The goal of this paper is to characterize the dynamic behavior of porous materials containing parallel cylindrical voids. Unlike static approaches, micro-inertia effects are accounted for in the modeling which infer a strong dependence of the dynamic response upon void geometry. Since cylindrical voids are considered, the void radius and void length both play a crucial role in the overall response of the porous material. A theoretical approach is developed, founded on the dynamic homogenization scheme proposed by Molinari and Mercier (J Mech Phys Solids 49:1497–1516, 2001) for spherical voids embedded in a viscoplastic matrix material. Considering a cylindrical unit cell, a constitutive response of porous material containing cylindrical void is developed for general homogeneous boundary conditions. For illustrative purpose, the analysis focuses on axisymmetric loadings considering a perfectly plastic matrix material. Micro-inertia effects are exemplified considering various loading conditions such as, among others, spherical loading and plane strain loading. In particular, the peculiar effect of the length of the cylindrical void is revealed. Indeed, particular attention has been paid to the response of short and elongated cylindrical voids. All predictions of the present model are verified against numerical simulations developed for various axisymmetric loading paths. Our findings can be used in several applications such as thick wall honeycomb structures or additively manufactured materials submitted to dynamic loading.

中文翻译：

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含有圆柱形空隙的延性材料的动态响应

本文的目的是表征包含平行圆柱空隙的多孔材料的动态行为。与静态方法不同，在建模中考虑了微惯性效应，这推断出动态响应对空隙几何形状的强烈依赖性。由于考虑了圆柱形空隙，空隙半径和空隙长度在多孔材料的整体响应中都起着至关重要的作用。基于 Molinari 和 Mercier (J Mech Phys Solids 49:1497–1516, 2001) 提出的用于嵌入粘塑性基质材料中的球形空隙的动态均化方案，开发了一种理论方法。考虑到圆柱形晶胞，对于一般均匀边界条件，开发了包含圆柱形空隙的多孔材料的本构响应。出于说明目的，该分析侧重于考虑完美塑性基体材料的轴对称载荷。考虑到各种载荷条件，例如球面载荷和平面应变载荷，举例说明了微惯性效应。特别是，揭示了圆柱形空隙长度的特殊影响。事实上，人们特别关注短而细长的圆柱形空隙的响应。本模型的所有预测都针对针对各种轴对称加载路径开发的数值模拟进行了验证。我们的发现可用于多种应用，例如厚壁蜂窝结构或承受动态载荷的增材制造材料。考虑到各种载荷条件，例如球面载荷和平面应变载荷，举例说明了微惯性效应。特别是，揭示了圆柱形空隙长度的特殊影响。事实上，人们特别关注短而细长的圆柱形空隙的响应。本模型的所有预测都针对针对各种轴对称加载路径开发的数值模拟进行了验证。我们的发现可用于多种应用，例如厚壁蜂窝结构或承受动态载荷的增材制造材料。考虑到各种载荷条件，例如球面载荷和平面应变载荷，举例说明了微惯性效应。特别是，揭示了圆柱形空隙长度的特殊影响。事实上，人们特别关注短而细长的圆柱形空隙的响应。本模型的所有预测都针对针对各种轴对称加载路径开发的数值模拟进行了验证。我们的发现可用于多种应用，例如厚壁蜂窝结构或承受动态载荷的增材制造材料。对短而细长的圆柱形空隙的响应给予了特别的关注。本模型的所有预测都针对针对各种轴对称加载路径开发的数值模拟进行了验证。我们的发现可用于多种应用，例如厚壁蜂窝结构或承受动态载荷的增材制造材料。对短而细长的圆柱形空隙的响应给予了特别的关注。本模型的所有预测都针对针对各种轴对称加载路径开发的数值模拟进行了验证。我们的发现可用于多种应用，例如厚壁蜂窝结构或承受动态载荷的增材制造材料。