Green-function Method for Nonlinear Interactions of Elastic Waves

In the linear wave propagation regime, an analytical mesh-free Green-function decomposition has been shown as a viable alternative to FDTD and FEM. However, its expansion into nonlinear regimes has remained elusive due to the inherent linear properties of the Green-function approach. This work presents a novel frequency-domain Green function method to describe and model nonlinear wave interactions in isotropic hyperelastic media. As an example of the capabilities of the method, we detail the generation of sum frequency waves when initial quasi-monochromatic waves are emitted in a fluid by finite sources. The method is supported by both numerical and experimental results using immersion ultrasonic techniques.