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Fast computational method for Hertzian contact theory is proposed. An incremental formula is introduced to calculate the ellipticity of the contact disk when two elastic bodies are in contact. This method can determine the ellipticity with…

Classical Physics · Physics 2026-01-22 Shintaro Hokada , Shunsuke Iizuka , Satoshi Takada

We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The…

Numerical Analysis · Mathematics 2016-01-20 Andre Massing , Mats G. Larson , Anders Logg , Marie E. Rognes

In this paper, we propose an efficient numerical treatment for solving contact problems with friction between deformable bodies. The discretized normal and tangential constraints at the candidate contact interface are expressed by using…

Numerical Analysis · Mathematics 2007-05-23 Laurent Baillet , Taoufik Sassi

With the increasing demand for the accuracy of numerical simulation of pavement mechanics, the variational inequality model and its induced finite element method which can simulate the interlayer contact state becomes a potential solution.…

Numerical Analysis · Mathematics 2024-06-10 Zhizhuo Zhang , Xiaobing Nie , Mikaël Barboteu , Jinde Cao

In recent years, a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on non-matching or overlapping meshes. Examples of such methods include the fictitious…

Numerical Analysis · Mathematics 2012-10-29 André Massing , Mats G. Larson , Anders Logg

In this work, we design and analyze a Discrete de Rham (DDR) scheme for a contact mechanics problem involving fractures along which a model of Tresca friction is considered. Our approach is based on a mixed formulation involving a…

Numerical Analysis · Mathematics 2026-04-08 Jerome Droniou , Raman Kumar , Roland Masson , Ritesh Singla

This paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems, and…

Numerical Analysis · Mathematics 2018-10-05 Tao Wang , Chaochao Yang , Xiaoping Xie

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

This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an…

Numerical Analysis · Mathematics 2018-06-04 Chao Chao Yang , Tao Wang , Xiaoping Xie

An equilibrium of a linear elastic body subject to loading and satisfying the friction and contact conditions can be described by a variational inequality of the second kind and the respective discrete model attains the form of a…

Optimization and Control · Mathematics 2021-03-04 Helmut Gfrerer , Jiri V. Outrata , Jan Valdman

Low-rank model order reduction strategies for contact mechanics show limited dimensionality reduction due to linear inseparability of contact pressure field. Therefore, a dictionary based strategy is explored for creating efficient models…

Numerical Analysis · Mathematics 2024-06-18 Kiran Sagar Kollepara , José V. Aguado , Yves Le Guennec , Luisa Silva , Domenico Borzacchiello

This paper proposes a deep unfitted Nitsche method for computing elliptic interface problems with high contrasts in high dimensions. To capture discontinuities of the solution caused by interfaces, we reformulate the problem as an energy…

Numerical Analysis · Mathematics 2022-08-12 Hailong Guo , Xu Yang

The Nitsche method is a method of "weak imposition" of the inhomogeneous Dirichlet boundary conditions for partial differential equations. This paper explains stability and convergence study of the Nitsche method applied to evolutionary…

Numerical Analysis · Mathematics 2018-03-28 Yuki Ueda , Norikazu Saito

We present a newly developed approach for the calculation of interfacial stiffness and contact area evolution between two rough bodies exhibiting self affine surface structures. Using spline assisted discretization to define localised…

Soft Condensed Matter · Physics 2021-06-04 Dorian Hanaor , Yixiang Gan , Itai Einav

In this paper, we consider a dynamic viscoelastic contact problem with friction and wear, and describe it as a system of nonlinear partial differential equations. We formulate the previous problem as a hyperbolic quasi-variational…

Optimization and Control · Mathematics 2019-10-10 Tao Chen , Nan-jing Huang , Yi-bin Xiao

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

Numerical Analysis · Mathematics 2025-12-04 Wei Li , Alberto F. Martín , Santiago Badia

We show that in the variational multiscale framework, the weak enforcement of essential boundary conditions via Nitsche's method corresponds directly to a particular choice of projection operator. The consistency, symmetry and penalty terms…

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

We investigate a quasi-static-antiplane contact problem, examining a thermo-electro-visco-elastic material with a friction law dependent on the slip rate, assuming that the foundation is electrically conductive. The mechanical problem is…

Analysis of PDEs · Mathematics 2024-02-06 Besma Fadlia , Mohamed Dalah , Delfim F. M. Torres

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