Quantifying the Effect of Distance on Post-Impact Compression Failures with Radio Square Difference Coloring Techniques

¹ Department of Mathematics, Francis Xavier Engineering College, Tirunelveli, India.
² Department of Mechanical Engineering, PSN College of Engineering and Technology, Tirunelveli, India.
³ Department of Mathematics, V.S.B College of Engineering Technical Campus, Coimbatore, India.
⁴ Department of Electrical and Electronics Engineering, PSN College of Engineering and Technology, India.
⁵ Department of Industrial Management, Faculty of Business, Liwa College, Abudhabi, UAE.

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 25 November 2025

Abstract

It is necessary to understand the impact distance on compression failure to design a safer and more resilient material and structural system. Traditional methods of post-impact assessment are generally concerned only with the damaged area itself and little consideration to the effects with respect to distance to the point of impact. In order to bridge this gap, the current work develops the Radio Square Difference (RSD) technique as one means of measuring the spatial variation of post-impact compression behavior. The RSD framework, originally applied in signal analysis and optimization of the network, is modified here to quantify changes in compression response at a greater distance to the point of impact. The method gives a better idea of the distribution of the damage intensity in a material by investigating the squared difference between the maximum and minimum compression values recorded at any distance. As demonstrated in experiments, the RSD measure is very useful in modeling the extent of deformation and the capacity of the material to sustain impact in various spatial areas. Although compression forces might seem to be similar, significant differences in the peak levels of stresses are observed, which demonstrates that deformation and failure behavior cannot be necessarily predicted by intuitive or consistent trends. These results find applications in such areas as materials science, civil engineering, or in the automotive safety domain, where the non-uniform distribution of strains is a key factor. The fact that the graph produced by MATLAB substantiates the effectiveness of the method also confirms the credibility of the method. Generally, the present study offers a new and workable methodology of measuring residual strength of structural elements after impact and offers a base to more sophisticated predictive models, which would be more effective in handling sophisticated, real-life impact scenarios.