The three-dimensional elastoplastic analysis of bi-directional functionally graded materials using a meshfree global radial basis reproducing kernel particle method

The meshless global radial basis reproducing kernel particle method (GRB-RKPM), constructed based on the global radial basis function and the reproducing kernel particle method (RKPM), is extended to the investigation of the three-dimensional (3D) elastoplastic problem of bi-directional functional gradient materials (BDFGMs). The discrete equations in the incremental form are established based on the Galerkin integral weak formulation of the 3D elastoplastic problem. The solution equations of the GRB-RKPM for the 3D elastoplastic problem of BDFGMs are derived using the incremental tangent stiffness method. The numerical accuracy, convergence, and stability of the GRB-RKPM are analyzed. BDFGMs based on the exponential and Voigt models are employed in the numerical examples. The numerical results demonstrate that the GRB-RKPM is effective in solving the 3D elastoplastic problem of BDFGMs. The computational accuracy of the GRB-RKPM is higher than that of the GRBF, the RKPM and the local radial basis reproducing kernel particle method. The displacement of the 3D elastoplastic of BDFGMs decreases with an increase in the gradient index.