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RKPM2D: an open-source implementation of nodally integrated reproducing kernel particle method for solving partial differential equations

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  1. Article

    Open Access

    Interpolation-based immersogeometric analysis methods for multi-material and multi-physics problems

    Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction ...

    Jennifer E. Fromm, Nils Wunsch, Kurt Maute, John A. Evans in Computational Mechanics (2024)

  2. Article

    Open Access

    A multi-resolution physics-informed recurrent neural network: formulation and application to musculoskeletal systems

    This work presents a multi-resolution physics-informed recurrent neural network (MR PI-RNN), for simultaneous prediction of musculoskeletal (MSK) motion and parameter identification of the MSK systems. The MSK...

    Karan Taneja, **aolong He, QiZhi He, Jiun-Shyan Chen in Computational Mechanics (2024)

  3. Article

    Open Access

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

    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...

    Yanran Wang, Jonghyuk Baek, Yichun Tang, **g Du, Mike Hillman in Computational Mechanics (2024)

  4. Article

    Open Access

    A deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling

    The numerical modelling of natural disasters such as landslides presents several challenges for conventional mesh-based methods such as the finite element method (FEM) due to the presence of numerically challe...

    Jonghyuk Baek, Ryan T. Schlinkman in Advanced Modeling and Simulation in Engine… (2022)

  5. Article

    Open Access

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

    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 m...

    Jonghyuk Baek, Jiun-Shyan Chen, Guohua Zhou, Kevin P. Arnett in Computational Mechanics (2021)

  6. Article

    Open Access

    A variational multiscale immersed meshfree method for heterogeneous materials

    We introduce an immersed meshfree formulation for modeling heterogeneous materials with flexible non-body-fitted discretizations, approximations, and quadrature rules. The interfacial compatibility condition i...

    Tsung-Hui Huang, Jiun-Shyan Chen, Michael R. Tupek in Computational Mechanics (2021)

  7. Article

    Correction to: A damage analysis for brittle materials using stochastic micro-structural information

    After publication of the original article [1], it has come to our attention that a citation of article [2] was missed.

    Shih-Po Lin, Jiun-Shyan Chen, Shixue Liang in Computational Mechanics (2018)

  8. Article

    Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems

    Galerkin meshfree methods can suffer from instability and suboptimal convergence if the issue of quadrature is not properly addressed. The instability due to quadrature is further magnified in high strain rate...

    Michael Hillman, Jiun-Shyan Chen, Sheng-Wei Chi in Computational Particle Mechanics (2014)

  9. Article

    Open Access

    An iterative asymptotic expansion method for elliptic eigenvalue problems with oscillating coefficients

    In this work we propose a method for obtaining fine-scale eigensolution based on the coarse-scale eigensolution in elliptic eigenvalue problems with oscillating coefficient. This is achieved by introducing a 2...

    Shafigh Mehraeen, Jiun-Shyan Chen, Wei Hu in Computational Mechanics (2010)