基于Direct FE2弹塑性多尺度方法的复合材料三维弹塑性力学行为模拟

Simulating the three-dimensional elastoplastic behavior of composite materials based on Direct FE2 elastoplastic multiscale method

  • 摘要: 发展了一种基于Direct FE2的弹塑性多尺度分析方法,适用于对三维复合材料层合板弹塑性力学响应进行数值模拟。将宏观模型和微观代表性体积单元(RVE)合并在同一个有限元分析中,并通过线性多点约束条件(MPCs)将宏观和微观两尺度模型的自由度进行耦合,从而实现尺度间信息传递。通过采用微观非均质材料组分的本构关系进行数值分析可直接获得宏观均质结构的力学响应。微观RVE模型包含弹性纤维和塑性基体两种材料组分,而基体的非线性力学行为采用弹塑性本构模型进行描述。基于径向回映法推导了基体弹塑性本构模型的数值算法及相应的数值一致性切线刚度矩阵,保证有限元分析采用 Newton-Raphson 迭代法解答非线性问题的计算效率,开发了用户自定义材料子程序UMAT并嵌于有限元程序ABAQUS v6.14。对不同加载情况下的T300/7901复合材料分别采用单个宏观单元、多向层合板RVE和单向层合板三种不同尺寸模型进行数值模拟,验证Direct FE2分析方法的有效性。结果显示,采用本文发展的Direct FE2弹塑性多尺度分析方法预测得到的宏观应力-应变曲线与试验结果吻合良好,同时能捕捉到微观RVE组分的应力应变演化,为复合材料微观结构的设计和制备提供一种有效分析方法。

     

    Abstract: An elastoplastic multiscale analysis approach based on the Direct FE2 is developed for the numerical simulation of elastoplastic mechanical behavior of three-dimensional composite laminates. In this method, the macroscale model and microscale representative volume element (RVE) are combined into a single finite element analysis problem, and the degrees of freedom (DOF) of the two-scale models are directly coupled by linear multi-point constrains (MPCs) to define the scale transition relations. The mechanical response of macroscale homogeneous structures can be obtained directly by numerical analysis using the constitutive relations of microscale heterogeneous material components. The heterogeneous RVE containing elastic fiber and plastic matrix is built, and the nonlinear elastoplastic mechanical behavior of matrix is described by an elastoplastic constitutive model. Based on the radial return algorithm, the numerical algorithm and the corresponding numerical consistency tangent stiffness matrix of elastoplastic model are derived to ensure the computational efficiency of Newton-Raphson method in the finite element analysis. A user-defined subroutine UMAT is developed and embedded in the finite element procedure ABAQUS v6.14 to implement the numerical integration algorithm of the matrix constitutive model. The effectiveness of the proposed Direct FE2 method is demonstrated through the numerical simulations of T300/7901 composites under different loading conditions using three different models: the single macroscale element model, the multidirectional laminated RVE model and the whole unidirectional laminate model. It is shown that the macroscale stress-strain curves predicted by the present Direct FE2-elastoplastic multiscale analysis approach agree well with the experimental results, and it is able to capture the evolution of the solution-dependent variables of the microscale RVE. The proposed approach provides an effective analysis method for designing and manufacturing of the microstructures of composite laminates.

     

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