Scaling laws of thin-walled circular tubes with wall thickness distortion

In scaled tests of thin-walled structures, wall thickness often cannot be reduced proportionally with other geometric dimensions, resulting in wall thickness distortion and deviations from classical similarity predictions. This study investigates the crashworthiness similitude of thin-walled circular tubes with wall thickness distortion under quasi-static axial crushing. A dimensionless distortion factor, γ ( γ = βt/β ), is introduced into the classical similarity framework to characterize non-proportional wall thickness scaling. Based on 42 finite element models covering different geometric scale factors and distortion levels, correction relationships are established for mean crushing force ( MCF ), energy absorption ( EA ), specific energy absorption ( SEA ), effectiveness of energy absorption ( EEA ), and initial peak force ( IPF ). Twelve additional cases are used for independent numerical validation, yielding a mean relative error of 3.79% for MCF and a maximum error of 9.96% among all examined crashworthiness indicators. Quasi-static compression tests are further conducted on scaled tubes with β = 0.5 and γ = 0.8 and 1.2, for which the maximum absolute deviation between the experimental averages and theoretical predictions is 4.6%. Within the investigated geometric range and progressive-folding regime, the proposed framework provides an effective approach for predicting the quasi-static crushing responses of prototypes from wall thickness distortion scaled models.