Article
Engineering, Multidisciplinary
Recep Emre Erkmen, Daniel Dias-da-Costa
Summary: This article investigates the performance of the XFEM for stiff embedded interfaces and inclusions, proposing a variational consistent method to overcome oscillatory behavior and ill-conditioning. The new approach is shown to be efficient and general at both element and structural levels.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Mathematics, Interdisciplinary Applications
Xiaofu Li, Zhi Zhang, Chuanpeng Ji, Hu Chen
Summary: This work proposes a combined finite-discrete element method that uses DE particles in specific regions and FE meshes in remaining regions to achieve computational efficiency. The coupling between FE and DE domains at the interface is achieved through the use of Lagrange multiplier method, addressing issues such as degree of freedom difference and material overlapping. Numerical examples demonstrate the effectiveness of this approach for similar and dissimilar materials.
COMPUTATIONAL PARTICLE MECHANICS
(2023)
Article
Mathematics, Applied
Hiroki Ishizaka, Kenta Kobayashi, Ryo Suzuki, Takuya Tsuchiya
Summary: This paper discusses the importance of the maximum angle condition in error analysis of Lagrange interpolation on tetrahedrons, and presents an equivalent geometric condition as a replacement for the maximum angle condition.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Junkai Wang, Qiaolin He
Summary: In this paper, a dimensionless model for pure-component two-phase compressible flows is derived with Van der Waals equation of state and generalized Navier boundary condition. Three energy-stable numerical schemes are proposed, one based on the scalar auxiliary variable (SAV) approach and the other based on the Lagrange multiplier approach. Numerical results are presented to demonstrate the effectiveness of the proposed methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Materials Science, Multidisciplinary
Kui Liu, Ang Zhao, Zhendong Hu
Summary: The fat boundary method (FBM), a fictitious domain method proposed for Poisson problems with small perforations, can achieve higher accuracy around holes. Despite strict restrictions on the original FBM, this article attempts to break these limitations and apply the method to elasticity by introducing Neumann boundary conditions and proposing a dual fat boundary method. The conditional convergence of the algorithm is mathematically proven and compared with the Lagrange multiplier method to show that FBM is a weak imposition method.
MATHEMATICS AND MECHANICS OF SOLIDS
(2021)
Article
Computer Science, Interdisciplinary Applications
Kirill Goncharuk, Oz Oshri, Yuri Feldman
Summary: A novel formulation of the direct forcing immersed boundary (IB) method is presented, which treats it as an integral part of a SIMPLE method for simulating incompressible flows. The incompressibility and no-slip kinematic constraints are treated implicitly as distributed Lagrange multipliers and are fully coupled with each other. The developed methodology shows promising capabilities in simulating shear-and buoyancy-driven confined flows with stationary immersed bodies.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jacobus D. Brandsen, Axelle Vire, Sergio R. Turteltaub, Gerard J. W. Van Bussel
Summary: This paper evaluates the penalty and Lagrange multiplier methods for enforcing the no-slip condition in fluid-structure interaction simulations. The Lagrange multiplier method provides accurate solutions without parameter tuning, but at a higher computational cost. The penalty method can achieve similar accuracy, but requires selecting the appropriate penalty factor.
ENGINEERING COMPUTATIONS
(2021)
Article
Engineering, Civil
Kaveh Salmalian, Ali Alijani, Habib Ramezannejad Azarboni
Summary: The research applied two energy-based techniques, Lagrange multiplier and conversion matrix, to incorporate crack parameters into the non-linear finite element relations of Euler-Bernoulli beams made of functionally graded materials. The techniques were used to enrich secant and tangent stiffness matrices and address issues in cracked structures. Case studies were conducted to evaluate results in the post-buckling analysis of cracked functionally graded material columns under mechanical and thermal loads.
PERIODICA POLYTECHNICA-CIVIL ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Amir Latifaghili, Milad Bybordiani, Recep Emre Erkmen, Daniel Dias-da-Costa
Summary: The generalized finite element method has shown efficiency in handling crack propagation and internal boundaries. A novel approach based on enrichment Laplace shape functions effectively eliminates sources of oscillations, with excellent agreement with experimental/numerical data in structural examples with highly stiff cracks.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Huangcheng Fang, Dingli Zhang, Mozhen Zhou, Qian Fang, Ming Wen, Xinyu Hu
Summary: In this article, a virtual interface-coupled technique is proposed for modeling three-dimensional contact behaviors of nonconforming interfaces. The method constructs an approximation of the displacement field by introducing enriched nodes and imposes the connection between virtual interface and discontinuous interface using the dual Lagrange multiplier method. The proposed method provides an effective, robust, and fast way to simulate arbitrary discontinuous interfaces in XFEM.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Polymer Science
Sorin Vlase, Marin Marin
Summary: This paper investigates the dynamic analysis of micropolar materials with voids, establishing equations of motion and using the finite element method. The Euler-Lagrangian formalism, along with expressions of kinetic energy, potential energy, and mechanical work, allows for studying the dynamic response of the system in the most general configuration case.
Article
Computer Science, Interdisciplinary Applications
Jae-Hoon Choi, Byung-Chai Lee, Gi-Dong Sim
Summary: A new mixed tetrahedral element based on the Lagrange multiplier is developed for the modified couple stress theory in this paper. By condensing out the Lagrange multipliers and introducing higher-order rotation modes, the total number of degrees of freedom is greatly reduced, maximizing computational efficiency.
COMPUTERS & STRUCTURES
(2021)
Article
Engineering, Multidisciplinary
Carolin Birk, Maximilian Reichel, Joerg Schroeder
Summary: In this work, a hybrid SBFEM-FEM approach is proposed for efficient calculation of magnetic stray fields in unbounded domains. The method divides the entire domain into finite and infinite sub-regions, models the interior domain using finite elements, reduces the exterior domain onto the boundary of the interior domain using SBFEM, and provides a semi-analytical solution for the magnetostatic problem in an unbounded domain.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mathematics, Applied
Daniele Boffi, Andrea Cangiani, Marco Feder, Lucia Gastaldi, Luca Heltai
Summary: This paper systematically compares various numerical schemes for approximating interface problems, focusing on implementation aspects and analyzing the costs of different simulation phases.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Ramon Macedo Correa, Marcos Arndt, Roberto Dalledone Machado
Summary: The Modified Local Green's Function Method (MLGFM) is an integral method that uses Green's function projections, determined by Finite Element Method, as fundamental solution to solve problems. This paper proposes an alternative formulation to the MLGFM that reduces computational effort by avoiding the need for obtaining these projections. The new formulation presents the same accuracy as the previous one and is applied to problems in solid mechanics and compared with the standard Finite Element Method and the Boundary Element Method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Mechanics
Andrew J. Stershic, John E. Dolbow, Nicolas Moes
ENGINEERING FRACTURE MECHANICS
(2017)
Article
Mechanics
A. Parrilla Gomez, C. Stolz, N. Moes, D. Gregoire, G. Pijaudier-Cabot
ENGINEERING FRACTURE MECHANICS
(2017)
Article
Mechanics
Benoit Le, Nicolas Moes, Gregory Legrain
ENGINEERING FRACTURE MECHANICS
(2018)
Article
Engineering, Multidisciplinary
G. Legrain, N. Moes
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2018)
Article
Materials Science, Multidisciplinary
J. Zghal, K. Moreau, N. Moes, D. Leguillon, C. Stolz
INTERNATIONAL JOURNAL OF FRACTURE
(2018)
Article
Nanoscience & Nanotechnology
Baptiste Reyne, Pierre-Yves Manach, Nicolas Moes
MATERIALS SCIENCE AND ENGINEERING A-STRUCTURAL MATERIALS PROPERTIES MICROSTRUCTURE AND PROCESSING
(2019)
Article
Mathematics, Interdisciplinary Applications
Marie Gorecki, Guillaume Peillex, Laurianne Pillon, Nicolas Moes
COMPUTATIONAL MECHANICS
(2020)
Article
Engineering, Mechanical
Baptiste Reyne, Nicolas Moes, Pierre-Yves Manach
INTERNATIONAL JOURNAL OF PLASTICITY
(2020)
Article
Engineering, Multidisciplinary
Zoltan Csati, Nicolas Moes, Thierry J. Massart
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Mathematics, Applied
T. Tiirats, N. Chevaugeon, N. Moes, C. Stolz, N. Marouf, E. Desdoit
FINITE ELEMENTS IN ANALYSIS AND DESIGN
(2020)
Editorial Material
Mechanics
L. De Lorenzis, O. Allix, M. Jirasek, N. Moes
ENGINEERING FRACTURE MECHANICS
(2021)
Correction
Materials Science, Multidisciplinary
Vasudevan Kamasamudram, Michel Coret, Nicolas Moes
INTERNATIONAL JOURNAL OF FRACTURE
(2021)
Article
Materials Science, Multidisciplinary
Vasudevan Kamasamudram, Michel Coret, Nicolas Moes
Summary: The investigation of dynamic fracture of elastomers is still considered an open area, with a focus on understanding transonic cracks and the impact of material properties on wave speeds. The experiments on Polyurethane elastomers suggest that viscoelasticity in the bulk material is crucial for describing and understanding transonic cracks, leading to the definition of the transonic regime based on rubbery wave speeds.
INTERNATIONAL JOURNAL OF FRACTURE
(2021)
Article
Astronomy & Astrophysics
Jihed Zghal, Nicolas Moes
COMPTES RENDUS PHYSIQUE
(2020)
Article
Engineering, Multidisciplinary
Kevin Moreau, Nicolas Moes, Nicolas Chevaugeon, Alexis Salzman
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2017)