This paper is interested in the computation of stresses within jammed packings of rigid polygonal cells. The cells are considered to follow a Tresca friction law. First, a constrained minimization problem is introduced where the friction energy is minimized while enforcing the non-interpenetration of neighboring cells as inequality constraints. The corresponding dual maximization problem is then deduced and its solutions provide normal stresses at the interface between cells. Finally, lowest order Raviart–Thomas finite elements are used to reconstruct a consistent stress field by solving local problems. Numerical results are presented to showcase the consistency and robustness of the proposed methodology.
Frédéric Marazzato 1 ; Shankar Venkataramani 2
Frédéric Marazzato; Shankar Venkataramani. Computation of stresses in jammed packings modeled with Tresca friction. The SMAI Journal of computational mathematics, Volume 12 (2026), pp. 171-186. doi: 10.5802/smai-jcm.146
@article{SMAI-JCM_2026__12__171_0,
author = {Fr\'ed\'eric Marazzato and Shankar Venkataramani},
title = {Computation of stresses in jammed packings modeled with {Tresca} friction},
journal = {The SMAI Journal of computational mathematics},
pages = {171--186},
year = {2026},
publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
volume = {12},
doi = {10.5802/smai-jcm.146},
language = {en},
url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.146/}
}
TY - JOUR AU - Frédéric Marazzato AU - Shankar Venkataramani TI - Computation of stresses in jammed packings modeled with Tresca friction JO - The SMAI Journal of computational mathematics PY - 2026 SP - 171 EP - 186 VL - 12 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.146/ DO - 10.5802/smai-jcm.146 LA - en ID - SMAI-JCM_2026__12__171_0 ER -
%0 Journal Article %A Frédéric Marazzato %A Shankar Venkataramani %T Computation of stresses in jammed packings modeled with Tresca friction %J The SMAI Journal of computational mathematics %D 2026 %P 171-186 %V 12 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.146/ %R 10.5802/smai-jcm.146 %G en %F SMAI-JCM_2026__12__171_0
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