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Pre-impregnated thermoplastic composites are widely used in the aerospace industry for their excellent mechanical properties, impact resistance and fatigue strength all at lower density than other common materials. In recent years, the automotive industry has shown increasing interest in the manufacturing processes of thermoplastic-matrix composites materials, especially in thermoforming techniques for their rapid cycle times and the possible use of preexisting equipment. An important step in the prediction of the mechanical properties and technical feasibility of parts with complex geometry is the use of modelling and numerical simulations of these forming processes which can also be capitalized to optimize manufacturing practices. This paper aims to present an approach to the simulation of thermoplastic prepreg composites forming. The proposed model is based on convolution integrals defined under the principles of irreversible thermodynamics and within a hyperelastic framework. The hyperelastic potential is built from the contribution of four major deformation modes that assumed independent: the elongation in the warp and weft directions, the in-plane shear, and the bending deformations. Consequently the corresponding strain energy potentials which are uncoupled can be identified by classical tests on textile composite shells, such as tension, in plane-shear and bending tests. The viscoelasticity is introduced exclusively for the in-plane shear mode. The simulation is composed of thermal analyses and forming simulations performed alternatively. This ensures a coupling between the mechanical and thermal simulations. The deformation of a unit cell and the modification of contacts with the tools change the local thermal properties and temperatures. The thermal conductivities are determined by mesoscopic analysis.The woven reinforced prepreg has a periodicity that can be exploited to perform a homogenization simulation and get the macroscopic conductivity from the geometry of the mesostructure and from the thermal properties of the yarns and the polymer [ABSTRACT FROM AUTHOR]