The trimechanic theory

From Galileo Galilei and Robert Hooke in the 17th century to David Julius and Ardem Patapoutian, who won the 2021 Nobel Prize in Physiology or Medicine, stiffness and elasticity have been a cornerstone of classical physics and now in biology. To characterize a mechanical role in biology, one task is to quantify the elasticity of a sample. In common terms, the elasticity of a material is characterized by measuring its stiffness, or the resistance of an object to the deformation under an external force.
Young’s modulus is the elastic constant that relates the deformation of a material to the stresses experienced by the elastic material. There are several technologies to measure the elasticity of soft or biological materials of which the most used is the atomic force microscopy (AFM) and its nano-indentation capability. The major difficulty is the indirect access to the value of the elastic constant through a mechanical model of indentation, which imposes a mathematical fitting of the force-distance curve, the experimental result of AFM indentations.
The new concept brought by this research of the AFM team of the Methods and Electron Microscopy Group is the trimechanic theory [1], which provides a mathematical framework to apply appropriate contact-based mechanical models such as those defined by Sneddon’s (1965) solutions for given shape of indenters. The trimechanic theory provides a new basis for dissecting the indentation path into segments where each one is fitted to the three restoring forces, a sum of constant, linear and nonlinear contributions. A critical step in this theory is the judicious resetting of the forces and especially the stiffness in each segment.

Nano-structural stiffness measure for soft biomaterials of heterogeneous elasticity. Chen SwW, Teulon JM, Kaur H, Godon C, Pellequer JL. Nanoscale Horizons 2023 ; 8:75-82.

Contact : Jean-Luc Pellequer (IBS/Methods and Electron Microscopy Group)


[1A nod to the trichromatic theory developed by Thomas Young which gives its name to the eponymous elastic constant