基于双重网格的混凝土自适应宏细观协同有限元分析方法

混凝土损伤开裂表现出明显的跨尺度特征，其演化过程与细观材料结构直接相关。如何在兼顾效率和精度前提下分析混凝土损伤开裂的跨尺度演化过程一直是比较棘手的问题。在假定处于弹性阶段的混凝土为宏观均匀材料和处于损伤开裂阶段的混凝土为细观非均匀材料的基础上，提出了一种基于双重网格的混凝土自适应宏细观协同有限元分析方法。该方法通过在分析域内布置宏细观双重网格分别建立宏观尺度和细观尺度有限元计算模型，通过宏观尺度至细观尺度的自适应转换在分析过程中动态确定宏细观协同分析的宏观区域和细观区域，通过基于形函数插值的多点位移约束实现宏细观协同有限元模型中的非协调重叠网格连接。算例分析表明，采用该文方法不仅可通过考虑损伤开裂区的细观材料结构保证模拟精度，亦可通过在分析中自适应确定细观尺度分析区域提高模拟效率。

ADAPTIVE MACRO-MESO-SCALE CONCURRENT FINITE ELEMENT ANALYSIS APPROACH OF CONCRETE USING DUAL MESH

The damage and cracking behavior of concrete is a trans-scale phenomenon since the macroscopic fracturing is greatly affected by the material structure on the mesoscale. How accurately and efficiently to simulate the trans-scale evolution process of concrete failure is still an open issue. In this work, an adaptive macro-meso-scale concurrent finite element (FE) based approach of concrete is proposed, in which concrete is considered as homogeneous in the elastic regime and as heterogeneous in the nonlinear regime. The macroscale and the mesoscale FE model should be parallelly generated for the whole analysis domain with a strategy of dual mesh containing both macroscale and mesoscale meshes. By defining an adaptive criterion of the scale transformation from macroscale to mesoscale, the macro-meso-scale concurrent model is adaptively updated depending on the stress status of the macroscale element. The shape function interpolation based a multi-point constraint method is adopted for the connection between the macroscale mesh and the mesoscale one. Numerical examples demonstrate that the proposed approach can reach a proper balance between the simulation precision by considering the mesoscale material structure of concrete and the efficient simulation by adaptively determining the mesoscale analysis region.