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Versatile data-adaptive hyperelastic energy functions for soft materials Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-11 Simon Wiesheier, Miguel Angel Moreno-Mateos, Paul Steinmann
Applications of soft materials are customarily linked to complex deformation scenarios and material nonlinearities. In the bioengineering field, soft materials typically mimic the low stiffness of biological matter subjected to extreme deformations. Computational frameworks surge as a versatile tool to assist the design of functional applications. The constitutive model lies at the core of such frameworks
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Topology optimization of curved thick shells using level set method and non-conforming multi-patch isogeometric analysis Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-11 Fernando Hübner Scherer, Malek Zarroug, Hakim Naceur, Andrei Constantinescu
We present a novel framework for topological shape optimization of curved non-conforming multi-patch and trimmed thick-shells subjected to external loads. Our method integrates the level set method (LSM) with a diffuse interface, a Hadamard shape derivative, and multi-patch isogeometric analysis (IGA) into a gradient descent algorithm to systematically capture the evolution of the shape. This integration
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Linear numerical schemes for a [formula omitted]-tensor system for nematic liquid crystals Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-10 Justin Swain, Giordano Tierra
In this work, we present three linear numerical schemes to model nematic liquid crystals using the Landau-de Gennes -tensor theory. The first scheme is based on using a truncation procedure of the energy, which allows for an unconditionally energy stable first order accurate decoupled scheme. The second scheme uses a modified second order accurate optimal dissipation algorithm, which gives a second
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Topology optimization of continuum structures for buckling resistance using a floating projection method Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-10 Tao Xu, Xiaodong Huang, Xiaoshan Lin, Yi Min Xie
Buckling resistance is crucial in structural design. This study addresses challenges associated with enhancing buckling resistance through topology optimization, focusing on avoiding incorrect buckling analyses and reducing reliance on parameter tuning. To eliminate pseudo buckling modes in low-density elements, this research employs a linear material model and a stress relaxation function, demonstrating
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Data-driven micromorphic mechanics for materials with strain localization Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-10 Jacinto Ulloa, Laurent Stainier, Michael Ortiz, José E. Andrade
This paper explores the role of generalized continuum mechanics, and the feasibility of model-free data-driven computing approaches thereof, in solids undergoing failure by strain localization. Specifically, we set forth a methodology for capturing material instabilities using data-driven mechanics without prior information regarding the failure mode. We show numerically that, in problems involving
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Multi-domain encoder–decoder neural networks for latent data assimilation in dynamical systems Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-09 Sibo Cheng, Yilin Zhuang, Lyes Kahouadji, Che Liu, Jianhua Chen, Omar K. Matar, Rossella Arcucci
High-dimensional dynamical systems often require computationally intensive physics-based simulations, making full physical space data assimilation impractical. Latent data assimilation methods perform assimilation in reduced-order latent space for efficiency but struggle with complex, nonlinear state-observation mappings. Recent solutions like Generalized Latent Data Assimilation (GLA) and Latent Space
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A ductile phase-field fracture formulation with regularized fracture toughness through a gradient-extended micromorphic approach Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-08 Dong Zhao, Bo Yin, Johannes Storm, Michael Kaliske
In this work, a phase-field formulation is proposed to describe ductile fracture in fiber-reinforced concrete materials. By incorporating an elastoplastic bulk material formulation into the promising (RCE) framework, physically meaningful kinematic behaviors at the crack surface could be observed when facing crack opening, closing and shear loading scenarios. A nonlocal -type plasticity formulation
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TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-08 Yanlai Chen, Yajie Ji, Akil Narayan, Zhenli Xu
We introduce the Generative Pre-Trained Physics-Informed Neural Networks (TGPT-PINN) for accomplishing nonlinear model order reduction (MOR) of transport-dominated partial differential equations in an MOR-integrating PINNs framework. Building on the recent development of the GPT-PINN that is a network-of-networks design achieving snapshot-based model reduction, we design and test a novel paradigm for
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An energy-based material model for the simulation of shape memory alloys under complex boundary value problems Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-08 Cem Erdogan, Tobias Bode, Philipp Junker
Shape memory alloys are remarkable ‘smart’ materials used in a broad spectrum of applications, ranging from aerospace to robotics, thanks to their unique thermomechanical coupling capabilities. Given the complex properties of shape memory alloys, which are largely influenced by thermal and mechanical loads, as well as their loading history, predicting their behavior can be challenging. Consequently
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An adaptive phase field modeling of fatigue crack growth using variable-node elements and explicit cycle jump scheme Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-05 Junlei Ding, Tiantang Yu, Weihua Fang, Sundararajan Natarajan
In this paper, we present a phase-field method combined with an explicit cycle jump scheme for simulating low-cycle fatigue fracture in brittle materials in both two and three dimensions. In order to improve the computation efficiency, an adaptive local mesh refinement strategy, which features a predictor–corrector scheme and an adaptive criterion, is developed. The incompatible meshes due to local
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FE-LSTM: A hybrid approach to accelerate multiscale simulations of architectured materials using Recurrent Neural Networks and Finite Element Analysis Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-05 Aymen Danoun, Etienne Prulière, Yves Chemisky
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Particle-based adaptive coupling of 3D and 2D fluid flow models Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-04 Pratik Suchde
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Uncertainty quantification of graph convolution neural network models of evolving processes Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-03 Jeremiah Hauth, Cosmin Safta, Xun Huan, Ravi G. Patel, Reese E. Jones
The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural networks have proved to be adept at modeling processes with spatial–temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there
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Adaptive and parallel multiscale framework for modeling cohesive failure in engineering scale systems Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-02 Sion Kim, Ezra Kissel, Karel Matouš
The high computational demands of multiscale modeling necessitate advanced parallel and adaptive strategies. To address this challenge, we introduce an adaptive method that utilizes two microscale models based on an offline database for multiscale modeling of curved interfaces (e.g., adhesive layers). This database employs nonlinear classifiers, developed using Support Vector Machines from microscale
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Partitioned neural network approximation for partial differential equations enhanced with Lagrange multipliers and localized loss functions Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-02 Deok-Kyu Jang, Kyungsoo Kim, Hyea Hyun Kim
Partitioned neural network functions are used to approximate the solution of partial differential equations. The problem domain is partitioned into non-overlapping subdomains and the partitioned neural network functions are defined on the given non-overlapping subdomains. Each neural network function then approximates the solution in one subdomain. To obtain the convergent neural network solution,
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A partitioned flexibility (PartFlex) method for structural analysis Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-02 K.C. Park, C.A. Felippa, S.H. Kang, J.A. González, S.J. Shin, Y.H. Park, J.G. Kim
A partitioned flexibility method is presented as a dual to the recently developed displacement-only partitioned (DP) method (Park et al., 2023). The proposed PartFlex method relies on existing FEM software to generate the partitioned block-diagonal mass and flexibility matrices, and associated FEM partitioned nodal topology information. Unlike the classical force method whose formulations are all critically
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A novel implicit FEM-MPM coupling framework using convex cone programming for elastoplastic problems Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-02 Xi-Wen Zhou, Yin-Fu Jin, Kai-Yuan He, Zhen-Yu Yin, Feng-Tao Liu
Most existing Finite Element Method and the Material Point Method (FEM-MPM) coupling is designed for explicit solvers. By contrast, implicit schemes offer the advantage of substantially larger time steps while maintaining enhanced stability, particularly beneficial for tackling stiff nonlinear problems. Despite this, the development of implicit FEM-MPM coupling has not been extensively explored, leaving
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GMC-PINNs: A new general Monte Carlo PINNs method for solving fractional partial differential equations on irregular domains Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-01 Shupeng Wang, George Em Karniadakis
Physics-Informed Neural Networks (PINNs) have been widely used for solving partial differential equations (PDEs) of different types, including fractional PDEs (fPDES) (Pang et al., 2019). Herein, we propose a new general (quasi) Monte Carlo PINN (GMC-PINNs) for solving fPDEs on irregular domains. Specifically, instead of approximating fractional derivatives by Monte Carlo approximations of integrals
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Novel gradient-enhanced Bayesian neural networks for uncertainty propagation Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-01 Yan Shi, Rui Chai, Michael Beer
Uncertainty propagation (UP) is crucial for assessing the impact of input uncertainty on structural responses, holding significant importance in engineering applications. However, achieving accurate and efficient UP remains challenging, especially for highly nonlinear structures. Bayesian neural networks (BNN) have gained attention for addressing UP issues, yet current BNN models only utilize input
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A three-dimensional meshless fluid–shell interaction framework based on smoothed particle hydrodynamics coupled with semi-meshless thin shell Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-01 Tianrun Gao, Lin Fu
Meshless methods are suitable for fluid–structure interaction simulations due to its Lagrangian feature and capability of handling large deformations. A three-dimensional meshless framework for the fluid–structure interaction simulation with shell structures is proposed in this study. The weakly compressible smoothed particle hydrodynamics is deployed in the fluid domain, where the boundary integral
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A 3D phase-field based Eulerian variational framework for multiphase fluid–structure interaction with contact dynamics Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-01 Xiaoyu Mao, Biswajeet Rath, Rajeev Jaiman
Using a fixed Eulerian mesh, interface-capturing approaches such as volume-of-fluid, level-set and phase-field methods have been successfully utilized for a broad range of moving boundary problems involving multiphase fluids and single-phase fluid–structure interaction. Nevertheless, multiphase fluids interacting with multiple solids are rarely explored, especially for large-scale finite element simulations
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Novel method for reliability optimization design based on rough set theory and hybrid surrogate model Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-01 Haoran Fan, Chong Wang, Shaohua Li
Considering the intricate correlation among uncertain parameters from multiple sources in engineering practice, the bounded region describing parameter uncertainty displays irregular boundary features. To facilitate effective reliability analysis and optimization within this context, this paper introduces a novel reliability optimization design methodology grounded in rough set theory and a hybrid
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Transfer learning for accelerating phase-field modeling of ferroelectric domain formation in large-scale 3D systems Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-01 Kévin Alhada-Lahbabi, Damien Deleruyelle, Brice Gautier
High-throughput phase-field simulations emerge as a compelling technique to predict the evolution of domain structures in ferroelectric materials. Despite their potential, their widespread use is impeded by significant computational costs, particularly for large 3D systems, limiting applicability in real-size scenarios and extensive parameter exploration. Here, we present a machine-learning approach
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Dynamic crack propagation in elasto-plastic materials using phase-field virtual modelling method Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-01 Yiyang Liu, Yuan Feng, Zhangming Wu, Mehrisadat Makki Alamdari, Di Wu, Zhen Luo, Xiaojun Chen, Wei Gao
In modern engineering, dynamic fracture failure because of unexpected load or human faults may lead to catastrophic disasters. Preventive structure design and real-time maintain suggestions based on accurate numerical simulation are critical, especially when plasticity develops. It remains a challenge to efficiently model dynamic crack propagation in elasto-plastic materials while the uncertain factors
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tLaSDI: Thermodynamics-informed latent space dynamics identification Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-07-01 Jun Sur Richard Park, Siu Wun Cheung, Youngsoo Choi, Yeonjong Shin
We propose a latent space dynamics identification method, namely tLaSDI, that embeds the first and second principles of thermodynamics. The latent variables are learned through an autoencoder as a nonlinear dimension reduction model. The latent dynamics are constructed by a neural network-based model that precisely preserves certain structures for the thermodynamic laws through the GENERIC formalism
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A PINN-DeepONet framework for extracting turbulent combustion closure from multiscalar measurements Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-28 Arsalan Taassob, Anuj Kumar, Kevin M. Gitushi, Rishikesh Ranade, Tarek Echekki
In this study, we develop a novel framework to extract turbulent combustion closure, including closure for species chemical source terms, from multiscalar and velocity measurements in turbulent flames. The technique is based on a physics-informed neural network (PINN) that combines models for velocity and scalar measurements and a deep operator network (DeepONet) to accommodate spatial measurements
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Points of inflection of special eigenvalue functions as indicators of stiffness maxima/minima of proportionally loaded structures Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-28 A. Wagner, J. Kalliauer, M. Aminbaghai, H.A. Mang
The stiffness of a proportionally loaded structure may continuously increase or decrease. As a special exception, it may be constant. On the other hand, an initially stiffening (softening) structure may turn into a softening (stiffening) structure. At the load level of such a change the stiffness of the structure attains an extreme value. The task of this work is to present mathematical conditions
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Topology optimization of finite strain elastoplastic materials using continuous adjoint method: Formulation, implementation, and applications Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-27 Jike Han, Kozo Furuta, Tsuguo Kondoh, Shinji Nishiwaki, Kenjiro Terada
This study presents a unified formulation of topology optimization for finite strain elastoplastic materials. As the primal problem to describe the elastoplastic behavior, we consider the standard -plasticity model incorporated into Neo-Hookean elasticity within the finite strain framework. For the optimization problem, the objective function is set to accommodate both single and multiple objectives
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An improved approximate integral method for nonlinear reliability analysis Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-27 Zhenzhong Chen, Guiming Qiu, Xiaoke Li, Zan Yang, Ge Chen, Xuehui Gan
In order to evaluate the failure probability corresponding to the Limit State Function (LSF) in structural reliability, the First Order Reliability Method (FORM) linearizes the LSF and directly calculates the failure probability based on the Most Probable Point (MPP). But this method is unable to effectively handle nonlinear problems. The Second Order Reliability Method (SORM), on the other hand, utilizes
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Non-probabilistic reliability analysis with both multi-super-ellipsoidal input and fuzzy state Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-27 Linxiong Hong, Shizheng Li, Mu Chen, Pengfei Xu, Huacong Li, Jiaming Cheng
In real-world engineering scenarios, incomplete uncertainty information and ambiguous failure states persist and pose significant challenges for structural reliability analysis. This paper introduces a non-probabilistic fuzzy reliability analysis (NPFRA) model featuring fuzzy output states, where the input uncertainties are quantified by a multi-super-ellipsoidal model. Initially, we define both reliability
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Variational temporal convolutional networks for I-FENN thermoelasticity Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-27 Diab W. Abueidda, Mostafa E. Mobasher
Machine learning (ML) has been used to solve multiphysics problems like thermoelasticity through multi-layer perceptron (MLP) networks. However, MLPs have high computational costs and need to be trained for each prediction instance. To overcome these limitations, we introduced an integrated finite element neural network (I-FENN) framework to solve transient thermoelasticity problems in Abueidda and
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On the benefits of a multiscale domain decomposition method to model-order reduction for frictional contact problems Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-26 D. Zeka, P.-A. Guidault, D. Néron, M. Guiton
In this paper, the efficiency of a multiscale strategy based on a domain decomposition method (DDM) for model-order reduction of time-dependent frictional contact problems is presented. The proposed strategy relies on the LArge Time INcrement (LATIN) nonlinear solver combined with model reduction based on the Proper Generalized Decomposition (PGD). The LATIN presents a robust treatment of contact conditions
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Topology optimization with accessibility constraint from multiple bi-directions using fictitious anisotropic diffusion equation based on coupled fictitious physical model Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-26 Mikihiro Tajima, Takayuki Yamada
In this study, we focus on topology optimization considering the accessibility constraint, which is a constraint that removes inaccessible regions from multiple linear directions. To detect inaccessible regions, we propose a method using a fictitious anisotropic diffusion equation. The proposed equation can simultaneously consider access from a bi-direction, which means one access direction and its
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Multiscale formulation for materials composed by a saturated porous matrix and solid inclusions Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-26 Reinaldo A. Anonis, Javier L. Mroginski, Pablo J. Sánchez
Despite all the progress achieved in the characterization of heterogeneous materials by using multiscale paradigms based on the Representative Volume Element concept (RVE), there are still many aspects that demand ongoing development. We mention, for instance, in-homogeneous media with internal micro-structure comprising a mixture of components that require a dissimilar number/character of primary
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A robust radial point interpolation method empowered with neural network solvers (RPIM-NNS) for nonlinear solid mechanics Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-26 Jinshuai Bai, Gui-Rong Liu, Timon Rabczuk, Yizheng Wang, Xi-Qiao Feng, YuanTong Gu
In this work, we proposed a robust radial point interpolation method empowered with neural network solvers (RPIM-NNS) for solving highly nonlinear solid mechanics problems. It is enabled by neural network solvers via minimizing an energy-based functional loss. The RPIM-NNS has the following key ingredients: (1) It uses radial basis functions (RBFs) for displacement interpolation at arbitrary points
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Data-driven identification of stable sparse differential operators using constrained regression Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-26 Aviral Prakash, Yongjie Jessica Zhang
Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics forecasting problems. In this article, we propose a novel methodology for learning differential operators that are theoretically linearly stable and have sparsity
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A phase-field fracture model in thermo-poro-elastic media with micromechanical strain energy degradation Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-24 Yuhao Liu, Keita Yoshioka, Tao You, Hanzhang Li, Fengshou Zhang
This work extends the hydro-mechanical phase-field fracture model to non-isothermal conditions with micromechanics based poroelasticity, which degrades Biot’s coefficient not only with the phase-field variable (damage) but also with the energy decomposition scheme. Furthermore, we propose a new approach to update porosity solely determined by the strain change rather than damage evolution as in the
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An MPMD approach coupling electromagnetic continuum mechanics approximations in ALEGRA Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-24 Allen C. Robinson, Richard R. Drake, Christopher B. Luchini, Ramón J. Moral, John H.J. Niederhaus, Sharon V. Petney
Two complementary approximations for describing aspects of continuum electromagnetics in moving media are discussed: electroquasistatic and magnetoquasistatic. Each has been implemented in the finite element shock code ALEGRA for modeling dynamic electromechanical phenomena on typical engineering time scales, with fully integrated circuit coupling (Niederhaus et al. 2023). The approximations can be
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Topological derivative based sensitivity analysis for three-dimensional discrete variable topology optimization Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-24 Kai Sun, Gengdong Cheng, Yuan Liang
This study introduces a novel Topological Derivative-based Sensitivity Analysis (TDSA) methodology for three-dimensional (3D) discrete variable topology optimization. Recently, the authors pointed out that the discrete variable sensitivity can be related to the topological derivative, and thus can be rationally approximated by the specially customized topological derivative for plane stress problems
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Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-24 Tobias Duswald, Brendan Keith, Boyan Lazarov, Socratis Petrides, Barbara Wohlmuth
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Machine learning predictive model for dynamic response of rising bubbles impacting on a horizontal wall Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-22 Xiangyu Zhang, Yang Zhang, K.M. Liew
The integrated behavior of the fluid flow, encompassing variation of some specific response, has received more attention than mere examination of velocity and pressure distributions. A machine learning framework is introduced for the first time to elucidate and predict the complex fluid dynamic responses across varying time scales. For the same class of fluid processes, the dynamic response curves
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Projection-based reduced-order modelling of time-periodic problems, with application to flow past flapping hydrofoils Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-21 Jacob E. Lotz, Gabriel D. Weymouth, Ido Akkerman
Simulating forced time-periodic flows in industrial applications presents significant computational challenges, partly due to the need to overcome costly transients before achieving time-periodicity. Reduced-order modelling emerges as a promising method to speed-up computations. We extend upon the work of Lotz et al. (2024) where a time-periodic space–time model is introduced. We present a time-periodic
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Enhancing CFD solver with Machine Learning techniques Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-21 Paulo Sousa, Carlos Veiga Rodrigues, Alexandre Afonso
This study addresses the computational challenges in fluid flow simulations arising from demanding computational grids, required to capture the temporal and length scales involved. Our approach focuses on the pressure solver, as this is a resource-intensive component in Computational Fluid Dynamics (CFD) solvers. We achieve this by integrating a Machine Learning (ML) surrogate model with an incompressible
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Koopman dynamic-oriented deep learning for invariant subspace identification and full-state prediction of complex systems Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-21 Jiaxin Wu, Min Luo, Dunhui Xiao, Christopher C. Pain, Boo Cheong Khoo
One strategy for predicting the state of nonlinear dynamical systems (typically of high dimensionality) is global linearization, such as utilizing the Koopman analysis model to transform the system state into an invariant subspace that evolves linearly. A critical challenge in the Koopman model is designing or deriving observation functions, typically nonlinear, to linearize the dynamical systems.
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Bayesian structural model updating with multimodal variational autoencoder Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-20 Tatsuya Itoi, Kazuho Amishiki, Sangwon Lee, Taro Yaoyama
A novel framework for Bayesian structural model updating is presented in this study. The proposed method utilizes the surrogate unimodal encoders of a multimodal variational autoencoder (VAE). The method facilitates an approximation of the likelihood when dealing with a small number of observations. It is particularly suitable for high-dimensional correlated simultaneous observations applicable to
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Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-20 Antareep Kumar Sarma, Sumanta Roy, Chandrasekhar Annavarapu, Pratanu Roy, Shriram Jagannathan
We present a novel physics-informed neural networks (PINNs) framework for modeling interface problems, termed Interface PINNs (I-PINNs). I-PINNs uses different neural networks for any two subdomains separated by a sharp interface such that the neural networks differ only through their activation functions while the other parameters remain identical. The performance of I-PINNs, conventional PINNs, and
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Multilevel domain decomposition-based architectures for physics-informed neural networks Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-20 Victorita Dolean, Alexander Heinlein, Siddhartha Mishra, Ben Moseley
Physics-informed neural networks (PINNs) are a powerful approach for solving problems involving differential equations, yet they often struggle to solve problems with high frequency and/or multi-scale solutions. Finite basis physics-informed neural networks (FBPINNs) improve the performance of PINNs in this regime by combining them with an overlapping domain decomposition approach. In this work, FBPINNs
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Solving large-scale variational inequalities with dynamically adjusting initial condition in physics-informed neural networks Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-19 Dawen Wu, Ludovic Chamoin, Abdel Lisser
This work aims to solve large-scale variational inequalities (VIs), which are equivalent to high-dimensional systems of ordinary differential equations (ODEs). The existing physics-informed neural network (PINN) approach (Wu and Lisser, 2023) shows superior performance for VIs with less than 1000 variables, but fails for VIs of larger size, due to the increasing number of equations and the requirement
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Bayesian reduced-order deep learning surrogate model for dynamic systems described by partial differential equations Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-19 Yuanzhe Wang, Yifei Zong, James L. McCreight, Joseph D. Hughes, Alexandre M. Tartakovsky
We propose a reduced-order deep-learning surrogate model for dynamic systems described by time-dependent partial differential equations. This method employs space–time Karhunen–Loève expansions (KLEs) of the state variables and space-dependent KLEs of space-varying parameters to identify the reduced (latent) dimensions. Subsequently, a deep neural network (DNN) is used to map the parameter latent space
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An immersed boundary fast meshfree integration methodology with consistent weight learning Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-17 Jijun Ying, Dongdong Wang, Like Deng, Zhiwei Lin
An immersed boundary fast integration methodology featured by a consistent weight learning is proposed to accelerate Galerkin meshfree computation. In the proposed approach, the problem domain is embedded in a rectangular spatial domain discretized by regular distributions of meshfree nodes and integration sampling points with virtual integration cells. A trimming operation of the rectangular spatial
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Phase-field modeling of fracture with physics-informed deep learning Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-17 M. Manav, R. Molinaro, S. Mishra, L. De Lorenzis
We explore the potential of the deep Ritz method to learn complex fracture processes such as quasistatic crack nucleation, propagation, kinking, branching, and coalescence within the unified variational framework of phase-field modeling of brittle fracture. We elucidate the challenges related to the neural-network-based approximation of the energy landscape, and the ability of an optimization approach
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Nonlinear fatigue damage constrained topology optimization Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-15 Jinyu Gu, Zhuo Chen, Kai Long, Yingjun Wang
In engineering applications, plenty of components are subjected to variable-amplitude cyclic loading, resulting in fatigue damage, which is one of the main forms of structural damage. While the linear damage rule has long served as a fundamental approach, its limitations necessitate advancements for more accurate fatigue life predictions. Hence, this paper introduces a pioneering method termed nonlinear
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Data-driven aerodynamic shape design with distributionally robust optimization approaches Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-15 Long Chen, Jan Rottmayer, Lisa Kusch, Nicolas Gauger, Yinyu Ye
We formulate and solve data-driven aerodynamic shape design problems with distributionally robust optimization (DRO) approaches. DRO aims to minimize the worst-case expected performance in a set of distributions that is informed by observed data with uncertainties. Building on the findings of the work Gotoh, et al. (2018), we study the connections between a class of DRO and robust design optimization
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Topology optimization of smart structures with embedded piezoelectric stack actuators using a composite geometry projection method Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-15 Breno Vincenzo de Almeida, Renato Pavanello, Matthijs Langelaar
The design of smart structures is challenging because of the integrated electromechanical modelling and optimization of actuators, sensors and load-bearing structures. To simplify the design process, it is common to decouple some of the components and physics and develop each part separately, which could lead to suboptimal systems. To improve the overall design of active structures, we propose an integrated
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Physics-informed MeshGraphNets (PI-MGNs): Neural finite element solvers for non-stationary and nonlinear simulations on arbitrary meshes Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-15 Tobias Würth, Niklas Freymuth, Clemens Zimmerling, Gerhard Neumann, Luise Kärger
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Buckling mode constraints for topology optimization using eigenvector aggregates Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-14 Bao Li, Graeme J. Kennedy
Buckling-constrained structural design problems have conventionally prioritized optimizing the buckling load factor with less consideration given to the buckling mode shape. In this work, mode shape constraints are imposed within a topology optimization problem using an eigenvector aggregate constraint that is a weighted sum of homogeneous quadratic functions of the linearized buckling eigenvectors
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A novel section–section potential for short-range interactions between plane beams Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-14 A. Borković, M.H. Gfrerer, R.A. Sauer, B. Marussig, T.Q. Bui
We derive a novel formulation for the interaction potential between deformable fibers due to short-range fields arising from intermolecular forces. The formulation improves the existing section–section interaction potential law for in-plane beams by considering an offset between interacting cross sections. The new law is asymptotically consistent, which is particularly beneficial for computationally
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Multiscale topology optimization for the design of spatially-varying three-dimensional lattice structure Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-14 Dongjin Kim, Jaewook Lee
This paper introduces three dimensional (3D) topology optimization specifically tailored for designing spatially-varying primitive-cubic (CP) type lattice structures. The developed design process consists of three steps: pre-processing, main processing, and post-processing. In the pre-processing step, a surrogate model between lattice geometry variables and effective elasticity tensor is constructed
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Design of the shell-infill structures using a phase field-based topology optimization method Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-14 Wenxuan Xie, Jiachen Feng, Qing Xia, Junseok Kim, Yibao Li
The design of shell-infill structures has been a focal point in the topology optimization community due to their advantages in energy absorption characteristics, strength-to weight ratio and bucking resistance. This paper introduces a phase field-based topology optimization method for designing shell-infill structures. Interface-related issues can be easily addressed through the phase field function
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A [formula omitted] continuous multi-patch framework for adaptive isogeometric topology optimization of plate structures Comput. Methods Appl. Mech. Eng. (IF 6.9) Pub Date : 2024-06-14 Philip Luke Karuthedath, Lokanath Barik, Abhinav Gupta, Abinash Kumar Swain, Rajib Chowdhury, Bhagath Mamindlapelly
This study proposes a novel computationally efficient methodology to perform topology optimization (TO) of fourth-order plate structures within the framework of multi-patch isogeometric analysis. This is realized by taking the multifold benefits of isogeometric PHT-Splines to (1) discretize the continuous weak form of plate structures, (2) develop a continuous density field for the material distribution