Abstract The current work proposes a novel approach for the implementation of periodic representative volume element (RVE) based multiscale modeling using the finite element method. The approach is based on a rigorous mechanics foundation that implements appropriate boundary conditions for the RVE analysis and simplifies the homogenization technique. Stress components are relaxed in the chosen periodic directions and associated strains are calculated while maintaining periodicity. Our concept ensures that for a displacement-based mechanics approach, the stresses and strains in the domain are periodic, rather than the displacements. This approach allows for computing homogenized effective mechanical properties of heterogeneous materials and capturing appropriate volume change and shape distortion of the RVE at lower length scales. We use the finite element based Multiphysics Object Oriented Simulation Environment (MOOSE, https://mooseframework.org) for implementing the proposed periodic RVE scheme. Our model has been verified with analytical calculations and effective property estimation from various micromechanical approaches. The effective stiffness of a composite material calculated from this approach is in good agreement with other computational and experimental findings. The proposed model has also been applied to different multiscale and multiphysics engineering applications.

中文翻译：

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一种基于有限元的应变周期性实现方法的开发

摘要 当前的工作提出了一种使用有限元方法实现基于周期代表体积元 (RVE) 的多尺度建模的新方法。该方法基于严格的力学基础，为 RVE 分析实施适当的边界条件并简化均质化技术。应力分量在选定的周期方向上松弛，并在保持周期性的同时计算相关应变。我们的概念确保对于基于位移的力学方法，域中的应力和应变是周期性的，而不是位移。这种方法允许计算异质材料的均质有效机械性能，并在较低的长度尺度上捕获 RVE 的适当体积变化和形状畸变。我们使用基于有限元的多物理场面向对象仿真环境 (MOOSE, https://mooseframework.org) 来实现建议的周期性 RVE 方案。我们的模型已经通过各种微机械方法的分析计算和有效的属性估计得到验证。通过这种方法计算的复合材料的有效刚度与其他计算和实验结果非常一致。所提出的模型也已应用于不同的多尺度和多物理场工程应用。通过这种方法计算的复合材料的有效刚度与其他计算和实验结果非常一致。所提出的模型也已应用于不同的多尺度和多物理场工程应用。通过这种方法计算的复合材料的有效刚度与其他计算和实验结果非常一致。所提出的模型也已应用于不同的多尺度和多物理场工程应用。