Transversal topics
Nonlinear elastodynamics
During my PhD studies, I also worked on the equations governing the motion of nonlinear elastic solids in one space dimension. The results are presented in a Wave Motion article, where I fully detailed the derivation of the analytical solution to the Riemann problem
\[\begin{aligned} \partial_t \varepsilon &= \partial_x v\\ \rho_0 \partial_t v &= \partial_x \sigma(\varepsilon) \end{aligned} \qquad\text{with}\qquad (\varepsilon, v)|_{t=0} = \begin{cases} (\varepsilon_L, v_L), & x<0\\ (\varepsilon_R, v_R), & x>0 \end{cases} \notag\]for various constitutive laws. The solution includes shock waves, rarefaction waves and compound waves, leading to an algorithm to solve the problem (development of a Matlab toolbox). The mathematical theory behind this kind of system of partial differential equations goes back to the 1970s.
During my first post-doctoral fellowship, I had the opportunity to investigate the diffraction of an acoustic beam propagating in a soft elastic solid along a given direction (Figure). This phenomenon is described by a system of coupled KZK-type equations, for which I developed a Finite Volume code from scratch. We published the results in Commun. Nonlinear Sci. Numer. Simul.
Soft solids
In relation with my research works on traumatic brain injury, I investigated several aspects of the modelling and characterisation of soft biological tissues. More specifically, I studied the propagation of shear waves in pre-stressed viscoelastic media, see the 2022 Int. J. Solids Struct. publication. Using these results, I adapted an experimental technique to measure the amount of mechanical stress in a material based on the propagation of two shear waves, see Extreme Mech. Lett. paper. Experimental measurements are currently being performed on various samples using the theory presented in a recent Math. Mech. Solids publication. Finally, I also became interested in the modelling of static torsional motions in soft porous solids (see study published in Int. J. Non-Linear Mech. publication).
Finite volume method
(In construction)