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Boundary Element Method

Over the past decades, the Boundary Element Method (BEM) has been used for the analysis of various engineering problems. For some applications, it has become a strong alternative to the Finite Element Method (FEM). In recent years, the Boundary Element Method has evolved to become the most efficient numerical technique in the field of Contact Mechanics where it is used with great success for the simulation of rough surfaces and adhesive contacts. The high efficiency of the method in this field stems from the fact that the boundary integrals over a half-space surface simplify to two-dimensional convolutions which can easily and rapidly be evaluated with the Fast Fourier Transformation (FFT). This FFT-based BEM has set new standards in recent years, becoming the method of choice both in academic and industrial research and development.

At the Department of System Dynamics and Friction Physics, efficient implementations of the FFT-based BEM have been developed which allow to run highly advanced studies. An exemplary project can be found in the 2017 special issue of Friction (see on the right).

The developed tools are at the foundation of several partnerships of the department with the industry, ranging from the automotive to the aerospace sector. The FFT-based BEM is continuously enhanced at the department and has so far been extended for the simulation of adhesion, power-law graded materials, and layered materials (see exemplary publications below).

Lupe [2]

Strength of adhesive contacts: Influence of contact geometry and material gradients [3]

Valentin L. Popov, Roman Pohrt, Qiang Li

Friction, vol. 5, no. 3, pp. 308–325, 2017

Lupe [5]

Adhesive contact simulation of elastic solids using local mesh-dependent detachment criterion in Boundary Elements Method [6]

R. Pohrt, V. L. Popov

Facta Universitatis, Series: Mechanical Engineering, vol. 13, no. 1, pp. 1-10, 2015

Lupe [8]

Complete Boundary Element formulation for normal and tangential contact problems [9]

R. Pohrt, Q. Li

Physical Mesomechanics, vol. 17, no. 4, pp. 334-340, 2014

Lupe [11]

Boundary Element Method for normal non-adhesive and adhesive contacts of power-law graded elastic materials [12]

Q. Li, V. L. Popov

Computational Mechanics, vol. 61, no. 3, pp. 319-329, 2018

Lupe [14]

Boundary Element Method for nonadhesive and adhesive contacts of a coated elastic half-space [15]

Q. Li, R. Pohrt, I. A. Lyashenko, V. L. Popov

Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, vol. 234, no. 1, pp. 73-83, 2020

Future visions of the department with regard to the Boundary Element Method include the extension of the FFT-based BEM in order to create even more versatile and powerful simulation tools. Not only do we expect that such improvements will lead to new discoveries in the area of Contact Mechanics and Friction, but we also believe that they will greatly enhance many industrial applications, allowing the design of safer, more energy efficient, and environmentally friendlier products. A particular benefit may be the positive impact such highly advanced computational techniques can have with regard to current automation trends in manufacturing (Industry 4.0).

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