周期性点阵类桁架材料等效弹性性能预测及尺度效应

PREDICTION OF EQUIVALENT ELASTIC PROPERTIES OF TRUSS MATERIALS WITH PERIODIC MICROSTRUCTURE AND THE SCALE EFFECTS

比较了D irichlet型和Neum ann型边界条件下的代表体元法及均匀化方法对具有周期性结构的点阵类桁架材料等效弹性性能的预测结果.数值结果表明,D irichlet型和Neum ann型边界条件下的代表体元法所得结果随着参与模拟的单胞(微结构的最小周期)个数的增加,分别从上下界逼近均匀化方法的结果.对于一类具有特殊微结构的桁架材料,只需一个单胞即可充分逼近均匀化结果.指出产生尺度效应的判据是,对D irichlet型边界条件下的代表体元法,单胞公共边界处的节点支反力是否平衡;对Neum ann型边界条件下的代表体元法,单胞边界间变形是否协调.最后,我们证明了对于一类均匀化方法求解中没有广义自由度的桁架材料,其均匀化结果就是各构件性能按照体积份数加权平均得到.

The equivalent elastic property of truss materials with periodic microstructure is predicted by the representative volume element （RVE） method based on the affine （Dirichlet-type） or homogeneous stress （Neumann-type） boundary conditions and the homogenization method. Numerical experiments show that, with increasing the number of unit cell,n, the results got from RVE method under the Dirichlet and Neumann boundary conditions converge towards those the obtained by the homogenization method from the upper and lower sides respectively. For some special types of the unit cell, RVE method with only one unit cell gives almost the same results as obtained from homogenization method. A simple criterion for the scale effects is proposed： the scal effects occurrence edpends on whether the equilibrium of the boundary nodal forces is guaranteed under Dirichlet boundary conditions, or whether the deformation compatibility at the unit cell boundaries is guaranteed under the Neumann boundary conditions for the RAV method. It is also proved that the volume average of the rods＇ properties gives the accurate prediction of the equivalent property for a special type of truss material of which the unit cell has no general freedoms in the homogenization equation.