TY - JOUR
T1 - Efficient prediction of strength and strain localisation in porous solids via microstructure-based limit analysis
AU - Hund, Jonas
AU - Kouznetsova, Varvara
AU - Andriollo, Tito
PY - 2025/2
Y1 - 2025/2
N2 - 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 within the framework of plastic limit analysis by minimising the total rate of internal work while ensuring compatible deformation across the solid. Accordingly, the predicted strength represents an upper bound. 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.
AB - 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 within the framework of plastic limit analysis by minimising the total rate of internal work while ensuring compatible deformation across the solid. Accordingly, the predicted strength represents an upper bound. 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.
KW - Heterogeneous solids
KW - Limit analysis
KW - Plasticity
KW - Porous solids
KW - Strain localisation
UR - http://www.scopus.com/inward/record.url?scp=85210536346&partnerID=8YFLogxK
U2 - 10.1016/j.mechmat.2024.105208
DO - 10.1016/j.mechmat.2024.105208
M3 - Journal article
SN - 0167-6636
VL - 201
JO - Mechanics of Materials
JF - Mechanics of Materials
M1 - 105208
ER -