A multiscale computational framework to capture stress concentrations and localized nonlinearity in composite structures is presented. An enriched approximation space, constructed using the generalized finite element method (GFEM), is used to incorporate nonlinear, heterogeneous material behavior into coarse-scale models on the fly. Enrichment functions are constructed using the GFEM with global–local enrichment functions (GFEMgl). The auxiliary local problems associated with the GFEMgl also define fine-scale constitutive behavior that is inherited by the coarse global problem. This allows a coarse homogenized global problem to learn about material heterogeneity and/or nonlinearity on the fly, considerably increasing the flexibility of the method. On top of the explicit definition of heterogeneity in local problems, the locally defined constitutive law can incorporate further levels of heterogeneity that are not explicitly modeled at the global scale. The proposed GFEMgl comes with the efficiency and scalability characteristic of the method and greatly increases the flexibility when applied to heterogeneous structures with localized material nonlinearity.

中文翻译：

---

使用广义有限元法对复合材料进行动态多尺度分析


提出了一种捕获复合结构中的应力集中和局部非线性的多尺度计算框架。使用广义有限元方法 (GFEM) 构建的丰富的近似空间用于将非线性、异质材料行为动态纳入粗尺度模型中。富集函数是使用具有全局-局部富集函数 (GFEMgl) 的 GFEM 构建的。与 GFEMgl 相关的辅助局部问题还定义了由粗略全局问题继承的精细尺度本构行为。这使得粗均质全局问题能够动态了解材料异质性和/或非线性，从而大大提高了该方法的灵活性。除了局部问题异质性的明确定义之外，局部定义的本构法还可以包含未在全球范围内明确建模的进一步水平的异质性。所提出的 GFEMgl 具有该方法的效率和可扩展性特征，并且在应用于具有局部材料非线性的异质结构时大大增加了灵活性。