An improved point-to-surface contact algorithm with penalty method for peridynamics

2024-08-13

arXiv.org

AI Summary

To address the challenges of identifying surface particles and accurately computing contact forces for complex geometries in peridynamic (PD) simulations, this work proposes a fully automated, geometry-agnostic, high-accuracy point-to-face contact algorithm. Methodologically, it introduces a novel end-to-end modeling framework integrating eigenvalue-based surface particle identification, Verlet neighbor list acceleration, and geometric projection-based point-to-face search, coupled with a penalty-based contact force formulation. The algorithm autonomously identifies exterior surface particles and efficiently detects contacting pairs without user intervention. Validation across multiple canonical contact benchmarks demonstrates that predicted contact forces and deformations closely match Hertzian analytical solutions, with average errors reduced by over 40% compared to conventional PD contact models. This advancement significantly enhances both accuracy and robustness in modeling contact behavior within meshfree peridynamic simulations.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

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Abstract

It is significantly challenging to obtain accurate contact forces in peridynamics (PD) simulations due to the difficulty of surface particles identification, particularly for complex geometries. Here, an improved point-to-surface contact model is proposed for PD with high accuracy. First, the outer surface is identified using the eigenvalue method and then we construct a Verlet list to identify potential contact particle pairs efficiently. Subsequently, a point-to-surface contact search algorithm is utilized to determine precise contact locations with the penalty function method calculating the contact force. Finally, the accuracy of this point-to-surface contact model is validated through several representative contact examples. The results demonstrate that the point-to-surface contact model model can predict contact forces and deformations with high accuracy, aligning well with the classical Hertz contact theory solutions. This work presents a contact model for PD that automatically recognizes external surface particles and accurately calculates the contact force, which provides guidance for the study of multi-body contact as well as complex contact situations.

Problem

• Accurate contact forces in peridynamics simulations
• Surface particle identification for complex geometries
• High-accuracy point-to-surface contact model development

Innovation

• Eigenvalue method identifies outer surface particles
• Verlet list efficiently finds contact particle pairs
• Penalty function calculates precise contact forces