An efficient multiscale method for 2D large displacement – Small strain analysis of heterogeneous materials

Abstract

A multiscale computational method is developed for 2D large displacement – small strain analysis of heterogeneous structures. The co-rotational approach is employed to obtain the equivalent tangent stiffness matrix of the coarse element in the global coordinate system. The equivalent tangent stiffness matrix of the whole heterogeneous structure with the coarse-scale mesh can be assembled naturally. The equilibrium iterations for each load step can be performed directly on the macroscopic scale and thus a large number of computational resources will be saved. Moreover, a new local displacement correction technique is proposed to calculate the microscopic stress and strain results. Two numerical examples are carried out to verify the validity and efficiency of the proposed multiscale method. It can be found that the proposed method not only ensure the accuracy but also save the computational resources greatly by comparison with the traditional finite element method (FEM).