Nonlocal plastic softening algorithm and numerical investigation based on the Drucker–Prager criterion

Abstract

Strain softening in geotechnical materials often leads to the ill condition of boundary value problems. That is, the regional governing equations or partial differential equations are no longer applicable under the original fixed solution conditions, and the over non-localization theory is used to solve the finite element equations to ensure the possibilities of the governing equations. Based on the Drucker–Prager (D–P) criterion, a nonlocal elastoplastic constitutive model and its numerical algorithm for geomaterials are established while considering the softening plasticity. Strain localization leads to high strain gradients and severe deformations in the zone. The introduction of characteristic lengths establishes the relationship between microstructure and macroscopic deformation. Accordingly, the surroundings will affect a certain point of a damaged rock material. When a Gaussian weight function is introduced, and the characterization is concerned on the damage point, the influence gradually decreases, and the characteristic length controls the influence range as the distance increases. When using the closest point projection method to calculate the stress regression of the D–P criterion, the plastic multiplier is weighted and averaged by the Gaussian weight function, and the local plastic multiplier is converted into a nonlocal plastic multiplier for numerical analysis. The results show that with the introduction of the weight function and the feature length, the localized zone width no longer depends on the grid size, that is, the grid sensitivity is overcome, and the result is more in line with the physical nature.