{
  "abstract": "We study rate-independent systems in which the evolution is obtained by incremental minimization of elastic energy and one-homogeneous dissipation under constraints on the admissible inelastic increments. Such constraints arise naturally in several models of inelastic materials, including shear-transformation-zone models, intermittent plasticity, and quantized plasticity, where evolution proceeds through prescribed elementary activation events rather than arbitrary plastic increments. We establish the existence of a continuous-time limit for the corresponding constrained incremental scheme under suitable assumptions. As an application, we formulate a simplified shear-transformation-zone model consisting of localized activation events on a lattice embedded in a two-dimensional elastic medium. We prove that this model generates shear-band formation through the successive activation of neighboring transformation zones. More precisely, we show that every admissible evolution remains localized on a growing line segment in the infinite-domain setting and that the same mechanism persists on sufficiently large bounded domains. These results provide a rigorous mathematical framework for constrained activation models and show that restrictions on admissible elementary events alone constitute a mechanism for localization in rate-independent systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37584",
  "author_total": 2,
  "authors": [
    {
      "name": "Heiner Olbermann"
    },
    {
      "name": "Hidde Schönberger"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4mxkr8tgrr0n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37584",
  "fulltext_url": null,
  "id": "d4mxkr8tgrr0n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37584",
  "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",
      "math.AP"
    ],
    [
      "openalex",
      "2505|Microstructure and mechanical properties"
    ]
  ],
  "openalex": "W7214990716",
  "pdf_url": "https://arxiv.org/pdf/2609.37584",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4mxkr8tgrr0n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37584",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37584"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Formation of shear bands through discrete localized plastic increments",
  "title_text": "Formation of shear bands through discrete localized plastic increments",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/d4mxkr8tgrr0n",
  "venue": "arXiv",
  "versions": []
}