@article{01K1MWMMGTYNQNGX5XA8MPFPNM,
  abstract     = {{A stabilized collocation method (SCM) employing reproducing kernel (RK) shape function is presented for solving the path-dependent nonlinear elastoplastic problems. Hencky's theory of plastic deformation and von Mises yield criterion are dragged to construct the plastic models. The shape function utilized in SCM possesses high-order continuity and SCM can achieve exact subdomain integration through low-order quadrature, which ensures that this method attains high-order continuity in the solution. This is critical for obtaining high accuracy and optimal convergence when solving path-dependent nonlinear problems. Subdomain integration also reduces the condition number of the discrete matrix, further boosting the algorithm's stability. The subdomains in SCM are located by the positions of particles, and domain deformation is illustrated by particle movement, which allows these subdomains to remain regular and undeformed. These characteristics make SCM a truly meshfree method. Effective parameters such as Young's modulus, Poisson's ratio, and shear modulus functioning as outputs of the final state of the stress field can be obtained iteratively through the projection method applied to uniaxial material curves. Several two-dimensional and three-dimensional numerical tests are examined, which show the high accuracy and good stability of SCM for elastoplastic analysis. All of these indications suggest that SCM holds immense potential for addressing material nonlinearity problems.}},
  author       = {{Xue, Zhiyuan and Wang, Lihua and Abdel Wahab, Magd}},
  issn         = {{0177-0667}},
  journal      = {{ENGINEERING WITH COMPUTERS}},
  keywords     = {{Stabilized collocation method,Nonlinear elastoplastic problems,Exact integration,Accuracy,Convergence}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{1657--1697}},
  title        = {{A truly meshfree solution of nonlinear elastoplastic problems based on stabilized collocation method}},
  url          = {{http://doi.org/10.1007/s00366-025-02165-5}},
  volume       = {{41}},
  year         = {{2025}},
}

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