{
  "abstract": "Constitutive models for history-dependent, path-dependent materials typically encode this dependence in prescribed functional forms through internal variables such as damage or plastic strain that are phenomenological, model-dependent, and not directly observable. These rigid forms lack flexibility to match observations, make calibration potentially non-unique, and complicate uncertainty quantification. This paper develops a Gaussian-process state-space model (GP-SSM) that replaces the fixed form of the constitutive model with a flexible GP regression, and the prescribed internal variables with latent state variables learned directly from observable stress-strain histories. As a GP, the model is naturally endowed with a measure of uncertainty and can be constrained to satisfy physical principles. We demonstrate this framework for quasi-brittle materials under triaxial compression, where the latent variable evolution is driven by the current-state stress invariants and the increment of equivalent strain to reflect irreversible, pressure-sensitive history. A sparse multi-output GP then maps the latent state and current strain tensor to the six-component stress response, trained by variational sparse inference. The trained model is exported into Abaqus/Explicit through a user material subroutine. Four verification cases are reported: (1) offline rollout on validation and test histories; (2) a single element under changing confinement; (3) a frozen-memory unloading-reloading extension; and (4) a multi-element structural model compared against the Karagozian and Case Concrete (KCC) model. These results show that the learned state-space update reproduces held-out RVE-scale histories in closed-loop rollout, tracks evolving confinement, supports unloading without violating the irreversibility of the learned history state, and reproduces structural-level behavior consistent with KCC.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33175",
  "author_total": 4,
  "authors": [
    {
      "name": "Houlin Xu"
    },
    {
      "name": "Chenyang Li"
    },
    {
      "name": "K. T. Ramesh"
    },
    {
      "name": "Michael D. Shields"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77zzn2tab5r38.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33175",
  "fulltext_url": null,
  "id": "77zzn2tab5r38",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33175",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CE"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "1702|Gaussian Processes and Bayesian Inference"
    ]
  ],
  "openalex": "W7223858728",
  "pdf_url": "https://arxiv.org/pdf/2610.33175",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77zzn2tab5r38.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33175",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33175"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A Gaussian Process State Space Formulation for Materials Constitutive Modeling: Application to Quasi-brittle Materials",
  "title_text": "A Gaussian Process State Space Formulation for Materials Constitutive Modeling: Application to Quasi-brittle Materials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/77zzn2tab5r38",
  "venue": "arXiv",
  "versions": []
}