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A dynamic high-frequency consistent continualization of beam-lattice materials

机译：梁晶格材料的动态高频一致性连续化

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摘要

The main purpose of the present paper is to solve the thermodynamic inconsistencies that result when deriving equivalent micropolar and/or higher order micropolar models of periodic beam-lattice materials through standard continualization schemes which provide a non-positive defined elastic potential energy. Despite this, such models are capable of accurately simulating the optical branches of the discrete Lagrangian model, a property lacking in the thermodynamically consistent standard micropolar continuum. To overcome these energetic inconsistencies while preserving good simulations of the frequency band structure, a dynamic highfrequency consistent continualization is proposed. This continualization scheme is based on a first order regularization approach coupled with a suitable transformation of the difference equation of motion of the discrete Lagrangian system into pseudo-differential equations. A formal Taylor expansion of the pseudodifferential operators allows to obtain differential field equations at various orders according to the continualization order. Thermodynamically consistent higher order micropolar continua having non-local positive defined elastic and kinetic energy are obtained. Finally, the convergence of the frequency band structure of the higher order micropolar models to that of the discrete Lagrangian system is shown as the continualization order increases.
机译：本文的主要目的是解决通过标准连续化方案通过提供非正阳性限定的弹性势能的标准连续化方案来导出相同的微柱和/或高阶微柱模型时产生的热力学不一致。尽管如此，这种模型能够准确地模拟离散拉格朗日模型的光学分支，缺乏热力学一致的标准微柱连续体的性能。为了克服这些能量不一致，同时保持频带结构的良好模拟，提出了动态初始丧失持续化。该持续化方案基于第一阶正则化方法，其与具有离散拉格朗日系统的差分方式的差分方程的合适转换为伪微分方程。伪变性运营商的正式泰勒膨胀允许根据持续顺序以各种订单获得差分现场方程。获得具有非局部阳性定义弹性和动能的热力学一致的高阶MICROPOLAL。最后，作为持续化顺序增加，显示了高阶微息型模型的频带结构与离散拉格朗日系统的频带结构的收敛。

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