After I completed my PhD, I became interested in finite-strain models of soft viscoelastic solids (Fung’s QLV theory). In this context, I established the dissipative character of the model by deriving the expression of the thermodynamic potential in terms of appropriate state variables. The results were published in Mechanics Research Communications (2021) link.
The effect of a large static pre-deformation is analysed in a recent arXiv preprint link. Application of this acoustoelasticity theory to pre-stressed phononic crystals was also considered (Figure). Computations show that dissipation shifts the band gaps (i.e., the frequency range in which waves cannot propagate), simultaneously increasing their width.
The formation of shock waves is analysed in a recent arXiv preprint link. Ongoing works concern nonlinear waves, experimental validations, and computer implementations.