Molecular Dynamics informed Continuum Modelling of Graphene Deposition on Metal Substrates via Mechanics-Guided Machine Learning
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Graphene synthesized via Chemical Vapor Deposition (CVD) holds immense potential for next-generation electronics. However, morphological defects such as wrinkles and steps frequently arise due to lattice mismatches and thermal expansion differences between the graphene and the metal substrate [1]. While Molecular Dynamics (MD) can accurately capture atomic-scale interactions, it is computationally limited for macro-scale simulation, for example, at the micron level. Conversely, continuum modeling techniques like Finite Element Methods (FEM) are more efficient but require ad-hoc constitutive laws that accurately describe the complex material behavior of graphene under different temperatures. To bridge this gap, we developed a MD-informed continuum modeling for graphene deposition process based on mechanics-guided machine learning approach. Following the approach of Surana et al. [1], the thin-layered deposit graphene is approximated via finite element shell theory, while the corresponding constitutive model is constructed by MD data. The MD simulations are executed at 1000K to systematically characterize the total free energy density by decomposing it into in-plane strain energy, bending energy and graphene-metal interface energy. To learn the representative corresponding surrogate energy functions from MD data with inherited anisotropy, nonlinearity, and orientation-induced effect, we employed Constitutive Artificial Neural Networks (CANNs) [3] with generalized invariants to encode graphene’s six-fold lattice symmetry, ensuring thermodynamic consistency with superior extrapolation capabilities compared to standard Multi-Layer Perceptron (MLP) architecture. The surrogate model is then implemented on FE shell model and is validated via a series of benchmark problems, successfully used for defect engineering in CVD.
