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 constraint. The corresponding dual maximization problem is then deduced and its solution provides 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.

翻译：本文致力于计算刚性多边形细胞堵塞堆积体内部的应力分布。假设细胞遵循Tresca摩擦定律。首先，引入一个约束最小化问题，其中在强制相邻细胞不发生相互穿透（作为不等式约束）的条件下最小化摩擦能量。随后推导出相应的对偶最大化问题，其解可提供细胞界面处的法向应力。最后，通过求解局部问题，采用最低阶Raviart-Thomas有限元重构协调的应力场。数值结果验证了所提方法的一致性与鲁棒性。