Under tension low carbon steel exhibits inhomogeneous plastic deformation. This instability called Piobert-Luders banding creates fronts of localized strain that propagate in the structure. To date, Luders banding has been studied experimentally and numerically only in simple geometries like sheets, tubes and normalized fracture mechanics specimens. This paper focuses on architectured materials and specifically lattice structures which can be defined as a tessellation of unit-cells periodically distributed in space. This class of advanced materials draws new mechanical properties from its inner architecture. We investigate the effect of the architecture on the global behavior of the structure. Especially, how bands interact with the lattice and how to control initiation and propagation of localized strain using the architecture. An elastoplastic material model is used in order to simulate the Piobert-Luders band formation and propagation. The model also considers a large deformation framework for elastoplasticity with periodic boundary conditions in order to represent the architectured material. Initiation and propagation of material instabilities depend on the geometry as well as its on the relative orientation with respect to the loading direction. Propagating and non-propagating behaviors are identified for the Piobert-Luders bands and related to the different types of geometry. Material instabilities affect the mechanical behavior of the structure as far as they are governed by the architecture. These conclusions are compared to experimental results from tensile tests on laser-architectured specimens made of ARMCO steel.

中文翻译：

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在平面结构材料中传播材料不稳定性

在张力下低碳钢表现出不均匀的塑性变形。这种称为 Piobert-Luders 带的不稳定性会产生在结构中传播的局部应变前沿。迄今为止，Luders 条带仅在简单的几何形状（如板材、管材和标准化断裂力学试样）中进行了实验和数值研究。本文重点介绍建筑材料，特别是晶格结构，可以将其定义为空间中周期性分布的晶胞的镶嵌。这类先进材料从其内部结构中汲取了新的机械性能。我们研究了架构对结构全局行为的影响。特别是，带如何与晶格相互作用以及如何使用该架构控制局部应变的引发和传播。弹塑性材料模型用于模拟 Piobert-Luders 带的形成和传播。该模型还考虑了具有周期性边界条件的弹塑性大变形框架，以表示建筑材料。材料不稳定性的引发和传播取决于几何形状及其相对于加载方向的相对方向。为 Piobert-Luders 带确定了传播和非传播行为，并与不同类型的几何形状相关。材料不稳定性会影响结构的机械性能，因为它们受架构的控制。这些结论与 ARMCO 钢制成的激光结构试样拉伸试验的实验结果进行了比较。