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A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…

Computational Engineering, Finance, and Science · Computer Science 2025-04-03 Jacopo Bonari , Maria R. Marulli , Nora Hagmeyer , Matthias Mayr , Alexander Popp , Marco Paggi

A highly accurate, single-pass, unbiased frictional contact algorithm for higher-order elements based on the concept of midplane is presented. Higher-order elements offer a lucrative choice for contact problems as they can better represent…

Computational Physics · Physics 2025-06-30 Indrajeet Sahu , Nik Petrinic

Finite element methods are used to study non-adhesive, frictionless contact between elastic solids with self-affine surfaces. We find that the total contact area rises linearly with load at small loads. The mean pressure in the contact…

Materials Science · Physics 2009-11-10 S. Hyun , L. Pei , J. -F. Molinari , M. O. Robbins

When two surfaces are brought into contact and slide against each other, junctions are formed at the interface. The dynamics of formation, rupture and evolution of these junctions governs the tribological response of the macro-contact.…

Soft Condensed Matter · Physics 2022-05-26 Vipul Vijigiri , Cedric Courbon , Guillaume Kermouche , Juliette Cayer-Barrioz

Contact and related phenomena, such as friction, wear or elastohydrodynamic lubrication, remain as one of the most challenging problem classes in nonlinear solid and structural mechanics. In the context of their computational treatment with…

Computational Engineering, Finance, and Science · Computer Science 2021-11-30 Alexander Popp , Ivo Steinbrecher

Real applications in structural mechanics, where the dynamic behavior is linear, are rare. Usually, structures are made of components assembled together by means of joints whose behavior maybe highly nonlinear. Depending on the amount of…

Dynamical Systems · Mathematics 2018-11-26 Stefano Zucca , Christian M. Firrone

Controlling the shape of deformable linear objects using robots and constraints provided by environmental fixtures has diverse industrial applications. In order to establish robust contacts with these fixtures, accurate estimation of the…

Robotics · Computer Science 2024-01-31 Kejia Chen , Zhenshan Bing , Yansong Wu , Fan Wu , Liding Zhang , Sami Haddadin , Alois Knoll

The Finite Elements with Switch Detection (FESD) is a high-accuracy method for the numerical simulation and solution of optimal control problems subject to discontinuous ODEs. In this article, we extend the FESD method [Nurkanovi\'c et al.,…

Optimization and Control · Mathematics 2023-05-29 Armin Nurkanović , Jonathan Frey , Anton Pozharskiy , Moritz Diehl

Frictional properties of interfaces with dynamic chemical bonds have been the subject of intensive experimental investigation and modeling, as it provides important insights into the molecular origin of the empirical rate and state laws,…

Mesoscale and Nanoscale Physics · Physics 2020-01-24 Wengen Ouyang , Yao Cheng , Ming Ma , Michael Urbakh

We consider the elasticity problem in a %heterogeneous domain with contact on multiple periodic open cracks. The contact is described by the Signorini and Coulomb-friction conditions. Problem is non-linear, the dissipative functional…

Analysis of PDEs · Mathematics 2020-01-08 G. Griso , J. Orlik

We introduce a PDE-based node-to-element contact formulation as an alternative to classical, purely geometrical formulations. It is challenging to devise solutions to nonsmooth contact problem with continuous gap using finite element…

Numerical Analysis · Mathematics 2023-02-28 P. Areias , N. Sukumar , J. Ambrósio

The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…

Computational Physics · Physics 2012-02-20 J. E. Sprittles , Y. D. Shikhmurzaev

With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent…

Numerical Analysis · Mathematics 2024-09-11 Zhizhuo Zhang , Mikaël Barboteu , Xiaobing Nie , Serge Dumont , Mahmoud Abdel-Aty , Jinde Cao

Continuum robots offer high flexibility and multiple degrees of freedom, making them ideal for navigating narrow lumens. However, accurately modeling their behavior under large deformations and frequent environmental contacts remains…

Robotics · Computer Science 2025-03-11 Hao Chen , Jian Chen , Xinran Liu , Zihui Zhang , Yuanrui Huang , Zhongkai Zhang , Hongbin Liu

In this paper, we study, from both variational and numerical points of view, a dynamic contact problem between a viscoelastic-viscoplastic piezoelectric body and a deformable obstacle. The contact is modelled using the classical normal…

Analysis of PDEs · Mathematics 2017-03-14 M. Campo , J. R. Fernández , Á. Rodríguez-Arós , J. M. Rodríguez

Frictional sliding contact in hydrodynamic environments can be found in a range of engineering applications. Accurate modeling requires an integrated numerical framework capable of resolving large relative motions, multiphase interactions,…

Computational Physics · Physics 2025-10-01 Biswajeet Rath , Rajeev K. Jaiman

The damping of built-up structures stems largely from the microscopic dry frictional interactions in the contact interfaces. The accurate prediction of friction damping has been an important scientific aim of the past several decades.…

Systems and Control · Electrical Eng. & Systems 2025-07-17 Hendrik D. Linder , Johann Gross , Malte Krack

This paper presents an analytical study about the behavior of arbitrary shaped and sized non-cohesive two-dimensional granular materials. Several mechanical properties and relations are unraveled by connecting micro and macro scales in an…

Geophysics · Physics 2013-02-06 Alex X. Jerves , José E. Andrade

We introduce a phase-field method for continuous modeling of cracks with frictional contacts. Compared with standard discrete methods for frictional contacts, the phase-field method has two attractive features: (1) it can represent…

Numerical Analysis · Mathematics 2020-01-29 Fan Fei , Jinhyun Choo

In a wide range of practical problems, such as forming operations and impact tests, assuming that one of the contacting bodies is rigid is an excellent approximation to the physical phenomenon. In this work, the well-established dual mortar…

Computational Engineering, Finance, and Science · Computer Science 2022-10-07 R. Pinto Carvalho , A. M. Couto Carneiro , F. M. Andrade Pires , A. Popp