石墨烯纳米复合材料的降阶均匀化方法及其数值实现

Reduced order homogenization of graphene nanocomposites and its numerical implementation

  • 摘要: 对石墨烯纳米复合材料进行三维有限元建模通常需极其精细的网格。在考虑塑性演变的情况下,细观代表性单元体模型的计算效率极其低下。为此,基于非均匀变换场分析理论,提出了石墨烯纳米复合材料的降阶均匀化方法。首先,针对不同加载路径进行预分析,提取细观塑性应变场信息;然后对这些信息进行本征正交分解,从而得到若干个塑性模态,用作降阶模型的基函数;基于宏、细观耗散功的等效原理,导出降阶变量的本构模型。该方法的离线分析部分通过MATLAB编程实现。为了便于工程计算,在线分析部分则由商业有限元软件ABAQUS的UMAT用户子程序接口实现。基于三维算例分析,验证了所提方法的有效性。结果显示,在保证较高精度的前提下,针对三维代表性单元体计算的加速率可达103~104量级。

     

    Abstract: A three-dimensional finite element modeling for graphene nanocomposites usually requires very fine meshes. In case of plasticity, the computational efficiency of a micro representative volume element model is extremely low. For a remedy, based on the theory of nonuniform transformation field analysis, a reduced order homogenization method for graphene nanocomposites was proposed. First, we performed a pre-analysis for different loading paths to extract micro plastic strain fields; then a proper orthogonal decomposition of those field information was performed to obtain several plastic modes, which were used as basis functions for model order reduction. A constitutive model of reduced variables was derived from the equivalence of macro and micro dissipation power. The offline analysis of this method was implemented in MATLAB. For engineering computations, the online analysis was implemented by the user subroutine interface UMAT of the commercial finite element software ABAQUS. The effectiveness of the proposed method was illustrated by three-dimensional numerical examples. The results show that the acceleration rate for 3D representative volume element computations is of the order of 103~104, while maintaining a sufficient accuracy level.

     

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