Here’s a good video covering stiffness and Young’s Modulus, he shows some good modeling and decent figures also mentions some studies.
Further reading about bike engineering, and materials analysis in some studies about frame types, geometries, and materials specifically referencing FEA (which is method for numerically solving differential equations arising in engineering and mathematical modeling)
Enjoy.
Derek Covilla, 2014. “Parametric finite element analysis of bicycle frame geometries”, the conference of the International Sports Engineering Association 2014, Elsevier Procedia Engineering 72 (2014) 441 – 446
Bharati A. Tayade, 2015. “A study on structural health of bicycle frame using Finite Element Analysis”, International Journal of Innovative and Emerging Research in Engineering Volume 2, Issue 4
Joachim Vanwalleghema, 2014. “Development of a multi- directional rating test method for bicycle stiffness”, the conference of the International Sports Engineering Association, 2014, Elsevier Procedia Engineering 72 (2014) 321 – 326
M.A. Maleque, 2010. “Materials Selection Of A Bicycle Frame Using Cost Per Unit Property And Digital Logic Methods”, International Journal Of Mechanical And Materials Engineering (Ijmme), Vol.5, No. 1, 95-100
M.V.Pazare, 2014. “Stress analysis of bicycle frame”, International Journal of Engineering Science and Technology (IJEST), ISSN: 0975=5462, vol. 6, No. 6
Aparna Deshpande, 2016. “Design and Optimization of Bicycle Frame for the Cyclist's Comfort”, International Journal on Recent and Innovation Trends in Computing and Communication, ISSN: 2321-8169, Volume: 4 Issue: 5 220 – 224