Stress concentration is a crucial source of mechanical failure in structural elements, especially those embedding voids. This paper examines periodic porous materials with porosity lower than 5%. We investigate their stress distribution under planar multiaxial loading, and presents a family of geometrically optimized void shapes for stress mitigation. We adopt a generalized description for both void geometry and planar tessellation patterns that can handle single and multiple voids of arbitrary void shape at a generic angle. The role of void shape evolution from diamond to rectellipse on the stress-distribution is captured at the edge of voids in a representative volume element (RVE) made of non-equal length periodic vectors. Theoretical derivations, numerical simulations along with experimental validation of the strain field in thermoplastic polymer samples fabricated by laser cutting unveil the role of geometric parameters, e.g. superellipse order, aspect ratio and rotation angle, that minimize stress peak and ameliorate stress distribution around voids. This work extends and complements classical theory by providing fundamental insights into the role that tessellation, void shape and inclination play in the stress distribution of low-porosity architected materials, thus introducing essential guidelines of broad application for stress-minimization and failure mitigation in diverse sectors.

应力集中是结构元件（尤其是那些嵌入空隙的结构元件）机械失效的重要来源。本文研究孔隙率低于5％的周期性多孔材料。我们研究了它们在平面多轴载荷下的应力分布，并提出了一系列用于缓解应力的几何优化空隙形状。我们对空隙几何形状和平面镶嵌图案都采用了通用的描述，它们可以以通用角度处理任意空隙形状的单个和多个空隙。在由非等长周期向量构成的代表性体积元素（RVE）中，空隙的边缘处捕获了空隙形状在应力分布上从金刚石演变为矩形的作用。理论推导 数值模拟以及通过激光切割制造的热塑性聚合物样品中应变场的实验验证揭示了几何参数的作用，例如，超椭圆级，长宽比和旋转角度，这些参数最小化了应力峰并改善了空隙周围的应力分布。这项工作提供了对细化，空隙形状和倾斜度在低孔隙率建筑材料的应力分布中所起的作用的基础见解，从而扩展了古典理论并对其进行了补充，从而为广泛应用应力最小化和减少破坏提供了重要的指导原则。使应力峰值最小化并改善空隙周围的应力分布。这项工作提供了对细化，空隙形状和倾斜度在低孔隙率建筑材料的应力分布中所起的作用的基础见解，从而扩展了古典理论并对其进行了补充，从而为广泛应用应力最小化和减少破坏提供了重要的指导原则。使应力峰值最小化并改善空隙周围的应力分布。这项工作提供了对细化，空隙形状和倾斜度在低孔隙率建筑材料的应力分布中所起的作用的基础见解，从而扩展了古典理论并对其进行了补充，从而为广泛应用应力最小化和减少破坏提供了重要的指导原则。