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We consider parallel splitting of a strip composed of two different chains.As a waveguide, the dissimilar-chain structure radically differs from thewell-studied identical-chain system. It is characterized by three speeds of thelong waves, two for the separate chains, and one for the intact strip where thechains are connected. Accordingly, there exist three ranges, the subsonic forboth chains, the intersonic and the supersonic. The speed in the latter rangeis supersonic for the intact strip and at the same time, it is subsonic for theseparate higher-speed chain. This fact allows the splitting wave to propagatein the strip supersonically. We derive steady-state analytical solutions andfind that the splitting can propagate steadily only in two of these speedranges, the subsonic and the supersonic, whereas the intersonic regime isforbidden. In the case of considerable difference in the chain stiffness, thelowest dynamic threshold corresponds to the supersonic regime. The peculiarityof the supersonic mode is that the supersonic energy delivery channel, beinginitially absent, is opening with the moving splitting point. Based on thediscrete and related continuous models we find which regime can be implementeddepending on the structure parameters and loading conditions. The analysisallows us to represent the characteristics of such processes and to demonstratestrengths and weaknesses of different formulations, quasi-static, dynamic,discrete or continuous. Analytical solutions for steady-state regimes areobtained and analyzed in detail. We find the force-speed relations and show thedifference between the static and dynamic thresholds. The parameters and energyof waves radiated by the propagating splitting are determined. We calculate thestrain distribution ahead of the transition point and check whether thesteady-state solutions are admissible.

How a dissimilar-chain system is splitting. Quasi-static, subsonic and supersonic regimes