A Finite Similitude Approach to Scaled Impact Mechanics

Abstract

The response characteristics of large-scale structures subjected to impact loading can in principle be determined by scaled experiments. Unfortunately, scaling suffers from scale effects and for impact mechanics, the non-scalability of strain rate and strain hardening can diminish the effectiveness of scaled trials. To resolve this difficulty, a new scaling method has recently appeared in the open literature called finite similitude. The theory is founded on the metaphysical concept of space scaling, where the idea is that by expanding or contracting space, changes in the governing mechanics can be assessed.In this paper the finite-similitude theory is further developed, where it is demonstrated how the constraints imposed by dimensional analysis can be broken. A new form of similarity is introduced but at the cost of requiring two scaled experiments at distinct scales. It is shown however, how the theory is able to combine the information from the two scaled trials to predict outcomes that can be markedly superior to what can be achieved with experiments at a single scale. All scale dependencies are accounted by the theory and consequently the new formulation attempts to capture scale effects, so provides a more realistic approach to scaled experimentation.Unlike dimensional analysis, the new first-order finite similitude theory can simultaneously target two independent physical properties of common dimension (e.g. initial-yield stress and linear strain hardening). The advantage offered by this feature is demonstrated analytically and numerically in the paper with a focus on axisymmetrical tube buckling and energy absorption. The analytical model serves to expound the theory and the numerical highlights its capabilities and the kinds of accuracy achievable with the new approach.

A first order finite similitude approach to scaled aseismic structures

“…Design II involves three grades of steel [28] provides values 1 0.365 g = , 2 0.173 g = and 1 2 R = on solution of Eqs. (27). Design III on the other hand did not provide a solution to Eqs.…”

“…which is the scaled invariance for first-order finite similitude and was first introduced in reference [27] for impact mechanics.…”

“…Design III on the other hand did not provide a solution to Eqs. (27), so was resolved in the same manner as Design I, i.e. by setting…”

Finite similitude in fracture mechanics

“…However, an alternative (and the approach adopted here) is to simply enforce a global 𝛽 − invariant condition and apply this in the design of experiments. First-order finite similitude [35] examines an alternative to Eq. ( 5) that involves an additional scaled experiment to shed additional light on changes that are taking place and to add extra flexibility.…”

Application of first‐order finite similitude in structural mechanics and earthquake engineering

“…The work presented here is concerned with both zeroth order and first-order similitude, so involves both one and two-scaled experiments although focusing on seismic studies. The proposed two-experiment approach to scaled experimentation first appeared in references 25,26 for the study of impact mechanics and discrete dynamic systems. The work here extends the application of the method to seismic systems involving steel buildings and non-linear damping, and for the first time the breaking of geometric similarity in structural members.…”