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arXiv Machine Learning By Houlin Xu, Chenyang Li, K. T. Ramesh, Michael D. Shields

A Gaussian Process State Space Formulation for Materials Constitutive Modeling: Application to Quasi-brittle Materials

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The paper introduces a Gaussian‑process state‑space model (GP‑SSM) for constitutive modeling of quasi‑brittle materials, replacing traditional internal variables with latent states learned from stress‑strain data. The GP‑SSM provides uncertainty quantification, enforces physical constraints, and maps latent states and strain tensors to stress responses via a sparse multi‑output GP. The trained model is implemented in Abaqus/Explicit and validated through four cases, demonstrating accurate reproduction of RVE‑scale histories, confinement effects, unloading behavior, and structural responses comparable to the KCC model.

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