Article
Engineering, Multidisciplinary
A. Giuliodori, J. A. Hernandez, E. Soudah
Summary: This study aims to efficiently model heterogeneous prismatic structures under small strains regime using reduced-order modeling (ROM) and domain decomposition techniques. By introducing fictitious interfaces and a low-dimensional parameterization scheme, the proposed partitioning framework avoids solving the nested local/global problem of other methods. The kinematics of the coarse-scale finite elements are not predefined by the user, but extracted from training computational experiments.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
History & Philosophy Of Science
Maxwell J. D. Ramstead, Michael D. Kirchhoff, Axel Constant, Karl J. Friston
Summary: This study presents a multiscale integrationist interpretation of cognitive system boundaries, aiming to correct the philosophical debate over internalist and externalist interpretations of cognitive boundaries and proposing a compromise position. By surveying radical views of cognition and describing an internalist interpretation based on the Markov blanket formalism, the study develops a positive multiscale account, arguing that the statistical seclusion of internal and external states can coexist with the system's multiscale integration. The relevance of cognitive boundaries depends on the level being characterized and the explanatory interests guiding investigation.
Article
Engineering, Multidisciplinary
Philipp Diercks, Karen Veroy, Annika Robens-Radermacher, Jorg F. Unger
Summary: This article proposes a methodology for fine scale modeling of large scale linear elastic structures by combining the variational multiscale method, domain decomposition, and model order reduction. The influence of the fine scale on the coarse scale is addressed by using an additive split of the displacement field, suitable for applications without clear scale separation. Local reduced spaces are constructed by solving an oversampling problem with random boundary conditions. The method is compared to existing approaches using physically meaningful correlated samples, showing its accuracy and efficiency in reducing the size of local spaces and training samples.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2023)
Article
Mathematics, Applied
Bo Zheng, Yueqiang Shang
Summary: A parallel stabilized finite element variational multiscale method for the incompressible Navier-Stokes equations is proposed, utilizing a fully overlapping domain decomposition approach. The method computes a stabilized solution in a given subdomain using a locally refined global mesh, without the need for substantial recoding of the existing Navier-Stokes sequential solver. Error bounds for the approximate solutions are estimated using local a priori error estimates for the stabilized solution.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Yongzheng Zhang
Summary: In this study, a nonlocal operator method (NOM) is proposed for the dynamic analysis of (thin) Kirchhoff plates. The NOM simplifies the analysis process for thin plates and derives the dynamic governing formulation and operator energy functional using a variational principle. The Verlet-velocity algorithm is used for time discretization.
ENGINEERING WITH COMPUTERS
(2023)
Article
Mathematics, Applied
Xin Su, Sai-Mang Pun
Summary: This paper introduces a multiscale method for solving the Signorini problem with a heterogeneous field. By constructing multiscale basis functions and utilizing the GMsFEM framework, the method effectively handles the unilateral condition of the problem, with theoretical analysis and numerical results provided.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Djulustan Nikiforov
Summary: In this paper, a new multiscale approach with a meshfree coarse scale is proposed. The approach is based on the Generalized Multiscale Finite Element Method (GMsFEM), which takes into account the heterogeneous parameters of the problem on a coarse scale using multiscale basis functions. The Discrete Fracture Model (DFM) is employed to represent fractures on a fine grid. Numerical solutions for two-dimensional and three-dimensional problems are presented.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Linfeng Chen, Steven J. Hulshoff, Yuhong Dong
Summary: The physical mechanism of residual-based large eddy simulation based on the variational multiscale method is clarified, showing advantages in predicting statistical results and analyzing the contributions of unresolved small-scale terms. The new stabilized finite element formulation proposed based on turbulent kinetic energy dissipation analysis demonstrates improved first-order and second-order statistical quantities in 2D and 3D turbulent flows.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Multidisciplinary
Wuyang Zhao, Paul Steinmann, Sebastian Pfaller
Summary: This paper presents a partitioned-domain method for multiscale simulations of inelastic amorphous polymers under isothermal conditions, coupling a particle domain and a continuum domain. A viscoelastic-viscoplastic constitutive model and temporal coupling scheme are used to capture the inelastic properties of the polymer. The study discusses the influence of time-related parameters on computational cost and accuracy, showcasing the method's capabilities for simulating the mechanical behavior of polymers under different loading conditions.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Computer Science, Interdisciplinary Applications
Yi Zhang, Joel Fisser, Marc Gerritsma
Summary: We introduce a domain decomposition structure-preserving method based on a hybrid mimetic spectral element method for three-dimensional linear elasticity problems. The method achieves pointwise equilibrium of forces and uses dual basis functions to simplify discretization and obtain higher sparsity. Numerical tests support the effectiveness of the method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Soonpil Kang, Arif Masud
Summary: This paper presents an immersed boundary method for weak enforcement of Dirichlet boundary conditions on immersed surfaces. The method combines the Variational Multiscale Discontinuous Galerkin method and an interface stabilized form. A significant contribution of this work is the analytically derived Lagrange multiplier for weak enforcement of the Dirichlet boundary conditions. Numerical experiments demonstrate the method's effectiveness with different types of meshes, and the norm of the stabilization tensor varies with the flow physics.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Saurabh Tomar, Mehakpreet Singh, Kuppalapalle Vajravelu, Higinio Ramos
Summary: This paper presents a novel method for calculating the Lagrange multiplier, which improves the efficiency of the variational iteration method in solving nonlinear problems.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Nanoscience & Nanotechnology
Xu Li, Zhi Tan, Jie Xing, Fei Wang, Lixu Xie, Wen Zhang, Ning Chen, Hao Chen, Jianguo Zhu
Summary: By employing a multiscale regulation strategy, this research successfully addresses the issues of early polarization saturation and low breakdown electric field in (Na0.5Bi0.5)(0.7)Sr0.3TiO3-based energy storage materials, resulting in excellent comprehensive performances.
ACS APPLIED MATERIALS & INTERFACES
(2022)
Article
Engineering, Mechanical
Fei Chen, Huajia Zhu, Wen Chen, Hengan Ou, Zhenshan Cui
Summary: The study developed a multiscale modeling framework, the MCAFE-dDRX model, to evaluate the dDRX microstructure evolution during hot working processes, facilitating the prediction of microstructure evolution during heterogeneous and non-isothermal deformation of materials.
INTERNATIONAL JOURNAL OF PLASTICITY
(2021)
Article
Materials Science, Multidisciplinary
Tao Fan
Summary: This study investigates the flexoelectricity incorporating electric polarization and strain gradients in all dielectrics. The function of Hamilton's principle of elastic dielectric materials considering the flexoelectric effect is established and its stationary conditions are obtained. A bilayer beam composed of elastic and piezoelectric parts is modeled to examine flexoelectricity under mechanical and electrical loads. The analytical solutions to the horizontal displacements are derived, and it is found that the flexoelectric effects depend heavily on size, being dominant at the nanoscale but negligible at larger scales. Adjusting the thickness ratio of the two parts enables better control of the bending flexibility of the piezoelectric/elastic bilayer beam. This research provides guidance for designing and optimizing nanoscale electronic devices.
MECHANICS OF ADVANCED MATERIALS AND STRUCTURES
(2023)
Article
Materials Science, Multidisciplinary
Xiao Sun, Bahador Bahmani, Nikolaos N. Vlassis, WaiChing Sun, Yanxun Xu
Summary: This paper presents a computational framework for generating ensemble predictive mechanics models with uncertainty quantification, and introduces a causal discovery algorithm for inferring causal relationships among time-history data.
Article
Mechanics
Nikolaos N. Vlassis, WaiChing Sun
Summary: Conventional training of neural network constitutive laws for path-dependent elastoplastic solids requires a large amount of data and lacks interpretability, which hinders their engineering applications. This study aims to simplify the training processes and improve interpretability by breaking down the training of material models into multiple supervised machine learning programs. The neural network model is tested against benchmark models, physical experiments, and numerical simulations to validate its versatility.
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME
(2022)
Article
Engineering, Multidisciplinary
Ran Ma, WaiChing Sun
Summary: This paper presents an explicit material point method for simulating micropolar continuum dynamics in the finite deformation and microrotation regime, ensuring conservation of microinertia and angular momentum through mapping and forward integration. The method is verified through analytical comparisons and demonstrated in various simulations, showcasing its capability to handle size effects in geometrically nonlinear regimes.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Geological
Hyoung Suk Suh, WaiChing Sun
Summary: This article presents a multi-phase-field poromechanics model that can simulate the growth and thaw of ice lenses and the resultant frozen heave and thaw settlement in frozen soils. The model introduces an immersed approach to capture the freezing influence on shear strength more accurately.
INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS
(2022)
Article
Engineering, Multidisciplinary
Bahador Bahmani, WaiChing Sun
Summary: This article presents an isometric manifold embedding data-driven paradigm for model-free simulations with noisy data. The proposed approach solves a global optimization problem to find admissible solutions for the balance principle and a local optimization problem to project the Euclidean space onto a nonlinear constitutive manifold. A geometric autoencoder is introduced to de-noise the database by mapping the high-dimensional constitutive manifold onto a flattened manifold. Numerical examples validate the implementation and show the accuracy, robustness, and limitations of the proposed paradigm.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Nikolaos N. Vlassis, WaiChing Sun
Summary: The history-dependent behaviors of classical plasticity models, driven by internal variables evolved according to phenomenological laws, have long been criticized for their difficulty in interpretation, lack of direct measurement for calibration and validation, and weak physical underpinning of those laws. This work uses geometric machine learning on graph data to establish a connection between nonlinear dimensional reduction techniques and plasticity models. By encoding rich time-history data onto a low-dimensional Euclidean space and predicting the evolution of plastic deformation, the dominating topological features of plastic deformation can be observed and analyzed with a corresponding decoder.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Ran Ma, WaiChing Sun, Catalin R. Picu, Tommy Sewell
Summary: Heterogeneous energetic materials (EMs) subjected to mechanical shock loading exhibit complex thermo-mechanical processes, and shock-induced pore collapse is one of the dominant mechanisms by which spatial energy localization occurs. In order to physically predict the shock sensitivity of EMs, a multiplicative crystal plasticity model is formulated with key features inferred from molecular dynamics (MD) simulations. The Material Point Method (MPM) is used to handle large deformation and evolving geometry, allowing for comprehensive simulations of shock-induced pore collapse and hotspot evolution. Comparative studies are performed to reveal the importance of frictional contact algorithm, pressure-dependent elastic stiffness, and non-Schmid critical resolved shear stress in the mesoscale model.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Mathematics, Interdisciplinary Applications
Ruben Villarreal, Nikolaos N. Vlassis, Nhon N. Phan, Tommie A. Catanach, Reese E. Jones, Nathaniel A. Trask, Sharlotte L. B. Kramer, WaiChing Sun
Summary: This paper presents a deep reinforcement learning algorithm for experimental design, using the Kalman filter to measure the information gain. The algorithm allows for rapid online experiments in high-dimensional parametric design space where trial-and-error is not feasible.
COMPUTATIONAL MECHANICS
(2023)
Article
Engineering, Multidisciplinary
Zeyu Xiong, Mian Xiao, Nikolaos Vlassis, Waiching Sun
Summary: This paper introduces a neural kernel method for generating machine learning models for complex materials that lack material symmetry and have internal structures. By introducing representation learning and constructing a feature vector space, this method enables more accurate characterization of these materials. Numerical examples validate the effectiveness of this method and compare it with other machine learning approaches.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Nikolaos N. Vlassis, WaiChing Sun
Summary: We propose a denoising diffusion algorithm for discovering microstructures with nonlinear fine-tuned properties. The algorithm utilizes generative models that gradually denoise images and generate realistic synthetic samples. By learning the reverse of a Markov diffusion process, it efficiently manipulates the topology of microstructures to generate prototypes with the desired nonlinear constitutive behaviors.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Multidisciplinary
Mian Xiao, Ran Ma, WaiChing Sun
Summary: This paper presents a graph-manifold iterative algorithm for predicting the configurations of geometrically exact shells under external loading. Finite element solutions are stored in a weighted graph and embedded onto a low-dimensional latent space. A graph isomorphism encoder reduces the dimensionality of the data, making it easier to construct a response surface. A decoder converts a point in the latent space back to a weighted graph representing a finite element solution. This algorithm allows obtaining the deformed shell configuration without additional finite element simulations and ensures accuracy in important locations.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Materials Science, Multidisciplinary
Hyoung Suk Suh, Chulmin Kweon, Brian Lester, Sharlotte Kramer, WaiChing Sun
Summary: This paper introduces a publicly available PyTorch-ABAQUS deep-learning framework for a family of plasticity models. The framework allows for engineering analysis with a user-defined material subroutine for ABAQUS. An interface code is introduced to convert the trained neural network weights and biases into a generic FORTRAN code. All the data sets, source code, and trained models are made available in a public repository for third-party validation. The practicality of the framework is demonstrated with numerical experiments on anisotropic yield function.
MECHANICS OF MATERIALS
(2023)
Proceedings Paper
Computer Science, Interdisciplinary Applications
Hyoung Suk Suh, WaiChing Sun
Summary: In this study, a multi-phase field thermo-hydro-mechanics model is developed to simulate the growth and thawing of ice lenses and the resulting frost heave and thawing settlement in multiphase porous media. The model implicitly captures the ice lens growth using two phase field variables and distinguishes the freezing effects on shear strength and stiffness through freezing characteristic function and driving force. The evolution of the phase field variables is induced by their own driving forces, capturing the ice-water phase transition and crack growth mechanisms.
GEO-CONGRESS 2023: GEOTECHNICAL DATA ANALYSIS AND COMPUTATION
(2023)
Article
Engineering, Multidisciplinary
Chen Cai, Nikolaos Vlassis, Lucas Magee, Ran Ma, Zeyu Xiong, Bahador Bahmani, Teng-Fong Wong, Yusu Wang, WaiChing Sun
Summary: We propose a SE(3)-equivariant graph neural network (GNN) approach to predict the formation factor and effective permeability from micro-CT images. The method uses FFT solvers to compute the formation factor and effective permeability, and represents the pore space topology and geometry using a persistence-based Morse graph. Experimental results show that the SE(3) approach generates more accurate predictions, especially with limited training data, and fulfills material frame indifference.
INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING
(2023)
Article
Engineering, Geological
Mohamad Chaaban, Yousef Heider, Waiching Sun, Bernd Markert
Summary: The paper investigates the utilization of artificial neural networks (ANNs) in learning models to address the nonlinear anisotropic flow and hysteresis retention behavior of deformable porous materials. Simulations and databases are used to model single-phase and biphasic flow, and two different ML approaches are compared for the accuracy and speed of training. The outcomes demonstrate the capability of ML models in accurately and efficiently representing constitutive relations for permeability and hysteretic retention curves.
INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS
(2023)
