Scaling of structures subject to impact loads when using a power law constitutive equation

Abstract

a b s t r a c tIt is well known that structures subjected to dynamic loads do not follow the usual similarity laws when the material is strain rate sensitive. As a consequence, it is not possible to use a scaled model to predict the prototype behaviour. In the present study, this problem is overcome by changing the impact velocity so that the model behaves exactly as the prototype. This exact solution is generated thanks to the use of an exponential constitutive law to infer the dynamic flow stress. Furthermore, it is shown that the adopted procedure does not rely on any previous knowledge of the structure response. Three analytical models are used to analyze the performance of the technique. It is shown that perfect similarity is achieved, regardless of the magnitude of the scaling factor. For the class of material used, the solution outlined has long been sought, inasmuch as it allows perfect similarity for strain rate sensitive structures subject to impact loads.

Scaling of An Impacted Reticulated Dome Using Partial Similitude Method

“…This new scaling method can also be applied by changing the initial impact speed according to Equation (5), as presented in the works of Oshiro & Alves (2009) and Mazzariol & Alves (2014). Several iterations may be need to determine the value of γ V .…”

“…Alves & Oshiro (2006) further exploited this idea, and properly scaled strain rate sensitive models by correcting either initial speed or the mass of the impactor. Based on the idea of changing the impact velocity, Oshiro & Alves (2009) dealt with the scaling of structures subjected to impact loads when using a power law constitutive equation. Mazzariol & Alves (2014) developed a method to represent impacted structures using scaled models made of different materials with a combination of modifying velocity and mass of the impactor.…”

A Review of Similitude Methods for Structural Engineering

“…The application of dimensional analysis to overcome the difficulties due to strain-rate sensitivity is the subject of several works by Alves and Oshiro [108][109][110][111][112][113]. There, the authors propose a new method to overcome the distortion problems in impacts.…”

“…Based on this consideration, the approach was further expanded in Ref. [111] in which the choice of constitutive law changes. Instead of a Cowper-Symonds law, the authors used a Norton-Hoff law.…”

The Dynamic Similitude Design Method of Thin Walled Structures and Experimental Validation

“…Ungbhakorn and Singhatanadgid [14][15][16] proposed a new approach of deducing scaling laws for stability and presented scaling laws of symmetrically laminated plates and cylindrical shells by considering the loads effects. Oshiro and Alves [17,18] employed a constitutive law to establish the model and the model reflected exactly as the prototype by changing the impact velocity. Oshiro and Alves [19] investigated the geometrically distorted scaling law in order to predict the behaviors of the prototype, and three problems of the prototype were analyzed.…”