Explicit FE (Finite Element) method offers distinct advantages for a variety of simulations, including nonlinear transient dynamics, large deformation due to buckling, and damage evolution in materials or structures. However, conventional computational homogenization techniques, such as the FE2 and direct FE2 (D-FE2) methods, have not yet been integrated with an explicit algorithm because of the implicit framework in their numerical implementation, and thus cannot be widely applied to concurrent multi-level modeling of transient dynamic issues in multiscale materials and structures. In this study, an explicit D-FE2 method was proposed by incorporating explicit integration algorithms into the numerical calculation of microscale RVEs based on the D-FE2 method proposed by Tan [1]. To facilitate this, an extended Hill–Mandel principle which considers the conservation of both kinetic and internal energies between macro- and micro-scales was derived, and the conventional D-FE2 method was modified using the explicit FE method. The proposed explicit D-FE2 method was validated using a series of experiments and numerical examples including drop-hammer impact on multiscale honeycomb, stress wave propagation in porous materials, compressive buckling of multi-stable metamaterials, damage and failure of fiber-reinforced composites, etc. It was validated that the proposed explicit D-FE2 method is feasible and efficient for transient dynamic analysis of multiscale materials and structures, which might be a new avenue of research in the field of impact dynamics.

中文翻译：

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用于瞬态多尺度分析的显式 D-FE2 方法


显式 FE（有限元）方法为各种仿真提供了明显的优势，包括非线性瞬态动力学、屈曲引起的大变形以及材料或结构的损伤演变。然而，传统的计算均质化技术，如 FE2 和直接 FE2 （D-FE2） 方法，由于其数值实现中的隐式框架，尚未与显式算法集成，因此不能广泛应用于多尺度材料和结构中瞬态动力学问题的并发多级建模。在本研究中，基于 Tan [1] 提出的 D-FE2 方法，通过将显式积分算法纳入微尺度 RVE 的数值计算中，提出了一种显式 D-FE2 方法。为了促进这一点，推导出了一个扩展的 Hill-Mandel 原理，该原理考虑了宏观和微观尺度之间的动能和内能守恒，并使用显式 FE 方法修改了传统的 D-FE2 方法。通过一系列实验和数值实例验证了所提出的显式 D-FE2 方法，包括落锤冲击多尺度蜂窝、应力波在多孔材料中的传播、多稳定超材料的压缩屈曲、纤维增强复合材料的损伤和失效等。验证了所提出的显式 D-FE2 方法对于多尺度材料和结构的瞬态动力学分析是可行且高效的，这可能是冲击动力学领域的一条新研究途径。