One neural network to rule them all: multimaterial experimental learning of nonlinear elasticity

Studying nonlinear elasticity allows us to describe industrial materials such as rubber, silicone, and neoprene, as well as soft tissues such as skin, muscle, liver, and arteries. A better understanding of these materials could help improve the safety of neoprene wetsuits, enable more precise liver surgery simulations, or detect cardiovascular diseases. Unlike most materials, for which applying a force causes a proportional deformation (elastic linearity), these ones deform in a highly complex and nonlinear way, which is difficult to describe with equations. A solution is to let the data speak: the behaviour can be discovered directly from experiments, using a neural network guided by physical laws. Instead of training a new model for each material (which is very time-consuming), this work proposes the first experimental learning strategy to study multiple materials simultaneously. A common neural network is trained and adapted to each material using a short numerical "fingerprint" that makes each material unique. This architecture thereby reduces the computational time to learn all the behaviour laws. The authors collected a unique and diverse dataset of exceptional richness using tensile tests and Digital Image Correlation, which tracks deformation pixel-by-pixel from camera images, on 12 silicone materials with different stiffnesses. Using only the displacements provided by this technique and the forces applied at the sample ends, the model provides experimental discovery of the internal forces in each material. The global behaviour law is then calculated for each material and fits the experimentally measured forces with a relative error below 2%, thereby outperforming single-material approaches. This method paves the way for a unified experimental description of vast families of materials, from industrial silicones to biological tissues.