基于单胞数字化模型的复合材料本构关系三维数值模拟

在渐进均匀化理论基础上, 建立了基于单胞数字化模型的复合材料宏观等效弹性性能的三维数值分析方法(DCB-FEA) 。该方法采用三维光栅化技术将三维单胞模型转化为三维光栅图形(数字化模型) , 并将光栅图形直接转化为三维有限元求解网格。产生的离散单元具有相同的几何尺寸和规则的形状, 单元刚度矩阵的数量将减少为单胞材料的个数。此外, 单胞数字化模型仅需记录每个离散单元的材料种类, 其他参数如单元节点编号、节点坐标等均可在求解过程中自动生成, 周期性边界条件也可以自动施加。随着分辨率的提高, 单胞数字化模型将产生更多数量的单元, 特别是对于三维单胞模型, 集成整体刚度矩阵时需要大量的计算机内存。采用基于Element-by-element 策略的预处理共轭梯度法( EBE- PCG) , 有限元方程的求解在单元级上进行, 避免了整体刚度矩阵的集成。通过对单向纤维增强复合材料的线弹性本构关系的数值模拟, 表明该方法可得到较为准确的复合材料等效模量。 

3D constitutive simulation of composite materialsbased on the digitized cell method

With the asymptotic homogenization theory,a novel digitized cell-based finite element method(DCB-FEA) is presented to simulate the constitutive properties of composite materials.In this method,a three-dimensional(3D) unit cell model to represent the actual geometry of the microstructure is converted into a raster graphic by 3D scan-conversion algorithms,and then directly interpreted to be a finite element model.Since all the elements have the regular shape and the same size,the number of element stiffness matrices actually needed is reduced to the number of materials.Furthermore,only the material ID's of each elements need to be stored;the other geometry information of the FE mesh,e.g.,the number of nodes and elements,element connectivities,and node coordinate values,can be automatically evaluated only if necessary in the computation.Otherwise,even the periodic boundary condition can be easily determined because the position of each boundary node is fixed.In the DCB-FE modeling,much more elements than usual are used with an improved resolution,especially for 3D cell models.This leads to huge memory required to store the result.So the element-by-element FEM with a preconditioned conjugate gradient method is utilized to avoid constructing the global stiffness matrix.Finally,numerical tests of 3D composite structure were conducted,and more accurate results of the effective modulus were obtained.