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<p>Accurate contact and impact detection remain key challenges in computational mechanics. This work presents a methodology for non-conformal contact detection between rigid convex bodies with superelliptical boundaries, represented using their respective Signed Distance Fields (SDFs). A method for approximating the SDF of discretized superelliptical boundaries is introduced, along with the concept of the Gap Distance Field (GDF). Reformulating the contact detection problem as an unconstrained minimization over the GDF simplifies the computation of minimum distance and overlap, while the closest contact point is obtained by projecting the SDF gradients. Numerical experiments involving superelliptical contact bodies validate the accuracy and robustness of the proposed approach. Additionally, the common normal (CN) condition naturally arises within this framework, and together with the optimality of the GDF minima, provides a sufficient condition for determining the minimum distance between the interacting bodies.</p>

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Contact detection in computational mechanics: a signed distance field approach for convex superelliptical bodies

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月29日

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  • Olivier R. Gouveia,
  • José M. Guedes,
  • Rui B. Ruben

摘要

Accurate contact and impact detection remain key challenges in computational mechanics. This work presents a methodology for non-conformal contact detection between rigid convex bodies with superelliptical boundaries, represented using their respective Signed Distance Fields (SDFs). A method for approximating the SDF of discretized superelliptical boundaries is introduced, along with the concept of the Gap Distance Field (GDF). Reformulating the contact detection problem as an unconstrained minimization over the GDF simplifies the computation of minimum distance and overlap, while the closest contact point is obtained by projecting the SDF gradients. Numerical experiments involving superelliptical contact bodies validate the accuracy and robustness of the proposed approach. Additionally, the common normal (CN) condition naturally arises within this framework, and together with the optimality of the GDF minima, provides a sufficient condition for determining the minimum distance between the interacting bodies.