The paper presents an assumed strain formulation over polygonal meshes to accurately evaluate the strain fields in nonlocal damage models. An assume strained technique based on the Hu-Washizu variational principle is employed to generate a new strain approximation instead of direct derivation from the basis functions and the displacement fields. The underlying idea embedded in arbitrary finite polygons is named as Polytopal composite finite elements (PCFEM). The PCFEM is accordingly applied within the framework of the nonlocal model of continuum damage mechanics to enhance the description of damage behaviours in which highly localized deformations must be captured accurately. This application is helpful to reduce the mesh-sensitivity and elaborate the process-zone of damage models. Several numerical examples are designed for various cases of fracture to discuss and validate the computational capability of the present method through comparison with published numerical results and experimental data from the literature.

中文翻译：

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用于基于非局部损伤模型的混凝土断裂建模的 Polytopal 复合有限元

本文提出了多边形网格上的假设应变公式，以准确评估非局部损伤模型中的应变场。采用基于 Hu-Washizu 变分原理的假设应变技术来生成新的应变近似，而不是直接从基函数和位移场推导。嵌入在任意有限多边形中的基本思想称为 Polytopal 复合有限元 (PCFEM)。PCFEM 相应地应用于连续介质损伤力学的非局部模型的框架内，以增强对损伤行为的描述，其中必须准确捕获高度局部化的变形。此应用程序有助于降低网格敏感性并详细说明损坏模型的过程区域。