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NUMERICAL SOLUTION OF BIDIRECTIONAL FUNCTIONALLY GRADED MATERIALS USING A NOVEL MESHLESS GLOBAL RADIAL BASIS reproducing kernel particle method

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JOURNAL OF MECHANICS OF MATERIALS AND STRUCTURES 2025年第1期20卷 33-53页

作者： Qin, Shaopeng Yin, Deshun Han, Baozhi Tian, Mingyuan Chen, Xuan Ma, Liangzhu Li, Lirui Hohai Univ Coll Mech & Engn Sci Nanjing 211100 Peoples R China

A novel meshless global radial basis reproducing kernel particle method (GRB-RKPM) is established based on the global radial basis function (GRBF) and the reproducing kernel particle method (RKPM). Subsequently, GRB-RKPM is used to solve the elastic mechanical of bidirectional functionally graded materials (BDFGMs). The influence of the shape parameter q, the shape parameter ac, the scale parameter dmax, and the penalty factor alpha on the GRB-RKPM solving the elastic mechanical of BDFGMs is analyzed, and the optimal value is given. The effectiveness of the GRB-RKPM in solving the elastic mechanical of BDFGMs is verified by comparing solutions calculated by the GRB-RKPM with reference solutions calculated by the finite element method (FEM). Compared with the RKPM, the GRB-RKPM converges faster. The GRB-RKPM solutions are compared with the local radial basis reproducing kernel particle method (LRB-RKPM) solutions and the RKPM solutions. It is proved that the GRB-RKPM has higher computational accuracy. The deformation behavior of the elastic mechanical of BDFGMs under different gradient indexes is studied.

关键词： meshless method global radial basis function reproducing kernel particle method bidirectional functionally graded materials elastic mechanical problem

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Finite volume reproducing kernel particle method

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2024年 167卷 150-159页

作者： Lin, Zeng Chinese Acad Sci Shenzhen Inst Adv Technol Shenzhen 518055 Peoples R China

In the realm of computational mechanics, the reproducing kernel particle method (RKPM) shines in addressing challenges associated with intricate geometries and substantial deformations. However, in the Galerkin framework, RKPM has a substantial computational workload due to the complexities of numerical integration. To mitigate this limitation, we present a pioneering approach: the finite volume reproducing kernel particle method (FV-RKPM). FV-RKPM amalgamates the strengths of meshfree methods and finite volume methods, offering benefits such as grid independence, conservation properties, and numerical stability. In this paper, we elaborate on the construction methodology for FV-RKPM, alongside its associated integration strategies. We consistently validate the efficacy of this innovative methodology through a series of numerical results.

关键词： Finite volume method reproducing kernel particle method Computational efficiency

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Research on elasticity behavior of Ni-Ti shape memory alloys using the reproducing kernel particle method

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JOURNAL OF STRAIN ANALYSIS FOR ENGINEERING DESIGN 2024年第4期59卷 291-302页

作者： Zhang, Yijie Wei, Gaofeng Liu, Tengda Qilu Univ Technol Shandong Acad Sci Sch Mech Engn Jinan Shandong Peoples R China Shandong Inst Mech Design & Res Jinan Shandong Peoples R China Qilu Univ Technol Shandong Acad Sci Sch Mech Engn 3501 Daxue Rd Jinan 250353 Shandong Peoples R China

The unique superelastic properties of the Ni-Ti shape memory alloys (SMAs) have been found extensive practical application in many engineering fields, but the Ni-Ti SMAs exhibits elastic behavior in small load, so the elastic behavior of the Ni-Ti SMAs is studied by using meshless method of reproducing kernel particle method (RKPM) in this paper. The displacement boundary conditions are applied by utilizing the penalty function method, and the impact of penalty factor and parameter of influence domain on errors are discussed, and computational stability is analyzed. At last, the correctness of the RKPM in studying the elastic behavior of the Ni-Ti SMAs is evidenced by using three numerical examples.

关键词： Meshless method shape memory alloys reproducing kernel particle method elasticity behavior penalty method

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Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method

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ENGINEERING WITH COMPUTERS 2024年 1-32页

作者： Susuki, Kristen Allen, Jeffery Chen, Jiun-Shyan Univ Calif San Diego Dept Struct Engn La Jolla CA 92093 USA Natl Renewable Energy Lab Computat Sci Ctr Golden CO USA

An interface-modified reproducing kernel particle method (IM-RKPM) is introduced in this work to allow for a direct model construction from image pixels of heterogeneous polycrystalline Li-ion battery microstructures. The interface-modified reproducing kernel (IM-RK) approximation is constructed through scaling of a kernel function by a regularized distance function in conjunction with strategic placement of interface node locations. This leads to RK shape functions with either weak or strong discontinuities across material interfaces, suitable for modeling various interface mechanics. With the placement of a triple junction node and distance-based scaling of kernel functions, the resulting IM-RK shape function also possesses proper discontinuities at the triple junctions. This IM-RK approximation effectively remedies the well-known Gibb's oscillation in the smooth approximation of discontinuities. Different from the conventional meshfree approaches for interface discontinuities, this IM-RK approach is done without additional degrees of freedom associated with the enrichment functions, and it is formulated with the standard procedures in the RK shape function construction. This work focuses on identifying the accuracy and convergence properties of IM-RKPM for modeling the coupled electro-chemo-mechanical system. A linear patch test is formulated and numerically tested for the electro-chemo-mechanical coupled problem with a Butler-Volmer boundary condition representing the physical conditions in Li-ion battery microstructures. This is followed by verification of the optimal rates of convergence of IM-RKPM for solving the coupled problem with higher order solutions. The image-based modeling of Li-ion battery microstructures in the numerical examples demonstrates the applicability of the proposed method to realistic Li-ion battery materials modeling.

关键词： reproducing kernel particle method Image based modeling Electro-chemo-mechanical coupling Interface-modified reproducing kernel approximation Li-ion battery

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Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures

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COMPUTATIONAL MECHANICS 2024年第4期73卷 907-942页

作者： Wang, Yanran Baek, Jonghyuk Tang, Yichun Du, Jing Hillman, Mike Chen, Jiun-Shyan Univ Calif San Diego Dept Struct Engn La Jolla CA 92093 USA Penn State Univ Dept Mech Engn University Pk PA 16802 USA Karagozian & Case Inc Glendale CA 91203 USA

This work presents an approach for automating the discretization and approximation procedures in constructing digital representations of composites from micro-CT images featuring intricate microstructures. The proposed method is guided by the Support Vector Machine (SVM) classification, offering an effective approach for discretizing microstructural images. An SVM soft margin training process is introduced as a classification of heterogeneous material points, and image segmentation is accomplished by identifying support vectors through a local regularized optimization problem. In addition, an Interface-Modified reproducing kernel particle method (IM-RKPM) is proposed for appropriate approximations of weak discontinuities across material interfaces. The proposed method modifies the smooth kernel functions with a regularized Heaviside function concerning the material interfaces to alleviate Gibb's oscillations. This IM-RKPM is formulated without introducing duplicated degrees of freedom associated with the interface nodes commonly needed in the conventional treatments of weak discontinuities in the meshfree methods. Moreover, IM-RKPM can be implemented with various domain integration techniques, such as Stabilized Conforming Nodal Integration (SCNI). The extension of the proposed method to 3-dimension is straightforward, and the effectiveness of the proposed method is validated through the image-based modeling of polymer-ceramic composite microstructures.

关键词： Image-based modeling Support vector machine reproducing kernel particle method Weak discontinuity Microstructures

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Radial Basis reproducing kernel particle method for Damped Elastic Dynamics Problems

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IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY-TRANSACTIONS OF MECHANICAL ENGINEERING 2024年第3期48卷 1161-1176页

作者： Liu, Tengda Wei, Gaofeng Zhang, Yijie Qilu Univ Technol Shandong Acad Sci Sch Mech Engn Jinan 250353 Shandong Peoples R China Shandong Inst Mech Design & Res Jinan 250353 Shandong Peoples R China

The reproducing kernel particle method (RKPM) is a widely used meshless method that has been extensively applied in numerical analysis. The drawback of RKPM is that when different kernel functions are chosen during the computation process, there are different calculation accuracy, and significant discreteness. To address this issue, the radial basis function is introduced to RKPM, and the radial basis reproducing kernel particle method (RB-RKPM) is proposed. The negative impacts of different kernel functions on calculation accuracy can be eliminated by RB-RKPM, which possesses some advantages, such as good convergence, high computational accuracy and efficiency. Furthermore, the RB-RKPM is applied to the damped elastic dynamics problems (DEDPs), the governing equations for the DEDPs are derived based on the weak integral formulation, and the time is integrated by using the Newmark-linear acceleration method. Finally, the correctness of the proposed method in analyzing the DEDPs is verified through numerical examples.

关键词： reproducing kernel particle method Meshless method Damped elastic dynamics problems Weak integral formulation Radial basis function

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The elastoplastic large deformation analysis based on meshless radial basis reproducing kernel particle method

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2023年第1期155卷 541-552页

作者： Qin, Shaopeng Yin, Deshun Wei, Gaofeng Han, Baozhi Tian, Mingyuan Ma, Liangzhu Hohai Univ Coll Mech & Mat Nanjing 211100 Peoples R China Qilu Univ Technol Shandong Acad Sci Sch Mech & Automot Engn Jinan 250353 Peoples R China Shandong Inst Mech Design & Res Jinan 250031 Peoples R China

In this paper, the radial basis reproducing kernel particle method (RB-RKPM) is extended to solve the elastoplastic large deformation problem. The Galerkin weak form of the elastoplastic large deformation problem based on the full Lagrange scheme is used to establish the solution equation, which is then solved using the Newton-Raphson iterative method. The RB-RKPM is established for the elastoplastic large deformation problem. The effect of the penalty factor, the scale parameter, and the shape parameter on the calculation accuracy are introduced, and the optimal parameters are obtained. Several numerical examples were used in the simulation. The RB-RKPM solution is compared with the reproducing kernel particle method (RKPM) solution and the finite element method (FEM) solution, the effectiveness of the RB-RKPM in solving elastoplastic large deformation problem is verified, and the RB-RKPM has high computational accuracy.

关键词： Elastoplastic large deformation problem Meshfree approach Radial basis reproducing kernel particle method reproducing kernel particle method

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Analyzing three-dimensional wave propagation with the hybrid reproducing kernel particle method based on the dimension splitting method

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ENGINEERING WITH COMPUTERS 2022年第SUPPL 2期38卷 1131-1147页

作者： Peng, Piaopiao Cheng, Yumin Shanghai Univ Sch Mech & Engn Sci Shanghai Inst Appl Math & Mech Shanghai Key Lab Mech Energy Engn Shanghai 200072 Peoples R China

By introducing the dimension splitting method into the reproducing kernel particle method (RKPM), a hybrid reproducing kernel particle method (HRKPM) for solving three-dimensional (3D) wave propagation problems is presented in this paper. Compared with the RKPM of 3D problems, the HRKPM needs only solving a set of two-dimensional (2D) problems in some subdomains, rather than solving a 3D problem in the 3D problem domain. The shape functions of 2D problems are much simpler than those of 3D problems, which results in that the HRKPM can save the CPU time greatly. Four numerical examples are selected to verify the validity and advantages of the proposed method. In addition, the error analysis and convergence of the proposed method are investigated. From the numerical results we can know that the HRKPM has higher computational efficiency than the RKPM and the element-free Galerkin method.

关键词： Meshless method Dimension splitting method reproducing kernel particle method Hybrid reproducing kernel particle method Wave propagation

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Research on Superelasticity of Shape Memory Alloys Based on reproducing kernel particle method

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INTERNATIONAL JOURNAL OF APPLIED MECHANICS 2024年第4期16卷

作者： Zhang, Yijie Wei, Gaofeng Liu, Tengda Li, Anqing Ren, Fei Qilu Univ Technol Shandong Acad Sci Sch Mech Engn Jinan 250353 Shandong Peoples R China Shandong Inst Mech Design & Res Jinan 250353 Shandong Peoples R China

Shape memory alloys (SMAs), known for their unique superelastic effect, exhibit superior mechanical properties compared to traditional materials. In this study, the reproducing kernel particle method (RKPM) is applied to investigate the superelastic effect of the SMAs. A segmented linearization RKPM model is developed to establish the stress-strain relationship for the superelastic effect, and relevant formulas of superelasticity for the SMAs are derived. Finally, the applicability and accuracy of the RKPM in analyzing the superelastic effect of the SMAs are demonstrated through numerical examples.

关键词： Shape memory alloys superelastic effect meshless method reproducing kernel particle method smart materials

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A semi-Lagrangian reproducing kernel particle method with particle-based shock algorithm for explosive welding simulation

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COMPUTATIONAL MECHANICS 2021年第6期67卷 1601-1627页

作者： Baek, Jonghyuk Chen, Jiun-Shyan Zhou, Guohua Arnett, Kevin P. Hillman, Michael C. Hegemier, Gilbert Hardesty, Scott Univ Calif San Diego Dept Struct Engn La Jolla CA 92093 USA Optimal Inc Plymouth MI 48170 USA US Mil Acad Dept Civil & Mech Engn West Point NY 10996 USA Penn State Univ Dept Civil & Environm Engn University Pk PA 16802 USA Appl Res Associates Inc Rocky Mt Div Littleton CO 80127 USA

The explosive welding process is an extreme-deformation problem that involves shock waves, large plastic deformation, and fragmentation around the collision point, which are extremely challenging features to model for the traditional mesh-based methods. In this work, a particle-based Godunov shock algorithm under a semi-Lagrangian reproducing kernel particle method (SL-RKPM) is introduced into the volumetric strain energy to accurately embed the key shock physics in the absence of a mesh or grid, which is shown to also ensure the conservation of linear momentum. For kernel stability, a deformation-dependent anisotropic kernel support update algorithm is proposed, which is shown to capture excessive plastic flow and material separation. A quasi-conforming nodal integration is adopted to avoid the need of updating conforming cells which is tedious in extreme deformations. It is shown that the proposed formulation effectively captures shocks, jet formation, and smooth-to-wavy interface morphology transition with good agreement with experimental results.

关键词： reproducing kernel particle method kernel stability Shocks Nodal integration Explosive welding

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