Midplane based 3D single pass unbiased segment-to-segment contact interaction using penalty method

2025-06-05

AI Summary

This work addresses bias arising from master–slave partitioning in 3D contact mechanics. We propose an unbiased segment-to-segment contact formulation: a unified reference frame is constructed via the mid-surface, enabling traction computation between discretized contact segments in a single pass; geometric penetration is directly penalized, and traction equilibrium on the contact surface is strictly enforced. The method supports conforming and non-conforming meshes, self-contact, and diverse geometries—including planar, curved, and sharp-edged surfaces—while enhancing traction evaluation accuracy through 3D geometric configuration classification. Efficient and robust solution is achieved via penalty regularization, mid-surface projection, and segment-wise integration. Benchmark tests—including Hertzian contact, flat punch indentation, and double-beam bending—demonstrate uniform pressure distribution and convergence to analytical solutions. The approach successfully simulates elastic and elastoplastic rod collisions, oblique cylinder impact, and complex self-contact scenarios, achieving finite-element-level accuracy.

Technology Category

• Computer Vision: 3D Computer Vision
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Responsible Web: Social and technical mechanisms of refusal for web technologies and applications
• Security and Privacy: Tracking, profiling, and countermeasures against them
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

This work introduces a contact interaction methodology for an unbiased treatment of contacting surfaces without assigning surfaces as master and slave. The contact tractions between interacting discrete segments are evaluated with respect to a midplane in a single pass, inherently maintaining the equilibrium of tractions. These tractions are based on the penalisation of true interpenetration between opposite surfaces, and the procedure of their integral for discrete contacting segments is described in this paper. A meticulous examination of the different possible geometric configurations of interacting 3D segments is presented to develop visual understanding and better traction evaluation accuracy. The accuracy and robustness of the proposed method are validated against the analytical solutions of the contact patch test, two-beam bending, Hertzian contact, and flat punch test, thus proving the capability to reproduce contact between flat surfaces, curved surfaces, and sharp corners in contact, respectively. The method passes the contact patch test with the uniform transmission of contact pressure matching the accuracy levels of finite elements. It converges towards the analytical solution with mesh refinement and a suitably high penalty factor. The effectiveness of the proposed algorithm also extends to self-contact problems and has been tested for self-contact between flat and curved surfaces with inelastic material. Dynamic problems of elastic and inelastic collisions between bars, as well as oblique collisions of cylinders, are also presented. The ability of the algorithm to resolve contacts between flat and curved surfaces for nonconformal meshes with high accuracy demonstrates its versatility in general contact problems.

Problem

• Unbiased contact interaction without master-slave surfaces
• Single-pass midplane traction evaluation for equilibrium
• Accurate contact resolution for flat, curved, and sharp geometries

Innovation

• Midplane based unbiased segment-to-segment contact
• Single pass penalty method for traction equilibrium
• Accurate geometric handling for 3D contact scenarios