Multi-scale computational homogenization of structured thin sheets
Multi-scale computational homogenization of structured thin sheets
复制标题
结构化薄片的多尺度计算均质化
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
V. Kouznetsova
中科院分区：
文献类型：
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作者：
M. Geers;E W C Coenen;V. Kouznetsova
结构化和分层的薄板用于各种创新应用，例如柔性显示器、可卷曲太阳能电池或柔性电子产品。因此，使用了不同材料的堆叠，其在层之间通常具有高度复杂的互连，其通常以弯曲结合固有的热机械失配来加载。因此，在分层子结构的水平发生不同的故障机制，这构成了一个严重的可靠性问题。本文讨论了结构薄板的双尺度均匀化问题，采用了高阶全厚度代表体积元。该方法依赖于微观结构力学的计算均匀化，在过去的十年中已经开发了一阶和二阶求解策略。结构化薄板的变形朝向壳型连续体的尺度放大在性质上是二阶的。高阶运动学是基于微观结构RVE定义的，其表示宏观结构和周期性平面内单元（例如，柔性显示器中的单个像素）的全厚度。讨论了边界条件的确定和微尺度边值问题的求解。所获得的微观尺度的应力状态均匀化朝向3D宏观壳结构，其中详细的方面将被强调。简要介绍了耦合数值求解策略。最后，给出了一个例子，并强调了一些实际问题的应用，其中的解决方案提供了每个规模上的直接信息。因此，在子结构水平上的失效事件的合并是自然的。
Structured and layered thin sheets are used in a variety of innovative applications, e.g. flexible displays, rollable solar cells or flexible electronics. Stacks of different materials, with often highly complex interconnects between layers, are thereby used, which are typically loaded in bending combined with intrinsic thermo-mechanical mismatches. As a result, different failure mechanisms at the level of the layered substructure occur, which constitutes a serious reliability concern. This paper deals with the two-scale homogenization of structured thin sheets, whereby a higher-order through-thickness representative volume element (RVE) is used. The methodology relies on the computational homogenization of the mechanics of microstructures, for which first-order and second-order solution strategies have been developed in the past decade. The upscaling of the deformation of structured thin sheets towards a shell-type continuum is second-order in nature. The higher-order kinematics is defined on the basis of a microstructural RVE, which represents the full thickness of the macroscopic structure and a periodic in-plane cell (e.g. a single pixel in a flexible display). The elaboration of the boundary conditions and the solution of the micro-scale boundary value problem are discussed. The obtained micro-scale stress state is homogenized towards a 3D macroscopic shell structure, for which detailed aspects will be emphasized. The coupled numerical solution strategy is briefly outlined. Finally, an example is given and the application to a number of practical problems is highlighted, where the solution provides direct information on each scale. The incorporation of failure events at the substructure level is thereby naturally at hand.