Meshless solution of the crack propagation in brittle elastic material under shear, compressible and tensile loading

• The first attempt to use spectral-split for the strain decomposition with the fourth-order phase-field formulated crack propagation using a strong-form meshless method. • An adaptive loading stepsize criterion is introduced to speed up the simulations. • Benchmark tests for tensile, shear and compressive loadings are solved, and different numerical and material parameters are analysed. • We found that the proposed strong-form meshless approach produces results comparable to those of the reference solutions in the literature. This study explores a robust and computationally efficient two-dimensional solution procedure for phase-field modelling of crack propagation under tensile, compressive, and shear loadings by using the meshless local radial basis function collocation method (LRBFCM). The mechanical model is based on the brittle elastic material, and the crack propagation is governed by the fourth-order phase field equation coupled in a staggered way. The spectral-split method for strain tensor decomposition of a brittle elastic material is used with LRBFCM for crack propagation for the first time. It ensures that the crack is propagated physically correctly under different loading types, filling the gap in our previous study [ 1 ], where crack propagation only under tensile loading was possible. The strong-form LRBFCM is constructed on 13-noded subdomains with augmented third-order polyharmonic spline shape functions. A novel adaptive loading step size criterion is introduced to increase computational efficiency by removing cumbersome internal iteration processes. The method’s performance is assessed with three benchmark tests subjected to mixed-mode tension, shear and compressive loading. The results are validated with the reference solutions regarding accuracy and convergence rates for scattered and regular node arrangements. The effects of the iterative and non-iterative processes with different loading step sizes are shown