An Embedded Mesh Approach for Isogeometric Boundary Layers in Contact Mechanics

2026-03-02

AI Summary

This work addresses the challenge of mesh compatibility arising from the coupled discretization of interfaces and bulk domains in contact mechanics. The authors propose a decoupled discretization approach that employs a NURBS-based boundary layer mesh, constructed directly from CAD boundary representations, to accurately capture the contact interface, while the bulk domain is discretized using a structured Cartesian grid. Non-matching meshes are coupled across scales via mortar-type embedded constraints. This method represents the first formulation that decouples isogeometric boundary layers from structured volume meshes, enabling independent optimization of element type and resolution for both interface and bulk domains. Consequently, it preserves high-order smoothness along the contact surface while significantly enhancing geometric accuracy, computational efficiency, and modeling flexibility.

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• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
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Abstract

This paper proposes a novel discretization workflow for contact problems in which the discretization of the contact interface is decoupled from that of the bulk domain. This separation enables independently tailored meshes for the contact interface and the bulk volume, allowing local requirements--such as element type and mesh resolution--to be addressed efficiently. Exploiting the boundary representation of CAD models, the contact interface of each body is discretized using a NURBS-based boundary layer mesh. This provides a smooth geometric description of the contact surface and enhanced inter-element continuity. The bulk domain is discretized using a structured Cartesian grid. To couple the resulting non-matching discretizations, an embedded mesh approach based on a mortar-type constraint formulation is employed. The paper describes in detail the proposed discretization workflow for generating both the isogeometric boundary layer and the structured Cartesian grid, and presents several strategies for constructing NURBS-based boundary layer meshes. Finally, a set of numerical examples is provided to validate the proposed approach.

Problem

• contact mechanics
• isogeometric boundary layer
• embedded mesh
• non-matching discretization
• NURBS

Innovation

• embedded mesh
• isogeometric boundary layer
• contact mechanics
• NURBS
• mortar coupling