TY - JOUR

T1 - Spline-based smooth beam-to-beam contact model

AU - Faccio Júnior, Celso Jaco

AU - Gay Neto, Alfredo

AU - Wriggers, Peter

N1 - Funding Information: The authors acknowledge the National Council for Scientific and Technological Development (CNPq) under the grants 168927/2018-7 and 304321/2021-4, and the São Paulo Research Foundation (FAPESP) under the grant 2020/13362-1.

PY - 2023/10

Y1 - 2023/10

N2 - The contact between bodies is a complex phenomenon that involves mechanical interaction, frictional sliding and heat transfer, among others. A common (and convenient) approach for the mechanical interaction in a finite element framework is to directly use the geometry of the elements to formulate the contact. The main drawback lies in the sharp corners that occur when straight finite elements are connected leading eventually to contact singularities. To circumvent this issue, particularly in the context of beam-to-beam contact, the present work proposes a pointwise contact formulation based on smooth C1 continuous spline contact elements. The proposed spline-based formulation, which can be directly attached to any quadratic beam finite element formulation, guarantees a smooth description for the whole set of elements, where contact takes place. A specific nonlinear normal contact interaction law and a rheological model for friction, both with elastic and viscous damping contributions, are developed increasing robustness in practical applications. To demonstrate this robustness, specific examples are considered including comparisons with a similar surface-to-surface formulation and an alternative smooth contact scheme, smooth contact with finite elements having sharp corners, modeling of a knot tightening with self-contact, and a simulation involving multiple pointwise contacts.

AB - The contact between bodies is a complex phenomenon that involves mechanical interaction, frictional sliding and heat transfer, among others. A common (and convenient) approach for the mechanical interaction in a finite element framework is to directly use the geometry of the elements to formulate the contact. The main drawback lies in the sharp corners that occur when straight finite elements are connected leading eventually to contact singularities. To circumvent this issue, particularly in the context of beam-to-beam contact, the present work proposes a pointwise contact formulation based on smooth C1 continuous spline contact elements. The proposed spline-based formulation, which can be directly attached to any quadratic beam finite element formulation, guarantees a smooth description for the whole set of elements, where contact takes place. A specific nonlinear normal contact interaction law and a rheological model for friction, both with elastic and viscous damping contributions, are developed increasing robustness in practical applications. To demonstrate this robustness, specific examples are considered including comparisons with a similar surface-to-surface formulation and an alternative smooth contact scheme, smooth contact with finite elements having sharp corners, modeling of a knot tightening with self-contact, and a simulation involving multiple pointwise contacts.

KW - Frictional contact

KW - Nonlinear normal contact

KW - Smooth contact

KW - Spline

UR - http://www.scopus.com/inward/record.url?scp=85151232274&partnerID=8YFLogxK

U2 - 10.1007/s00466-023-02283-1

DO - 10.1007/s00466-023-02283-1

M3 - Article

AN - SCOPUS:85151232274

VL - 72

SP - 663

EP - 692

JO - Computational mechanics

JF - Computational mechanics

SN - 0178-7675

IS - 4

ER -