Finite Element Continuation Analysis for Cnoidal Waves in Solids
Under compression, rate-dependent solids subject to hydro-mechanical processes have been shown to accommodate singular cnoidal wave solutions [1], as a material instability at the stationary wave limit. Given the numerical complexity to solve the corresponding equation, we use a physical regularization approach [2] to cap the infinite stress growth with chemical pressurization of the material around the singularities. In this contribution, we show the results of a stability analysis of the underlying equation using a pseudo-arclength continuation algorithm with Finite Elements [3]. This allows to identify various solutions of the system with different numbers of peaks as a function of the problem parameters. We show the influence of the main material parameter, the existence of its critical values for different types of solutions, as well the evolution of peak spacing for the different admissible solutions. Finally, we investigate which initial conditions lead to solutions with stress peaks.
