previous works also define the correction factor of density and the geometry (for geometrically-distorted scaling). Since the three correction methods can convert to each other [23,24], the velocity correction factor Eq. (3), as one of the typical representatives, is mainly discussed in this paper.…”

“…However, this method can only provide inexact prediction ability and usually result in obvious errors for similarity. In further research, Wang and Xu et al [23,24] proposed geometric distortion similarity ability that adding a basic correction factor of geometrical thickness to compensate distortion of the different materials. But the average strain and average strain rate of the structure was required in the basic correction factor.…”

Scaling behaviour of corrugated sandwich panels under impact load

“…Recently, Xu et al suggested a similarity law for density–length–velocity (DLV) bases. 13 The DLV system, which exhibits the same scaling relationships as the VSG method, expresses the well-established Johnson’s damage number and Zhao’s response number. Furthermore, they expanded the scalar characteristic length L to three spatial directional characteristic lengths, i.e., Lx , Ly , and Lz .…”

A directional framework of similarity laws for geometrically distorted structures subjected to impact loads

“…Variable Dai (2019) proposed the density-length-velocity (DLV) dimensional analysis, instead of the VSG system, to express the similarity laws of structural impact. In the DLV system, fifteen dimensionless numbers were expressed as follows:…”