周期性微结构材料损伤扩展的相场法
A phase field approach for damage propagation in periodic microstructured materials
摘要：
本文采用一种新的基于有限元的多尺度计算方法研究了周期性复合材料的损伤演化。该方法是通过原始的相场方法的裂缝的均匀化方法相结合的手段。这最后一个应用在宏观尺度上的等效均匀连续，其本构性质得到封闭的形式，通过两个尺度的渐近均匀化计划。该公式允许考虑在微观尺度上对损伤演变的不同假设（例如，基体中的损伤而不是夹杂物/纤维中的损伤），以及微观结构拓扑所起的作用。数值结果表明，该配方导致的表观抗拉强度和峰后分支的无缺口和缺口试样不仅依赖于内部长度尺度的相场方法，作为均匀材料，但也对夹杂物的体积含量和形状。降尺度关系允许在宏观模型的任何点处完全重建微观场，作为简单的后处理操作。
英文摘要：
In the present work, the evolution of damage in periodic composite materials is investigated through a novel finite element-based multiscale computational approach. The methodology is developed by means of the original combination of homogenization methods with the phase field approach of fracture. This last is applied at the macroscale level on the equivalent homogeneous continuum, whose constitutive properties are obtained in closed form via a two-scale asymptotic homogenization scheme. The formulation allows considering different assumptions on the evolution of damage at the microscale (e.g., damage in the matrix and not in the inclusion/fiber), as well as the role played by the microstructural topology. Numerical results show that the proposed formulation leads to an apparent tensile strength and a post-peak branch of unnotched and notched specimens dependent not only on the internal length scale of the phase field approach, as for homogeneous materials, but also on the inclusion volumetric content and its shape. Down-scaling relations allow the full reconstruction of the microscopic fields at any point of the macroscopic model, as a simple post-processing operation.
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