Article
Engineering, Multidisciplinary
Simon Essongue, Guillaume Couegnat, Eric Martin
Summary: This article investigates the convergence properties of the augmented finite element method (AFEM), showing that it converges with an error of O(h^0.5) in the energy norm. The AFEM has the advantage of not introducing additional global unknowns compared to other partition of unity methods, and is on par with the finite element method for certain homogenization problems.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Mathematics, Applied
Xuyang Na, Xuejun Xu
Summary: This paper presents a nonoverlapping domain decomposition method for Stokes equations using mixed finite elements with discontinuous pressures. Both conforming and nonconforming finite element spaces are considered for velocities. By employing Robin boundary conditions, the indefinite Stokes problem is reduced to a positive definite problem for the interface Robin transmission data. A new preconditioner for the Stokes problem is proposed based on the Robin-type domain decomposition method, with numerical results provided to support the theoretical findings.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mechanics
Simon Essongue, Guillaume Couegnat, Eric Martin
Summary: This paper investigates the accuracy and convergence properties of the augmented finite element method (AFEM), which is used to model strong discontinuities independently of the underlying mesh without introducing additional global unknowns to represent cracks. The numerical 2D experiments show that AFEM outperforms other methods when cracks are loaded in Mode I.
ENGINEERING FRACTURE MECHANICS
(2021)
Article
Engineering, Multidisciplinary
Vedad Tojaga, Artem Kulachenko, Soren Ostlund, T. Christian Gasser
Summary: A new elastoplastic Timoshenko beam finite element method with embedded discontinuities has been developed to model fiber failures in random fiber networks. The formulation accounts for a fracture process zone in the bulk material and retains traction continuity across the discontinuity. The method proposes a quasi-brittle fracture model and neglects fracture-related softening to maintain the positive definite finite element stiffness matrix of the bulk material.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Engineering, Multidisciplinary
Serafeim Bakalakos, Manolis Georgioudakis, Manolis Papadrakakis
Summary: The extended finite element method (XFEM) has been successfully applied to solve crack propagation problems without remeshing. However, the enrichment in XFEM leads to ill-conditioned algebraic systems and slow convergence of iterative solvers. In this paper, two efficient domain decomposition solvers, FETI-DP and P-FETI-DP, are proposed for large-scale 3D XFEM crack propagation analysis, offering parallelization and reduced computational time.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Materials Science, Multidisciplinary
Yu Foong Lam, Taufiq Abdullah, Kedar Kirane
Summary: This work investigates the relationship between dynamic crack penetration and deflection at a material interface for materials with strain rate dependent damage evolution. A strain rate dependent continuum damage mechanics (CDM) model is used to analyze the behavior, where the material point softening damage law scales with the strain rate. The model is calibrated and validated with experimental data, and shows good prediction of crack behavior. It is found that the local strain rates at the interface significantly affect the bulk and interface strengths and toughnesses, resulting in increased crack penetration. Boundary conditions also play a significant role in predicting cracking behavior.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2023)
Article
Mathematics, Applied
Manu Jayadharan, Michel Kern, Martin Vohrali, Ivan Yotov
Summary: We propose a space-time mortar mixed finite element method for parabolic problems, which handles nonmatching spatial grids and asynchronous time steps. This method combines mixed finite elements and discontinuous Galerkin method, and enforces continuity of flux across space-time interfaces via a coarse-scale mortar variable. We establish uniqueness, existence, stability, and error estimates for the spatial and temporal errors. Additionally, we develop a space-time nonoverlapping domain decomposition method that reduces the global problem to a coarse-scale mortar interface problem, solving parallel subdomain problems at each interface iteration. The numerical experiments demonstrate the theoretical results and the flexibility of the method in modeling localized space-time features.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2023)
Article
Mechanics
Soheil Niknafs, Mohammad Silani, Franco Concli, Ramin Aghababaei
Summary: This paper introduces a concurrent multiscale method for modeling crack propagation, which combines the continuum finite element domain with a coarse-grained atomistic potential. This method effectively captures crack formation while reducing computational costs.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2022)
Article
Mechanics
Soheil Niknafs, Mohammad Silani, Franco Concli, Ramin Aghababaei
Summary: This paper introduces a novel method for modeling crack propagation in brittle solids, by coupling the continuum finite element domain with coarse-grained atomistic potential to suppress dislocation nucleation, thereby increasing computational efficiency.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2022)
Article
Computer Science, Interdisciplinary Applications
Matthias Mayr, Alexander Popp
Summary: This paper presents computational kernels for efficient computations in mortar finite element methods on parallel hardware architectures. By addressing bottlenecks in parallel data layout and domain decomposition, the paper proposes computational strategies to optimize parallel communication and scalability for the evaluation of mortar terms. The proposed algorithms have been demonstrated to have strong and weak scalability in three-dimensional contact mechanics simulations, and improvements in parallel communication related to mortar finite element methods have been studied and discussed. Additionally, dynamic load balancing has been successfully applied to mortar contact problems with evolving contact zones to achieve balanced computational work among parallel processors.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mathematics, Applied
Jiangyong Hou, Dan Hu, Xuejian Li, Xiaoming He
Summary: In this paper, a steady state Dual-Porosity-Navier-Stokes model is proposed and analyzed. A domain decomposition method is developed for efficiently solving this complex system. The convergence of the method with finite element discretization is analyzed and the effect of Robin parameters on the convergence is investigated. Numerical experiments are presented to verify the theoretical conclusions, illustrate the practical use of the model and method, and show their features.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Engineering, Multidisciplinary
Anthony Royer, Christophe Geuzaine, Eric Bechet, Axel Modave
Summary: This work presents a non-overlapping substructured DDM with PML transmission conditions for checkerboard decompositions, considering cross-points. The continuity of Dirichlet traces is enforced at the interfaces between subdomains and PMLs using Lagrange multipliers, allowing for the computation of Neumann traces and the use of PMLs as discrete operators approximating the exact Dirichlet-to-Neumann maps.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Wei Tian, Xingding Chen, Jingjing Huang, Rongliang Chen
Summary: In this paper, a domain decomposition based preconditioning method is proposed to accelerate the Krylov subspace method for solving linear systems arising from the extended finite element discretization of dynamic crack problems. The method partitions the finite element mesh into regular subdomains and crack tip subdomains, and constructs an additive Schwarz preconditioner by solving submatrices in the crack tip subdomains exactly and in the regular subdomains inexactly. The method also updates the subdomain problems as the crack propagates and uses an auxiliary subproblem for a better initial guess.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Acoustics
Juliette Chabassier, Roman Auvray
Summary: This article investigates the computation of modal expression parameters for the input impedance and input admittance of wind instruments. The Telegrapher equations with radiating boundary conditions and one-dimensional finite elements are used for spatial discretization. By solving a generalized eigenvalue problem, the modal parameters can be directly computed, taking into account viscothermal effects and open/closed toneholes. Modal shapes can also be visualized along the instrument.
JOURNAL OF SOUND AND VIBRATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Humberto Breves Coda
Summary: Flory's decomposition is used to write hyperelastic constitutive models, but this study introduces it for plastic flow directions in elastoplastic models. The proposed total Lagrangian elastoplastic framework offers a simple implementation with good response.
COMPUTATIONAL MECHANICS
(2022)
Article
Engineering, Multidisciplinary
Emma Lejeune, Christian Linder
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2020)
Article
Engineering, Multidisciplinary
Berkin Dortdivanlioglu, Nil Ezgi Dincer Yilmaz, K. B. Goh, Xiaolin Zheng, Christian Linder
Summary: This study investigates the formation and transient growth of interface creases in bilayer hydrogels through experimental and computational approaches. It shows that both the equilibrium and transient characteristics of interface creases can be tuned by controlling the material properties. The computational results demonstrate that the formation of creases is energetically more favorable than wrinkle formation at the interface, in agreement with experimental observations.
JOURNAL OF ELASTICITY
(2021)
Article
Engineering, Electrical & Electronic
Weichen Wang, Sihong Wang, Reza Rastak, Yuto Ochiai, Simiao Niu, Yuanwen Jiang, Prajwal Kammardi Arunachala, Yu Zheng, Jie Xu, Naoji Matsuhisa, Xuzhou Yan, Soon-Ki Kwon, Masashi Miyakawa, Zhitao Zhang, Rui Ning, Amir M. Foudeh, Youngjun Yun, Christian Linder, Jeffrey B. -H. Tok, Zhenan Bao
Summary: The study demonstrates an all-elastomer strain engineering approach to create strain-insensitive intrinsically stretchable transistor arrays, achieving stable performance by adjusting stiffness through patterned elastomer layers. This method is suitable for developing devices for monitoring physiological signals with intimate interfaces to the human body.
NATURE ELECTRONICS
(2021)
Article
Electrochemistry
Xiaoxuan Zhang, Markus Klinsmann, Sergei Chumakov, Xiaobai Li, Sun Ung Kim, Michael Metzger, Munir M. Besli, Reinhardt Klein, Christian Linder, Jake Christensen
Summary: This study investigates the coupling between mechanical deformation and electrochemical response in battery cells, proposing a coupled electrochemomechanical model and verifying its effectiveness through simulations. The results demonstrate that mechanical effects significantly impact the electrochemical response of the cell at high charge/discharge rates.
JOURNAL OF THE ELECTROCHEMICAL SOCIETY
(2021)
Article
Materials Science, Multidisciplinary
Prajwal Kammardi Arunachala, Reza Rastak, Christian Linder
Summary: Fracture prediction is crucial for polymers like rubbers, with high extensibility and various applications. The study introduces a criterion based on internal bond energy and crystallization effects to predict fracture initiation in rubber-like materials with pre-existing cracks. The validation of the model's capability in predicting the impact of crystallization on fracture initiation adds to its significance in fracture modeling.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2021)
Article
Mechanics
Arun Raina
Summary: This study experimentally and numerically investigates the quasi-brittle and volume dependent behavior of titanium aluminide (TiAl) alloys, providing insights for new product development and application.
ENGINEERING FRACTURE MECHANICS
(2022)
Article
Materials Science, Multidisciplinary
Arun Raina
Summary: This study investigates the quasi-brittle behavior of intermetallic TiAl alloys experimentally and numerically. The results confirm the size effect in TiAl alloys, with larger volumes exhibiting lower fracture energy density. A novel size effect law based on physically motivated coefficients is proposed, providing a quantitative understanding of the size-dependent fracture energy and a predictive capability for intermetallic alloys.
EXPERIMENTAL MECHANICS
(2022)
Article
Engineering, Multidisciplinary
Sina Abrari Vajari, Matthias Neuner, Prajwal Kammardi Arunachala, Andy Ziccarelli, Gregory Deierlein, Christian Linder
Summary: Phase field models for ductile fracture have been widely studied, but most existing methods only consider the effects of plastic deformation and neglect the multi-axial stress states in practical designs. In this work, a thermodynamically consistent phase field method coupled with finite strain plasticity is proposed to address this issue. The Stress-Weighted Ductile Fracture Model (SWDFM) is utilized to capture the coupling between plasticity and stress states. The excellent performance of the SWDFM in predicting ductile crack initiation motivates its incorporation into the phase field approach for predicting crack initiation and propagation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Mechanics
Matthias Neuner, Richard A. Regueiro, Christian Linder
Summary: In this work, a novel framework for modeling quasi-brittle crack propagation and shear band dominated failure of cohesive-frictional materials is proposed. The framework combines the gradient-enhanced continuum and the micropolar continuum, and is formulated based on the thermodynamically sound theory of hyperelasto-plasticity. The approach is assessed through constitutive models for particular materials and validated by numerical benchmark examples and experimental comparisons.
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2022)
Article
Chemistry, Physical
Yitao Qiu, Xiaoxuan Zhang, Camille Usubelli, Daniel Mayer, Christian Linder, Jake Christensen
Summary: Lithium plating is a main concern for cell durability, and its driving forces can be influenced by thermal and mechanical loads. The effects of mechanical deformation and different temperatures on lithium plating in a lithium-ion battery are investigated using 1D and 3D models.
JOURNAL OF POWER SOURCES
(2022)
Article
Engineering, Mechanical
Yitao Qiu, Prajwal Kammardi Arunachala, Christian Linder
Summary: Shape sensing is an emerging technique that reconstructs deformed shapes using data from a network of strain sensors. The development of SenseNet, a physics-informed deep learning model, allows for more accurate shape sensing without relying solely on training data. SenseNet incorporates knowledge of the physics of the problem and offers convenience for problems with complex geometries. It has been validated and proven to accurately reconstruct deformations in both two and three dimensions, utilizing surface strain data.
JOURNAL OF ENGINEERING MECHANICS
(2023)
Article
Thermodynamics
Arun Raina, Vikram S. Deshpande, Emilio Martinez-Paneda, Norman A. Fleck
Summary: The presence of hydrogen traps within a metallic alloy affects the rate of hydrogen diffusion. The electro-permeation (EP) test measures the permeation of hydrogen through a thin metallic sheet by controlling the hydrogen concentration and recording the hydrogen flux. The three stage EP test provides additional insight by setting and varying the concentration of free lattice hydrogen.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2023)
Article
Engineering, Multidisciplinary
Sina Abrari Vajari, Matthias Neuner, Prajwal Kammardi Arunachala, Christian Linder
Summary: Concrete, with its complex quasi-brittle cracking behavior, poses challenges in predicting failure mechanisms and patterns. Computational fracture modeling, particularly the phase field approach, has been proven to be effective. This study presents a thermodynamically consistent phase field approach for quasi-brittle fracture in concrete and investigates its ability to capture complex mixed mode cracking.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Correction
Multidisciplinary Sciences
Lihua Jin, Alex Chortos, Feifei Lian, Eric Pop, Christian Linder, Zhenan Bao, Wei Cai
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2021)
Article
Electrochemistry
Xiaoxuan Zhang, Sergei Chumakov, Xiaobai Li, Markus Klinsmann, Sun Ung Kim, Christian Linder, Jake Christensen
JOURNAL OF THE ELECTROCHEMICAL SOCIETY
(2020)
Article
Engineering, Multidisciplinary
Akshay J. Thomas, Mateusz Jaszczuk, Eduardo Barocio, Gourab Ghosh, Ilias Bilionis, R. Byron Pipes
Summary: We propose a physics-guided transfer learning approach to predict the thermal conductivity of additively manufactured short-fiber reinforced polymers using micro-structural characteristics obtained from tensile tests. A Bayesian framework is developed to transfer the thermal conductivity properties across different extrusion deposition additive manufacturing systems. The experimental results demonstrate the effectiveness and reliability of our method in accounting for epistemic and aleatory uncertainties.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Zhen Zhang, Zongren Zou, Ellen Kuhl, George Em Karniadakis
Summary: In this study, deep learning and artificial intelligence were used to discover a mathematical model for the progression of Alzheimer's disease. By analyzing longitudinal tau positron emission tomography data, a reaction-diffusion type partial differential equation for tau protein misfolding and spreading was discovered. The results showed different misfolding models for Alzheimer's and healthy control groups, indicating faster misfolding in Alzheimer's group. The study provides a foundation for early diagnosis and treatment of Alzheimer's disease and other misfolding-protein based neurodegenerative disorders using image-based technologies.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jonghyuk Baek, Jiun-Shyan Chen
Summary: This paper introduces an improved neural network-enhanced reproducing kernel particle method for modeling the localization of brittle fractures. By adding a neural network approximation to the background reproducing kernel approximation, the method allows for the automatic location and insertion of discontinuities in the function space, enhancing the modeling effectiveness. The proposed method uses an energy-based loss function for optimization and regularizes the approximation results through constraints on the spatial gradient of the parametric coordinates, ensuring convergence.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Bodhinanda Chandra, Ryota Hashimoto, Shinnosuke Matsumi, Ken Kamrin, Kenichi Soga
Summary: This paper proposes new and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). The proposed approach adopts a monolithic displacement-pressure formulation and integrates two stabilization strategies to ensure stability. The effectiveness of the proposed method is validated through benchmark cases and real-world scenarios involving violent free-surface fluid motion.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Chao Peng, Alessandro Tasora, Dario Fusai, Dario Mangoni
Summary: This article discusses the importance of the tangent stiffness matrix of constraints in multibody systems and provides a general formulation based on quaternion parametrization. The article also presents the analytical expression of the tangent stiffness matrix derived through linearization. Examples demonstrate the positive effect of this additional stiffness term on static and eigenvalue analyses.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Thibaut Vadcard, Fabrice Thouverez, Alain Batailly
Summary: This contribution presents a methodology for detecting isolated branches of periodic solutions to nonlinear mechanical equations. The method combines harmonic balance method-based solving procedure with the Melnikov energy principle. It is able to predict the location of isolated branches of solutions near families of autonomous periodic solutions. The relevance and accuracy of this methodology are demonstrated through academic and industrial applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Weisheng Zhang, Yue Wang, Sung-Kie Youn, Xu Guo
Summary: This study proposes a sketch-guided topology optimization approach based on machine learning, which incorporates computer sketches as constraint functions to improve the efficiency of computer-aided structural design models and meet the design intention and requirements of designers.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Leilei Chen, Zhongwang Wang, Haojie Lian, Yujing Ma, Zhuxuan Meng, Pei Li, Chensen Ding, Stephane P. A. Bordas
Summary: This paper presents a model order reduction method for electromagnetic boundary element analysis and extends it to computer-aided design integrated shape optimization of multi-frequency electromagnetic scattering problems. The proposed method utilizes a series expansion technique and the second-order Arnoldi procedure to reduce the order of original systems. It also employs the isogeometric boundary element method to ensure geometric exactness and avoid re-meshing during shape optimization. The Grey Wolf Optimization-Artificial Neural Network is used as a surrogate model for shape optimization, with radar cross section as the objective function.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
C. Pilloton, P. N. Sun, X. Zhang, A. Colagrossi
Summary: This paper investigates the smoothed particle hydrodynamics (SPH) simulations of violent sloshing flows and discusses the impact of volume conservation errors on the simulation results. Different techniques are used to directly measure the particles' volumes and stabilization terms are introduced to control the errors. Experimental comparisons demonstrate the effectiveness of the numerical techniques.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Ye Lu, Weidong Zhu
Summary: This work presents a novel global digital image correlation (DIC) method based on a convolution finite element (C-FE) approximation. The C-FE based DIC provides highly smooth and accurate displacement and strain results with the same element size as the usual finite element (FE) based DIC. The proposed method's formulation and implementation, as well as the controlling parameters, have been discussed in detail. The C-FE method outperformed the FE method in all tested examples, demonstrating its potential for highly smooth, accurate, and robust DIC analysis.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Mojtaba Ghasemi, Mohsen Zare, Amir Zahedi, Pavel Trojovsky, Laith Abualigah, Eva Trojovska
Summary: This paper introduces Lung performance-based optimization (LPO), a novel algorithm that draws inspiration from the efficient oxygen exchange in the lungs. Through experiments and comparisons with contemporary algorithms, LPO demonstrates its effectiveness in solving complex optimization problems and shows potential for a wide range of applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jingyu Hu, Yang Liu, Huixin Huang, Shutian Liu
Summary: In this study, a new topology optimization method is proposed for structures with embedded components, considering the tension/compression asymmetric interface stress constraint. The method optimizes the topology of the host structure and the layout of embedded components simultaneously, and a new interpolation model is developed to determine interface layers between the host structure and embedded components.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Qiang Liu, Wei Zhu, Xiyu Jia, Feng Ma, Jun Wen, Yixiong Wu, Kuangqi Chen, Zhenhai Zhang, Shuang Wang
Summary: In this study, a multiscale and nonlinear turbulence characteristic extraction model using a graph neural network was designed. This model can directly compute turbulence data without resorting to simplified formulas. Experimental results demonstrate that the model has high computational performance in turbulence calculation.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Jacinto Ulloa, Geert Degrande, Jose E. Andrade, Stijn Francois
Summary: This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. The proper generalized decomposition (PGD) is leveraged to decompose the displacements into multiple time scales, separating the spatial and intra-cyclic dependence from the inter-cyclic variation, thereby reducing computational burden.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Engineering, Multidisciplinary
Utkarsh Utkarsh, Valentin Churavy, Yingbo Ma, Tim Besard, Prakitr Srisuma, Tim Gymnich, Adam R. Gerlach, Alan Edelman, George Barbastathis, Richard D. Braatz, Christopher Rackauckas
Summary: This article presents a high-performance vendor-agnostic method for massively parallel solving of ordinary and stochastic differential equations on GPUs. The method integrates with a popular differential equation solver library and achieves state-of-the-art performance compared to hand-optimized kernels.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)