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Abstract: Thermoplastic composite materials offer new perspective in the mechanical industry, especially in aeronautic industry. The assembly of huge structures by welding is made possible by the ability of the matrix to melt. This paper focuses on ultrasonic welding process where heating is confined at the welding interface. This is achieved thanks to a local mechanical dissipation in triangles specially located at the interface, called energy director. In order to better understand the phenomena that occur at the energy director scale, we propose to model and simulate the polymer flow at the interface. Based on a previous work, the flow under vibration is modeled using three coupled boundary value problems. A specific simulation tool is then developed for solving those three problems. It entails specific numerical methods: a level set method allows to handle the large geometry change, and an iterative solver manages the multiphysical aspects. The novel simulation obtained is validated with a qualitative comparison to experiments. Then, an analysis of the numerical results allows to understand the phenomena that enable welding. A thermomechanical localization heats the tip of the energy director. This initiates a fold of polymer that progressively fills the gap between the two plates to weld, and ensures conditions for adhesion. [Copyright &y& Elsevier]