Soft materials with engineered microstructure support nonlinear waves which can be harnessed for various applications, from signal communication to impact mitigation. Such waves are governed by nonlinear coupled differential equations whose analytical solution is seldom trackable, hence emerges the need for suitable numerical solvers. Based on a finite-volume method in one space dimension, we here develop a designated scheme for nonlinear waves with two coupled components that propagate in soft laminates. We apply our scheme to a periodic laminate made of two alternating compressible Gent layers, and consider two cases. In one case, we analyze a motion whose component along the lamination direction is coupled to a component in the layers plane, and discover vector solitary waves in a continuum medium. In the second case, we analyze a motion with two coupled components in the plane of the layers, and observe a train of linearly polarized solitary waves, followed by a single circularly polarized wave. The framework we developed offers a platform for further investigation of these waves and their extension to higher dimensional problems.
On the numerical simulation of the nonbreaking solitary waves run up on sloping beaches
