Computation of stresses in jammed packings modeled with Tresca friction

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.

💡 Research Summary

The paper presents a novel computational framework for determining internal stress fields in dense packings of rigid polygonal cells—such as brick walls or vaults—using only a Tresca friction law. The authors first model each cell as a rigid body with a translational degree of freedom (rotations are neglected) and define a mesh M of convex polygons. Contact between neighboring cells occurs along internal edges E_i, where a Tresca friction energy E_e(u)=s_T|e|·|