Material similarity of scaled models

Abstract

When different strain hardening and strain rate sensitive materials are used for scaled model and prototype, the traditional pure geometrical similarity laws of solid mechanics will fail. Although correcting the basic scaling factors of velocity, density and geometry have been developed to compensate for the material distortion in recent non-geometric scaling works, it is difficult to be widely used because of its inherent indirect (depending on the structural strain and strain rate responses) and inexact (having significant prediction errors for prototype) defects.In this paper, a framework of material similarity, based on the new suggested material dimensionless numbers and the 'Material number vs. strain/strain-rate' function curves, are further developed, which represents the objective requirement of similarity theory for the basic mechanical properties of materials. It is demonstrated what is similitude materials of solid mechanics and how to use the best similitude materials to overcome the non-scalabilities of materials for identical or different materials. The direct and exact solution of the basic correction factors is further obtained and therefore overcomes the previous inherent indirect and inexact defects radically. Based on the similarity evaluation of different materials of the classical

Similarity laws of geometric and material distortion for anisotropic elastic plate subjected to impact loads

“…Another example was that the geometry of the structures cannot be manufactured efficiently, especially in the thickness directions of scaled models. To solve the difficulty of distortion of metal materials, in the last two decades, some researchers extended the traditional similarity laws by using a new scaling relation with the basic scaling factor of length, density and velocity [13][14][15][16][17][18] and reasonably designing the optimal similitude materials [19,20]. On this basis, the initial conditions (impact velocity and density/mass) of the scaled model were corrected to compensate for distortion of different materials with strain hardening, strain-rate sensitive and thermal effects.…”

“…Some studies further considered the influence of geometric distortion of thickness and obtained the simple scaling relations by empirical iterate methods [21][22][23] and by dimensionless analysis method for impacted simple beam and plate [24]. Since the defects of traditional similarity laws were overcome fundamentally, these works established a new scaling system and had gradually become widely used in the last twenty years [20]. However, the new similarity laws have not been applied to study the impact problem of anisotropic materials due to its complexity.…”