Abstract：A new multiscale computational method is developed to study the mechanical properties of periodic lattice truss materials. The underlying idea is to construct numerically the multiscale base functions to reflect the heterogeneities of the unit cells and obtain the equivalent stiffness matrix of the unit cells of periodic truss materials. Then the problems only need to be solved on the large–scale meshes and the computational cost can be dramatically reduced. To consider the coupled effect among different directions in the multi-dimensional problems, the coupled additional terms of base functions for the interpolation of the vector fields are introduced. Numerical experiments show that the base functions constructed by the linear boundary conditions sometimes will have a strong boundary effect. While the oscillatory boundary conditions obtained by the oversampling technique and the periodic boundary conditions can greatly reduce the errors induced by the forcible deformations of the unit cells. Especially for the unit cells whose coarse-mesh scales are close to the small scales of heterogeneities, the periodic boundary conditions proposed can improve greatly the accuracy of the results. The advantage of the method developed is that the downscaling computation could be realized easily and the stress and strain in the unit cell can be obtained simultaneously in the multiscale computation. Thus the multiscale method studied here has good potential in the strength analysis of heterogeneous materials.
2011, Vol. 32 
