{
  "abstract": "Multistable systems admit distinct stable equilibria for the same loading and boundary conditions. Shape optimization of multistable structures offers a promising route to engineer the mechanical response of advanced materials and metamaterials. In this work, we develop a formulation and algorithm for controlling the energy jump associated with snap-through behaviour in hyperelastic metamaterials by optimizing the shape of the domain. The key challenge is that classical shape optimization theory assumes a single-valued domain-to-solution map, which does not hold in the multistable setting. We address this by extending the theory to settings with non-unique solutions, treating the scaling of the domain deformation as a continuation parameter and applying the implicit function theorem to give sufficient conditions for the continued existence of multiple solution branches as the shape varies. This theoretical foundation underpins a practical algorithm that targets a prescribed energy jump between stable states, enabling the systematic design of structures whose snap-through response can be tuned on demand.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12816",
  "author_total": 4,
  "authors": [
    {
      "name": "Arselane Hadj Slimane"
    },
    {
      "name": "Patrick E. Farrell"
    },
    {
      "name": "Alberto Paganini"
    },
    {
      "name": "Àlex Ferrer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2537eb81tvsmz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12816",
  "fulltext_url": null,
  "id": "2537eb81tvsmz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12816",
  "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.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2205|Topology Optimization in Engineering"
    ]
  ],
  "openalex": "W7212777376",
  "pdf_url": "https://arxiv.org/pdf/2609.12816",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2537eb81tvsmz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12816",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12816"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Controlling the energy jump of multistable structures using shape optimization",
  "title_text": "Controlling the energy jump of multistable structures using shape optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/2537eb81tvsmz",
  "venue": "arXiv",
  "versions": []
}