Efficient Prediction of Strength and Strain Localisation in Porous Solids Via Microstructure-Based Limit Analysis

A new method is presented to predict strength and strain localisation in solids containing voids or soft particles at reduced computational cost compared to traditional micro-mechanical approaches. The method leverages the fact that strain localisation in such materials occurs in the form of narrow shear bands connecting the voids. Accordingly, the model domain is discretised with rigid triangular blocks defined by the Delaunay triangulation of the void centroids. Deformation and energy dissipation are assumed to be confined to discontinuities of the velocity field introduced along the block edges, representing the narrow zones of strain localisation within the shear bands. The block velocities are computed under a plastic limit analysis framework by minimising the total rate of internal work while ensuring compatible deformation across the solid. The adopted microstructure-based discretisation strategy effectively limits the number of potential discontinuities compared to similar methods proposed in the literature, thereby increasing the computational efficiency. To demonstrate the capabilities of the method, predicted macroscopic strength under uniaxial tension and strain localisation patterns in 2D porous microstructures with varying porosity fractions are compared to the finite element results.