Boundary condition strategies for strain localization in a discrete periodic unit cell

Boundary condition strategies for strain localization in a discrete periodic unit cell

Paper in proceedings outside WoS and Scopus

Inmultiscalemodelingofheterogeneous softening materials, the choice of boundary conditions (BCs) applied to the fine-scale (micro/meso scale) model significantly influences both the strain localization pat terns and the macroscopic response. Commonly used Periodic BCs tend to produce artificially ductile behavior, characterized by excessive energy dissipation, when the localization band inclination does not match the peri odicity directions. To address this limitation, recently proposed Tessellation and Percolation-path-aligned BCs adapt the periodicity frame to align with the evolving localization zones and enable the formation of arbitrary localization bands. In this work, we perform a numerical study to assess the applicability of these BCs to a discrete lattice particle model of concrete at the mesoscale. A two-dimensional square fine-scale model is subjected to uniaxial tension under varying loading directions. The resulting macroscopic responses and localization patterns are compared against those obtained using conventional periodic BCs. The results indicate that Percolation-path-aligned BCs exhibit major shortcomings: they can lead to multiple localization bands due to uneven straining of their two boundary sections, with the weakly constrained section prone to spurious localization. In contrast, Tessellation BCs consistently produce a single, well-defined localiza tion band. The band length is determined solely by the square geometry of the model, making it straightforward to account for during post-processing. Consequently, the observed dependency of the dissipated energy on the loading direction can be clearly attributed to the geometry of the model rather than artifacts of the boundary conditions.

Inmultiscalemodelingofheterogeneous softening materials, the choice of boundary conditions (BCs) applied to the fine-scale (micro/meso scale) model significantly influences both the strain localization pat terns and the macroscopic response. Commonly used Periodic BCs tend to produce artificially ductile behavior, characterized by excessive energy dissipation, when the localization band inclination does not match the peri odicity directions. To address this limitation, recently proposed Tessellation and Percolation-path-aligned BCs adapt the periodicity frame to align with the evolving localization zones and enable the formation of arbitrary localization bands. In this work, we perform a numerical study to assess the applicability of these BCs to a discrete lattice particle model of concrete at the mesoscale. A two-dimensional square fine-scale model is subjected to uniaxial tension under varying loading directions. The resulting macroscopic responses and localization patterns are compared against those obtained using conventional periodic BCs. The results indicate that Percolation-path-aligned BCs exhibit major shortcomings: they can lead to multiple localization bands due to uneven straining of their two boundary sections, with the weakly constrained section prone to spurious localization. In contrast, Tessellation BCs consistently produce a single, well-defined localiza tion band. The band length is determined solely by the square geometry of the model, making it straightforward to account for during post-processing. Consequently, the observed dependency of the dissipated energy on the loading direction can be clearly attributed to the geometry of the model rather than artifacts of the boundary conditions.

Boundary conditions, homogenization, localization, discrete model

Boundary conditions, homogenization, localization, discrete model

RAISINGER, J.; ELIÁŠ, J.

09.03.2026

CRC Press

London

9781003660026

Computational Modelling of Concrete and Concrete Structures

723

730

8

https://www.taylorfrancis.com/chapters/oa-edit/10.1201/9781003660026-84/boundary-condition-strategies-strain-localization-discrete-periodic-unit-cell-raisinger-eli%C3%A1%C5%A1?context=ubx