Abstract Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response at the macroscopic level. Such techniques allow the use of fully detailed models to be avoided, thus resulting in a notable decrease in the overall computational cost at fixed numerical accuracy compared to the so-called direct numerical simulations. In the present work, two different multiscale modeling approaches are presented for the analysis of microstructural instability-induced failure in locally periodic fiber-reinforced composite materials subjected to general loading conditions involving large deformations. The first approach, which is of a semi-concurrent kind, consists in the “on-the-fly” derivation of the macroscopic constitutive response of the composite structure together with its microscopic stability properties through a two-way computational homogenization scheme. The latter one is a novel hybrid hierarchical/concurrent multiscale approach relying on a two-level domain decomposition scheme used in conjunction with a nonlinear homogenization scheme performed at the preprocessing stage. Both multiscale approaches have been suitably validated through comparisons with reference direct numerical simulations, by which the ability of the latter approach in capturing boundary layer effects has been demonstrated.

中文翻译：

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通过替代建模方法对纤维增强复合材料结构中不稳定引起的失效机制进行多尺度分析

摘要 多尺度技术已被广泛证明有可能克服均质化方案在表示非均质介质中的微观失效机制以及它们在宏观水平上对其结构响应的影响方面的局限性。此类技术允许避免使用完全详细的模型，因此与所谓的直接数值模拟相比，在固定数值精度下的整体计算成本显着降低。在目前的工作中，提出了两种不同的多尺度建模方法，用于分析局部周期性纤维增强复合材料在涉及大变形的一般载荷条件下的微观结构不稳定引起的失效。第一种方法是半并发的，包括通过双向计算均质化方案对复合结构的宏观本构响应及其微观稳定性特性进行“即时”推导。后者是一种新颖的混合分层/并发多尺度方法，它依赖于与在预处理阶段执行的非线性同质化方案结合使用的两级域分解方案。通过与参考直接数值模拟的比较，这两种多尺度方法都得到了适当的验证，从而证明了后一种方法在捕捉边界层效应方面的能力。后者是一种新颖的混合分层/并发多尺度方法，它依赖于与在预处理阶段执行的非线性同质化方案结合使用的两级域分解方案。通过与参考直接数值模拟的比较，这两种多尺度方法都得到了适当的验证，从而证明了后一种方法在捕捉边界层效应方面的能力。后者是一种新颖的混合分层/并发多尺度方法，它依赖于与在预处理阶段执行的非线性同质化方案结合使用的两级域分解方案。通过与参考直接数值模拟的比较，这两种多尺度方法都得到了适当的验证，从而证明了后一种方法在捕捉边界层效应方面的能力。