arXiv subjects

Leiting Dong

Publications and source records attributed to Leiting Dong.

13 recordsLinked to original sources

arXiv2023

A Fuzzy-set-based Joint Distribution Adaptation Method for Regression and its Application to Online Damage Quantification for Structural Digital Twin

Online damage quantification suffers from insufficient labeled data that weakens its accuracy. In this context, adopting the domain adaptation on historical labeled data from similar structures/damages or simulated digital twin data to assist the current diagnosis task would be beneficial. However, most domain adaptation methods are designed for classification and cannot efficiently address damage quantification, a regression problem with continuous real-valued labels. This study first proposes a novel domain adaptation method, the Online Fuzzy-set-based Joint Distribution Adaptation for Regression, to address this challenge. By converting the continuous real-valued labels to fuzzy class labels via fuzzy sets, the marginal and conditional distribution discrepancy are simultaneously measured to achieve the domain adaptation for the damage quantification task. Thanks to the superiority of the proposed method, a state-of-the-art online damage quantification framework based on domain adaptation is presented. Finally, the framework has been comprehensively demonstrated with a damaged helicopter panel, in which three types of damage domain adaptations (across different damage locations, across different damage types, and from simulation to experiment) are all conducted, proving the accuracy of damage quantification can be significantly improved in a realistic environment. It is expected that the proposed approach to be applied to the fleet-level digital twin considering the individual differences.

cs.CE↗

arXiv2022

An Explicit Total Lagrangian Fragile Points Method for Finite Deformation of Hyperelastic Materials

This research explored a novel explicit total Lagrangian Fragile Points Method (FPM) for finite deformation of hyperelastic materials. In contrast to mesh-based methods, where mesh distortion may pose numerical challenges, meshless methods are more suitable for large deformation modelling since they use enriched shape functions for the approximation of displacements. However, this comes at the expense of extra computational overhead and higher-order quadrature is required to obtain accurate results. In this work, the novel meshless method FPM was used to derive an explicit total Lagrangian algorithm for finite deformation. FPM uses simple one-point integration for exact integration of the Galerkin weak form since it employs simple discontinuous polynomials as trial and test functions, leading to accurate results even with single-point quadrature. The proposed method was evaluated by comparing it with FEM in several case studies considering both the extension and compression of a hyperelastic material. It was demonstrated that FPM maintained good accuracy even for large deformations where FEM failed to converge.

math.NA↗

arXiv2022

Real-Time Prediction of Probabilistic Crack Growth with a Helicopter Component Digital Twin

To deploy the airframe digital twin or to conduct probabilistic evaluations of the remaining life of a structural component, a (near) real-time crack-growth simulation method is critical. In this paper, a reduced-order simulation approach is developed to achieve this goal by leveraging two methods. On the one hand, the symmetric Galerkin boundary element method - finite element method (SGBEM-FEM) coupling method is combined with parametric modeling to generate the database of computed stress intensity factors for cracks with various sizes/shapes in a complex structural component, by which hundreds of samples are automatically simulated within a day. On the other hand, machine learning methods are applied to establish the relation between crack sizes/shapes and crack-front stress intensity factors. By combining the reduced-order computational model with load inputs and fatigue growth laws, a real-time prediction of probabilistic crack growth in complex structures with minimum computational burden is realized. In an example of a round-robin helicopter component, even though the fatigue crack growth is simulated cycle by cycle, the simulation is faster than real-time (as compared with the physical test). The proposed approach is a key simulation technology toward realizing the digital twin of complex structures, which further requires fusion of model predictions with flight/inspection/monitoring data.

physics.app-ph↗

arXiv2021

A Fragile Points Method, with an interface debonding model, to simulate damage and fracture of U-notched structures

Notched components are commonly used in engineering structures, where stress concentration may easily lead to crack initiation and development. The main goal of this work is to develop a simple numerical method to predict the structural strength and crack-growth-path of U-notched specimens made of brittle materials. For this purpose, the Fragile Points Method (FPM), as previously proposed by the authors, has been augmented by an interface debonding model at the interfaces of the FPM domains, to simulate crack initiation and development. The formulations of FPM are based on a discontinuous Galerkin weak form where point-based piece-wise-continuous polynomial test and trial functions are used instead of element-based basis functions. In this work, the numerical fluxes introduced across interior interfaces between subdomains are postulated as the tractions acting on the interface derived from an interface damage model. The interface damage is triggered when the numerical flux reaches the interface strength, and the process of crack-surface separation is governed by the fracture energy. In this way, arbitrary crack initiation and propagation can be naturally simulated without the need for knowing the fracture-patch before-hand. Additionally, a small penalty parameter is sufficient to enforce the weak-form continuity condition before damage initiation, without causing problems such as artificial compliance and numerical ill-conditioning. As validations, the proposed FPM method with the interface damage model is used to predict the structural strength and crack-development from U-notched structures made of brittle materials, which is useful but challenging in engineering structural design practices.

math.NA↗

arXiv2021

Meshfree implementation of the cardiac monodomain model through the Fragile Points Method

Meshfree methods for in silico modelling and simulation of cardiac electrophysiology are gaining more and more popularity. These methods do not require a mesh and are more suitable than the Finite Element Method (FEM) to simulate the activity of complex geometrical structures like the human heart. However, challenges such as numerical integration accuracy and time efficiency remain and limit their applicability. Recently, the Fragile Points Method (FPM) has been introduced in the meshfree methods family. It uses local, simple, polynomial, discontinuous functions to construct trial and test functions in the Galerkin weak form. This allows for accurate integration and improved efficiency while enabling the imposition of essential and natural boundary conditions as in the FEM. In this work, we consider the application of FPM for cardiac electrophysiology simulation. We derive the cardiac monodomain model using the FPM formulation and we solve several benchmark problems in 2D and 3D. We show that FPM leads to solutions of similar accuracy and efficiency with FEM while alleviating the need for a mesh. Additionally, FPM demonstrates better convergence than FEM in the considered benchmarks.

math.NA↗

arXiv2020

A Simple Galerkin Meshless Method, the Fragile Points Method (FPM) Using Point Stiffness Matrices, for 2D Linear Elastic Problems in Complex Domains with Crack and Rupture Propagation

The Fragile Points Method (FPM) is an elementarily simple Galerkin meshless method, employing Point-based discontinuous trial and test functions only, without using element-based trial and test functions. In this study, the algorithmic formulations of FPM for linear elasticity are given in detail, by exploring the concepts of point stiffness matrices and numerical flux corrections. Advantages of FPM for simulating the deformations of complex structures, and for simulating complex crack propagations and rupture developments, are also thoroughly discussed. Numerical examples of deformation and stress analyses of benchmark problems, as well as of realistic structures with complex geometries, demonstrate the accuracy, efficiency and robustness of the proposed FPM. Simulations of crack initiation and propagations are also given in this study, demonstrating the advantages of the present FPM in modeling complex rupture and fracture phenomena. The crack and rupture propagation modeling in FPM is achieved without remeshing or augmenting the trial functions as in standard, extended or generalized FEM. The simulation of impact, penetration and other extreme problems by FPM will be discussed in our future papers.

math.NA↗

arXiv2020

A New Meshless Fragile Points Method (FPM) With Minimum Unknowns at Each Point, For Flexoelectric Analysis Under Two Theories with Crack Propagation. Part I: Theory and Implementation

Flexoelectricity refers to a phenomenon which involves a coupling of the mechanical strain gradient and electric polarization. In this study, a meshless Fragile Points Method (FPM), is presented for analyzing flexoelectric effects in dielectric solids. Local, simple, polynomial and discontinuous trial and test functions are generated with the help of a local meshless Differential Quadrature approximation of derivatives. Both primal and mixed FPM are developed, based on two alternate flexoelectric theories, with or without the electric gradient effect and Maxwell stress. In the present primal as well as mixed FPM, only the displacements and electric potential are retained as explicit unknown variables at each internal Fragile Point in the final algebraic equations. Thus the number of unknowns in the final system of algebraic equations is kept to be absolutely minimal. An algorithm for simulating crack initiation and propagation using the present FPM is presented, with classic stress-based criterion as well as a Bonding-Energy-Rate(BER)-based criterion for crack development. The present primal and mixed FPM approaches represent clear advantages as compared to the current methods for computational flexoelectric analyses, using primal as well as mixed Finite Element Methods, Element Free Galerkin (EFG) Methods, Meshless Local Petrov Galerkin (MLPG) Methods, and Isogeometric Analysis (IGA) Methods, because of the following new features: they are simpler Galerkin meshless methods using polynomial trial and test functions; minimal DoFs per Point make it very user-friendly; arbitrary polygonal subdomains make it flexible for modeling complex geometries; the numerical integration of the primal as well as mixed FPM weak forms is trivially simple; and FPM can be easily employed in crack development simulations without remeshing or trial function enhancement.

math.NA↗

arXiv2020

A New Meshless Fragile Points Method (FPM) With Minimum Unknowns at Each Point, For Flexoelectric Analysis Under Two Theories with Crack Propagation. Part II: Validation and discussion

In the first part of this two-paper series, a new Fragile Points Method (FPM), in both primal and mixed formulations, is presented for analyzing flexoelectric effects in 2D dielectric materials. In the present paper, a number of numerical results are provided as validations, including linear and quadratic patch tests, flexoelectric effects in continuous domains, and analyses of stationary cracks in dielectric materials. A discussion of the influence of the electroelastic stress is also given, showing that Maxwell stress could be significant and thus the full flexoelectric theory is recommended to be employed for nano-scale structures. The present primal as well as mixed FPMs also show their suitability and effectiveness in simulating crack initiation and propagation with flexoelectric effect. Flexoelectricity, coupled with piezoelectric effect, can help, hinder, or deflect the crack propagation paths and should not be neglected in nano-scale crack analysis. In FPM, no remeshing or trial function enhancement are required in modeling crack propagation. A new Bonding-Energy-Rate(BER)-based crack criterion as well as classic stress-based criterion are used for crack development simulations. Other complex problems such as dynamic crack developments, fracture, fragmentation and 3D flexoelectric analyses will be given in our future studies.

math.NA↗

arXiv2020

A New Meshless "Fragile Points Method (FPM)" Based on A Galerkin Weak-Form for 2D Flexoelectric Analysis

A meshless Fragile Points Method (FPM) is presented for analyzing 2D flexoelectric problems. Local, simple, polynomial and discontinuous trial and test functions are generated with the help of a local meshless differential quadrature approximation of the first three derivatives. Interior Penalty Numerical Fluxes are employed to ensure the consistency of the method. Based on a Galerkin weak-form formulation, the present FPM leads to symmetric and sparse matrices, and avoids the difficulties of numerical integration in the previous meshfree methods. Numerical examples including isotropic and anisotropic materials with flexoelectric and piezoelectric effects are provided as validations. The present method is much simpler than the Finite Element Method, or the Element-Free Galerkin (EFG) and Meshless Local Petrov-Galerkin (MLPG) methods, and the numerical integration of the weak form is trivially simple.

cs.CE↗

arXiv2020

A New Meshless "Fragile Points Method" and A Local Variational Iteration Method for General Transient Heat Conduction in Anisotropic Nonhomogeneous Media

A new and effective computational approach is presented for analyzing transient heat conduction problems. The approach consists of a meshless Fragile Points Method (FPM) being utilized for spatial discretization, and a Local Variational Iteration (LVI) scheme for time discretization. Anisotropy and nonhomogeneity do not give rise to any difficulties in the present implementation. The meshless FPM is based on a Galerkin weak-form formulation and thus leads to symmetric matrices. Local, very simple, polynomial and discontinuous trial and test functions are employed. In the meshless FPM, Interior Penalty Numerical Fluxes are introduced to ensure the consistency of the method. The LVIM in the time domain is generated as a combination of the Variational Iteration Method (VIM) applied over a large time interval and numerical algorithms. A set of collocation nodes are employed in each finitely large time interval. The FPM + LVIM approach is capable of solving transient heat transfer problems in complex geometries with mixed boundary conditions, including pre-existing cracks. Numerical examples are presented in 2D and 3D domains. Both functionally graded materials and composite materials are considered. It is shown that, with suitable computational parameters, the FPM + LVIM approach is not only accurate, but also efficient, and has reliable stability under relatively large time intervals. The present methodology represents a considerable improvement to the current state of science in computational transient heat conduction in anisotropic nonhomogeneous media.

cs.CE↗

arXiv2019

A new Fragile Points Method (FPM) in computational mechanics, based on the concepts of Point Stiffnesses and Numerical Flux Corrections

In this paper, a new method, named the Fragile Points Method (FPM), is developed for computer modeling in engineering and sciences. In the FPM, simple, local, polynomial, discontinuous and Point-based trial and test functions are proposed based on randomly scattered points in the problem domain. The local discontinuous polynomial trial and test functions are postulated by using the Generalized Finite Difference method. These functions are only piece-wise continuous over the global domain. By implementing the Point-based trial and test functions into the Galerkin weak form, we define the concept of Point Stiffnesses as the contribution of each Point in the problem domain to the global stiffness matrix. However, due to the discontinuity of trial and test functions in the domain, directly using the Galerkin weak form leads to inconsistency. To resolve this, Numerical Flux Corrections, which are frequently used in Discontinuous Galerkin methods are further employed in the FPM. The resulting global stiffness matrix is symmetric and sparse, which is advantageous for large-scale engineering computations. Several numerical examples of 1D and 2D Poisson equations are given in this paper to demonstrate the high accuracy, robustness and convergence of the FPM. Because of the locality and discontinuity of the Point-based trial and test functions, this method can be easily extended to model extreme problems in mechanics, such as fragility, rupture, fracture, damage, and fragmentation. These extreme problems will be discussed in our future studies.

physics.comp-ph↗

arXiv2019

Eshelby tensors and overall properties of nano-composites considering both interface stretching and bending effects

In this study, the fundamental framework of analytical micromechanics is generalized to consider nano-composites with both interface stretching and bending effects. The interior and exterior Eshelby tensors for a spherical nano-inclusion, with an interface defined by the Steigmann-Ogden model, subjected to an arbitrary uniform eigenstrain are derived for the first time. Correspondingly, the stress/strain concentration tensors for a spherical nano-inhomogeneity subjected to arbitrary uniform far-field stress/strain loadings are also derived. Using the obtained concentration tensors, the effective bulk and shear moduli are derived by employing the dilute approximation and the Mori-Tanaka method, respectively, which can be used for both nano-composites and nano-porous materials. An equivalent interface curvature parameter reflecting the influence of the interface bending resistance is found, which can significantly simplify the complex expressions of the effective properties. In addition to size-dependency, the closed form expressions show that the effective bulk modulus is invariant to interface bending resistance parameters, in contrast to the effective shear modulus. We also put forward for the first time a characteristic interface curvature parameter, near which the effective shear modulus is affected significantly. Numerical results show that the effective shear moduli of nano-composites and nano-porous materials can be greatly improved by an appropriate surface modification. Finally, the derived effective modulus with the Steigmann-Ogden interface model is provided in the supplemental MATLAB code, which can be easily executed, and used as a benchmark for semi-analytical solutions and numerical solutions in future studies.

physics.comp-ph↗

arXiv2019

Spherical nano-inhomogeneity with the Steigmann-Ogden interface model under general uniform far-field stress loading

An explicit solution, considering the interface bending resistance as described by the Steigmann-Ogden interface model, is derived for the problem of a spherical nano-inhomogeneity (nanoscale void/inclusion) embedded in an infinite linear-elastic matrix under a general uniform far-field-stress (including tensile and shear stresses). The Papkovich-Neuber (P-N) general solutions, which are expressed in terms of spherical harmonics, are used to derive the analytical solution. A superposition technique is used to overcome the mathematical complexity brought on by the assumed interfacial residual stress in the Steigmann-Ogden interface model. Numerical examples show that the stress field, considering the interface bending resistance as with the Steigmann-Ogden interface model, differs significantly from that considering only the interface stretching resistance as with the Gurtin-Murdoch interface model. In addition to the size-dependency, another interesting phenomenon is observed: some stress components are invariant to interface bending stiffness parameters along a certain circle in the inclusion/matrix. Moreover, a characteristic line for the interface bending stiffness parameters is presented, near which the stress concentration becomes quite severe. Finally, the derived analytical solution with the Steigmann-Ogden interface model is provided in the supplemental MATLAB code, which can be easily executed, and used as a benchmark for semi-analytical solutions and numerical solutions in future studies.

physics.class-ph↗