Design-oriented power-law model for predicting crushing forces and energy absorption in composite tubes under axial compression

A unified regression-based predictive framework for estimating peak-crushing force, mean crushing force, and energy absorption in glass fiber–reinforced polymer (GFRP) tubes subjected to axial compression is proposed in this work. In contrast to existing models that separately address peak load or rely on configuration-specific empirical correlations, the present approach establishes an explicit analytical linkage among peak force, post-peak crushing behavior, and absorbed energy using a reduced set of mechanically interpretable design variables. An experimental database compiled from the literature, incorporating variations in fiber orientation, tube diameter, wall thickness, and number of plies, was used to develop the model. A strong linear relationship between peak and mean crushing forces was identified, with the mean force representing approximately 70.56% of the peak force ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> = 0.9615), thereby allowing direct estimation of the post-peak response without full force–displacement integration. Peak-crushing force was predicted using a power-law model linearized through logarithmic transformation and calibrated via multiple regression ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> = 0.9677). Energy absorption estimates derived from the combined formulation showed good agreement with experimental results ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> ≈ 0.98). The principal contribution lies in integrating peak force prediction, mean force estimation, and energy absorption evaluation into a single computationally efficient, design-oriented analytical framework, providing a practical alternative to configuration-dependent empirical models and computationally intensive simulations for preliminary crashworthiness design.