The complex behavior of inelastic woven composites stems primarily from their inherent heterogeneity. Achieving accurate predictions of their linear and nonlinear responses, while considering their microstructures, appears feasible through the application of multi-scale modeling approaches. However, effectively incorporating these methodologies into real-scale applications, particularly within FE 2 analyses, remains challenging due to the significant computational requirements they entail. To overcome this issue, while considering the scale effects, this study introduces an alternative approach based on Artificial Neural Networks (ANNs) to perform a macroscopic surrogate model of composites. This model, referred to as Multiscale Thermodynamics Informed Neural Networks (MuTINN), is founded on thermodynamic principles and introduces specific quantities of interest that serve as internal state variables at the macroscopic level. This captures efficiently the state and evolution laws governing the history-dependent behavior of these composites while retaining the thermodynamic admissibility and the physical interpretability of their overall responses. Moreover, to facilitate its numerical implementation within a FE code, a Meta-UMat has been developed, streamlining the application of multiscale FE-MuTINN approach for composite structure computations. The prediction capabilities of the proposed approach is demonstrated across the material scales, exemplified through diverse instances of woven composite structures. Theses applications account for anisotropic yarn damage and an elastoplastic polymer matrix behavior. The numerical results and the related comparison with experimental findings and FE computations demonstrate remarkable consistency across a wide range of non-proportional loading paths. This promises a potential solution to alleviate the computational challenges associated with multiscale simulations of large composite structures.