The Physics of Paintless Dent Repair

Works Cited

A note on sources. As of September 2026 a search of Scopus returns no peer-reviewed study of the mechanics of paintless dent repair. The literature cited here is therefore adjacent rather than direct. It concerns how panels are formed, how they resist denting, and how metal behaves when it is bent and unbent. Where a claim in this book rests on that literature it is footnoted; where it rests on the bench it is not, and the difference is deliberate.

1. Thomas, Dylan, Blake Hodgins, Michael Worswick, Mark J. Finn, and Kevin Gong. “Static and Dynamic Denting of Paint Baked AA6111 Panels: Comparison of Finite Element Predictions and Experiments.” SAE Transactions 110 (2001): 993–1006. JSTOR 44699863.
2. Wagoner, R. H., J. F. Wang, and M. Li. “Springback.” In ASM Handbook, vol. 14B, Metalworking: Sheet Forming, edited by S. L. Semiatin, 733–755. Materials Park, OH: ASM International, 2006. doi:10.31399/asm.hb.v14b.a0005131.
3. He, Yan Lin. “Conventional High-Strength Automotive Steels.” In ASM Handbook, vol. 1, Properties and Selection: Irons, Steels, and High-Performance Alloys. Materials Park, OH: ASM International, 2026. doi:10.31399/asm.hb.v01.a0007110.
4. Kazanowski, Pawel. “Forming of Aluminum Alloys.” In ASM Handbook, vol. 14B, Metalworking: Sheet Forming. Materials Park, OH: ASM International, 2006. doi:10.31399/asm.hb.v14b.a0005141.
5. “Bending of Sheet Metal.” In ASM Handbook, vol. 14B, Metalworking: Sheet Forming. Materials Park, OH: ASM International, 2006. doi:10.31399/asm.hb.v14b.a0005161.
6. Palaniswamy, Hari. “Plastic Deformation: State of Stress, Yield Criteria, Flow Rule, and Hardening Rules.” In Sheet Metal Forming Fundamentals. Materials Park, OH: ASM International, 2012. doi:10.31399/asm.tb.smff.t53400053.
7. Dinovitzer, Aaron, Sanjay Tiku, and Mark Piazza. “Dent Assessment and Management: API Recommended Practice 1183.” In Proceedings of the 13th International Pipeline Conference, IPC2020-9724. New York: ASME, 2020. doi:10.1115/IPC2020-9724.
8. Simmons, Frank, III, Jose Veciana, and John Wallace. “Effects of Dent Removal on the Design Properties of Fuselage Skin Material.” In Collection of Technical Papers , AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 891–901. Reston, VA: AIAA, 2000.
9. Chan, Ching-Yao. Fundamentals of Crash Sensing in Automotive Air Bag Systems. Warrendale, PA: Society of Automotive Engineers, 2000. Read closely: the crush zone and non-crush zone sensor locations (29–30) and the door-cavity pressure sensor described after A. Hartl et al., SAE 950348 (140–141).
10. Davies, Geoff. Materials for Automobile Bodies. 2nd ed. Oxford: Butterworth-Heinemann. Chapter 3, “Materials for consideration and use in automotive body structures,” read closely: §3.3.1 steel reduction and vacuum degassing (103), §3.3.4 and table 3.9 higher-strength grades (117–118), §3.4.2 aluminum alloys (129), §3.5 magnesium (132), and the note on Japanese versus European strength conventions (102).
11. Sargent, Frank T. The Key to Metal Bumping. 3rd ed. Fort Worth, TX: Tool & Forge Division, Fairmount Sprocket & Gear, 1953. Foreword and the analysis chapter read closely: the reverse-order rule (13), the seventy/thirty split between bent and merely flexed metal (7), and the note that the all-steel body obsoleted the techniques of the previous generation (foreword).
12. Hasluck, Paul N. Metalworking: Old-Fashioned Tools, Materials, and Processes for the Handyman. London, 1907. Read closely: the cast/hammered division and the note on bronze (1–2), and the chapter on repoussé work (329), including its account of the trade secrecy and self-made tools of the embossers.
13. Archard, J. F. “Elastic Deformation and the Laws of Friction.” Proceedings of the Royal Society A 243 (1957).
14. Gauss, Carl Friedrich. Disquisitiones Generales circa Superficies Curvas. Göttingen: Dieterich, 1828. Art. 12, the theorema egregium: Gaussian curvature is invariant under bending. Chapter six rests on it for the claim that a dish cannot be returned to flat without the metal moving within the surface.
15. do Carmo, Manfredo P. Differential Geometry of Curves and Surfaces. Englewood Cliffs, NJ: Prentice-Hall, 1976. Sec. 4-3, for a modern statement of the same theorem.
16. Vogel, H. “A Better Way to Construct the Sunflower Head.” Mathematical Biosciences 44, nos. 3–4 (1979): 179–89. The model behind the sunflower pattern: θ = n × 137.5°, r = c√n.
17. Ridley, J. N. “Packing Efficiency in Sunflower Heads.” Mathematical Biosciences 58, no. 1 (1982): 129–39.
18. Hardy, G. H., and E. M. Wright. An Introduction to the Theory of Numbers. 6th ed. Oxford: Oxford University Press, 2008. Chap. 11, on continued fractions and the extremal irrationality of the golden ratio.
19. Timoshenko, S., and S. Woinowsky-Krieger. Theory of Plates and Shells. 2nd ed. New York: McGraw-Hill, 1959. Chaps. 15–16, on membrane versus bending action in shallow shells, behind the island pattern.
20. Lankford, W. T., S. C. Snyder, and J. A. Bauscher. “New Criteria for Predicting the Press Performance of Deep-Drawing Sheets.” Transactions of the American Society for Metals 42 (1950): 1197–1232. The r-value, and planar anisotropy as the cause of earing.
21. Hosford, William F., and Robert M. Caddell. Metal Forming: Mechanics and Metallurgy. 4th ed. Cambridge: Cambridge University Press, 2011. Chap. 15, on anisotropy and earing.
22. Jeswiet, J., F. Micari, G. Hirt, A. Bramley, J. Duflou, and J. Allwood. “Asymmetric Single Point Incremental Forming of Sheet Metal.” CIRP Annals 54, no. 2 (2005): 88–114. Incremental forming reaches shapes single-stroke stamping cannot; the basis for the ten percent pass.
23. Johnson, K. L. Contact Mechanics. Cambridge: Cambridge University Press, 1985. Chap. 4, Hertzian contact, behind the rule relating tip radius to delivered pressure.
24. Cerda, E., and L. Mahadevan. “Conical Surfaces and Crescent Singularities in Crumpled Sheets.” Physical Review Letters 80, no. 11 (1998): 2358–61.
25. Lobkovsky, A. E., S. Gentges, H. Li, D. Morse, and T. A. Witten. “Scaling Properties of Stretching Ridges in a Crumpled Elastic Sheet.” Science 270, no. 5241 (1995): 1482–85. Energy condensation into ridges and vertices, behind the walk-back rule.
26. Witten, T. A. “Stress Focusing in Elastic Sheets.” Reviews of Modern Physics 79, no. 2 (2007): 643–75.
27. Weisstein, Eric W. “Archimedean Spiral,” “Logarithmic Spiral,” and “Fermat’s Spiral.” MathWorld. For the standard forms of the three curves whose contact densities are derived in chapter six.