{
  "abstract": "Accurate stress integration at large strain increments requires control of both trajectory error and yield-surface drift. This study presents RK-RM, a hybrid strategy combining explicit Runge–Kutta integration with cutting-plane return mapping. A forward–backward calculation constructs complementary internal variables, which are combined with the forward stress to initialize the correction. The method is examined with the Modified Cam-Clay and Unified Hardening (UH) models in material-point tests, triaxial simulations, and a foundation loading example. The UH triaxial comparisons show smaller deviatoric-stress errors than the tested closest point projection (CPPM) implementation, while additional undrained material-point comparisons show lower local constitutive cost. Accuracy depends on the loading path, step size, and correction strategy. The results support RK-RM as a practical stress-integration option for the constitutive models and loading conditions considered.",
  "abstract_shown": true,
  "affiliations": [
    "POWERCHINA Chengdu Engineering Corporation Limited, Chengdu 610072, China",
    "State Key Laboratory of Hydroscience and Engineering, Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 5,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Xiangxian Dou"
    },
    {
      "affs": [
        1
      ],
      "name": "Li Wan"
    },
    {
      "affs": [
        1
      ],
      "name": "Jinlong Xie"
    },
    {
      "affs": [
        1
      ],
      "name": "Qianhui Liu"
    },
    {
      "affs": [
        1
      ],
      "name": "Yuzhen Yu",
      "orcid": "0000-0002-6249-5075"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8rnd39yjxt2aa.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203831",
  "fulltext_url": null,
  "id": "8rnd39yjxt2aa",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3831",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2211|Soil, Finite Element Methods"
    ]
  ],
  "openalex": "W7223175081",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/8rnd39yjxt2aa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203831",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3831"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "A Runge–Kutta Enhancement Strategy Based on the Return Mapping Method",
  "title_text": "A Runge–Kutta Enhancement Strategy Based on the Return Mapping Method",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/8rnd39yjxt2aa",
  "venue": "Mathematics",
  "versions": []
}