# 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 (2017) link, where I fully detailed the derivation of the analytical solution to the Riemann problem

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 *Communications in Nonlinear Science and Numerical Simulation* (2021) link.