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<p>Necking during uniaxial tension is a widely studied mechanical phenomenon of both theoretical and practical importance. This study investigates how to capture its onset accurately and efficiently using finite element methods. Various element types and boundary conditions are examined, including hexahedral, tetrahedral, and reduced-dimensional truss elements, under both displacement- and force-controlled loading. A counterintuitive force application issue is identified in commercial software when using tetrahedral elements, and the impact of mixed-element meshes is evaluated. It is shown that accurate necking prediction with hexahedral elements under displacement control requires a high aspect ratio and a fine mesh, while force control achieves similar accuracy with only a few elements. Truss elements perform reliably across all settings, even with minimal discretization. In contrast, mixing tetrahedral and hexahedral elements introduces errors: mesh refinement can reduce strain non-uniformity but not fully eliminate instability prediction deviations. These findings provide practical guidance for selecting element types and mesh strategies in necking simulations.</p>

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Discussions on Accurately and Efficiently Capturing Necking Onset in Uniaxial Tension Using Finite Element Modeling

  • 期刊论文

  • 发表日期：

    2025年8月13日

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  • Hengyi Zhao,
  • Peidong Lei,
  • Pengfei Yang,
  • Bin Liu

摘要

Necking during uniaxial tension is a widely studied mechanical phenomenon of both theoretical and practical importance. This study investigates how to capture its onset accurately and efficiently using finite element methods. Various element types and boundary conditions are examined, including hexahedral, tetrahedral, and reduced-dimensional truss elements, under both displacement- and force-controlled loading. A counterintuitive force application issue is identified in commercial software when using tetrahedral elements, and the impact of mixed-element meshes is evaluated. It is shown that accurate necking prediction with hexahedral elements under displacement control requires a high aspect ratio and a fine mesh, while force control achieves similar accuracy with only a few elements. Truss elements perform reliably across all settings, even with minimal discretization. In contrast, mixing tetrahedral and hexahedral elements introduces errors: mesh refinement can reduce strain non-uniformity but not fully eliminate instability prediction deviations. These findings provide practical guidance for selecting element types and mesh strategies in necking simulations.