Digital Twins are revolutionizing engineering and industrial domains, providing capabilities for real-time monitoring, optimization, and predictive maintenance of intricate systems. Central to their reliability and robustness is the precise simulation of physical behaviours, a challenging task particularly in scenarios involving complex material properties. Conventional computational techniques, while accurate, often face limitations in terms of computational efficiency due to the high dimensionality and non-linear nature of these systems. In this work, we introduce an innovative methodology based on Thermodynamics-informed Graph Neural Networks (TIGNNs) [1] in a local form [2] to construct efficient and accurate digital twins of dissipative solids. Our approach leverages the GENERIC (General Equation for Non-Equilibrium Reversible Irreversible Coupling) [3] framework, a thermodynamic formalism that ensures the physical consistency of the resulting models. By embedding thermodynamic principles directly into the neural network's architecture, we achieve enhanced stability and physical coherence in the simulations. The TIGNN framework integrates geometric and thermodynamic biases to significantly reduce computational costs and the dependence on large synthetic datasets. This results in digital twins capable of accurately predicting the response of viscous-hyperelastic structures under diverse loading conditions and unseen geometries, offering a powerful tool for real-time simulation and predictive analysis. [1] Hernández, Q., Badías, A., Chinesta, F., Cueto, E. (2022) (Thermodynamics informed graph neural networks. arXiv preprint arXiv:2203.01874 [2] Tierz, A., Alfaro, I., González, D., Chinesta, F., Cueto, E. (2024) Graph Neural Networks Informed Locally by Thermodynamics. arXiv preprint arXiv:2405.13093 [3] Grmela, M. and Öttinger, H.C. Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Physical Review E, 56(6), p.6620, 1997.