Mortar contact formulation for hierarchical basis functions using smooth active set strategy

Ignatios Athanasiadis1; Lukasz Kaczmarczyk; Zahur Ullah; Chris J Pearce

Mortar contact formulation for hierarchical basis functions using smooth active set strategy

Ignatios Athanasiadis1, Lukasz Kaczmarczyk, Zahur Ullah, Chris J Pearce

School of Mechanical and Aerospace Engineering

Research output: Contribution to conference › Paper › peer-review

Abstract

This work focuses on 3D modelling of elastic two-body frictionless contact by means of the mortar method for small strains extended for hierarchical shape functions. Surfaces of two bodies discretised by tetrahedral elements are denoted as master and slave surfaces. When two triangular faces of tetrahedral elements are candidates for contact, with one face belonging to the master and the other to the slave surface, they are used to create a special prism element. These prisms are used as integration domains to solve the contact problem. For a given prism configuration, triangular faces can either be in contact or form a gap denoting an active or passive state, respectively. This state is determined by evaluation of the complementarity function proposed in [1], that is modified in the present work to yield a smooth Newton algorithm. Finally, results for sphere-to-sphere Hertz contact are compared to analytical solution for different orders of approximation.

Original language	English
Publication status	Published - 10 Apr 2019
Event	UK Association for Computational Mechanics Conference - City, University of London, London, United Kingdom Duration: 10 Apr 2019 → 12 Apr 2019 http://ukacm.org

Conference

Conference	UK Association for Computational Mechanics Conference
Country	United Kingdom
City	London
Period	10/04/2019 → 12/04/2019
Internet address	http://ukacm.org

Keywords

Mortar Contact
Smooth Active Set
Hierarchical Basis Functions

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title = "Mortar contact formulation for hierarchical basis functions using smooth active set strategy",

abstract = "This work focuses on 3D modelling of elastic two-body frictionless contact by means of the mortar method for small strains extended for hierarchical shape functions. Surfaces of two bodies discretised by tetrahedral elements are denoted as master and slave surfaces. When two triangular faces of tetrahedral elements are candidates for contact, with one face belonging to the master and the other to the slave surface, they are used to create a special prism element. These prisms are used as integration domains to solve the contact problem. For a given prism configuration, triangular faces can either be in contact or form a gap denoting an active or passive state, respectively. This state is determined by evaluation of the complementarity function proposed in [1], that is modified in the present work to yield a smooth Newton algorithm. Finally, results for sphere-to-sphere Hertz contact are compared to analytical solution for different orders of approximation.",

keywords = "Mortar Contact, Smooth Active Set, Hierarchical Basis Functions",

author = "Ignatios Athanasiadis1 and Lukasz Kaczmarczyk and Zahur Ullah and Pearce, {Chris J}",

year = "2019",

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language = "English",

note = "UK Association for Computational Mechanics Conference ; Conference date: 10-04-2019 Through 12-04-2019",

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TY - CONF

T1 - Mortar contact formulation for hierarchical basis functions using smooth active set strategy

AU - Athanasiadis1, Ignatios

AU - Kaczmarczyk, Lukasz

AU - Ullah, Zahur

AU - Pearce, Chris J

PY - 2019/4/10

Y1 - 2019/4/10

N2 - This work focuses on 3D modelling of elastic two-body frictionless contact by means of the mortar method for small strains extended for hierarchical shape functions. Surfaces of two bodies discretised by tetrahedral elements are denoted as master and slave surfaces. When two triangular faces of tetrahedral elements are candidates for contact, with one face belonging to the master and the other to the slave surface, they are used to create a special prism element. These prisms are used as integration domains to solve the contact problem. For a given prism configuration, triangular faces can either be in contact or form a gap denoting an active or passive state, respectively. This state is determined by evaluation of the complementarity function proposed in [1], that is modified in the present work to yield a smooth Newton algorithm. Finally, results for sphere-to-sphere Hertz contact are compared to analytical solution for different orders of approximation.

AB - This work focuses on 3D modelling of elastic two-body frictionless contact by means of the mortar method for small strains extended for hierarchical shape functions. Surfaces of two bodies discretised by tetrahedral elements are denoted as master and slave surfaces. When two triangular faces of tetrahedral elements are candidates for contact, with one face belonging to the master and the other to the slave surface, they are used to create a special prism element. These prisms are used as integration domains to solve the contact problem. For a given prism configuration, triangular faces can either be in contact or form a gap denoting an active or passive state, respectively. This state is determined by evaluation of the complementarity function proposed in [1], that is modified in the present work to yield a smooth Newton algorithm. Finally, results for sphere-to-sphere Hertz contact are compared to analytical solution for different orders of approximation.

KW - Mortar Contact

KW - Smooth Active Set

KW - Hierarchical Basis Functions

M3 - Paper

T2 - UK Association for Computational Mechanics Conference

Y2 - 10 April 2019 through 12 April 2019

ER -