An enhanced asymptotic homogenization method of the static and dynamics of elastic composite laminates

Abstract

The homogenization method has been used often in analyzing the composite materials but has had limited use with the laminated structures. This is due to a limitation of the homogenization theory, which assumes the unit cell should be periodically represented in any specific area. The main attraction of the homogenization method is its systematic capability to develop the homogenized macroscopic constitutive relation of composite materials and to compute the stresses in the microstructure of composites. In other words, both the macro- and micromechanics can be treated in the same context. In this paper, we will develop an enhanced asymptotic homogenization method (EHM); this method is developed from the partial asymptotic expansion and the condensed third-order shear deformation theory. This theory uses the reduced matrix method to consolidate all the stiffness matrices into four stiffness matrices (the extension; coupling; bending and transverse shear stiffness matrices) in the same manner as with the first-order shear deformation theory (FSDT). Two FORTRAN programs PRELAM and POSTLAM [Int. J. Comput. Struct. 76 (2000) 319; An enhanced asymptotic homogenization method of elastic composite laminates, Ph.D. Thesis, The University of Michigan, 1999] were also developed from the finite element implementation of the enhanced homogenization method. The pre-processor, PRELAM, reads the unit cell model and generates the homogeneous material stiffness matrix for a laminated structure. The post-processor, POSTLAM, calculates the local stress distribution based on the strains and curvatures obtained from the global structure analysis generated by the commercial finite element software, i.e., ABAQUS or MSC/NASTRAN. By the nature of homogenization method, these computational methods are capable of handling geometrically complicated microstructures and predicting the microscopic stress distributions. Since, the number of unknown variables for EHM and FSDT are the same, this implies that the results from EHM is easily utilized by ABAQUS in the global analysis. Therefore, one of the main benefits to EHM is that it is readily applied in commercial FEM packages, but not that it is as accurate as other methods. Numerical examples are also presented to validate these two programs.