基于三维纤维计算晶粒的纤维复合材料直接细观力学建模

3D computational grains with embedded fibers for the direct micromechanical modeling of fiber composites

面向纤维复合材料与结构的优化设计需要,建立高效准确的纤维复材细观力学仿真工具具有重要意义.本文首次提出了包含内嵌纤维的三维计算晶粒(computational grains),用于纤维增强复合材料的直接细观力学建模,基于所开发的纤维计算晶粒方法,可以直接构造含有多根随机分布纤维的代表性体积单元(RVE).此外,本文提出了一种基于缩放柱调和函数的Papkovich-Neuber解来表征纤维和基体中独立的Trefftz试函数位移场,并且开发了一种新的多场边界变分原理来计算纤维计算晶粒的刚度矩阵.数值算例表明,对于内嵌大量随机分布纤维的RVE,纤维计算晶粒不需要构造复杂的网格,即可快速计算RVE的精确应力场,并预测其有效力学性能.此外,这也是内嵌纤维的三维有限元单元的首次提出.

For the integrated design of composite material and structures,it is essential to have an effective micromechanical numerical tool to link macroscopic material properties to microstructural configurations.In this paper,3D computational grains(CGs)with embedded fibers are proposed for the first time,for the direct micromechanical modeling of fiber composites.The microstructure of a unidirectional lamina with random fibers can be assembled by many CGs,and the stiffness matrix of each CG with an embedded fiber can be directly computed by combining two new algorithms.On one hand,a new kind of Trefftz trial displacement field based on scaled cylindrical harmonics is independently assumed,in addition to inter-elemental displacement interpolations with surface nodal degrees of freedom(DoFs).On the other hand,a new kind of multi-field boundary variational principle is proposed to relate independently assumed Trefftz fields to nodal DoFs and to derive the stiffness matrix.Numerical examples demonstrate that without the traditional fine meshing,accurate distribution of microstresses in a representative volume element(RVE)with thousands of fibers can be directly computed,and the equivalent orthotropic properties of fiber composites can be predicted.This is also the first time that a three-dimensional finite element with an embedded fiber is developed.