Multiscale static analysis of notched and unnotched laminates using the generalized method of cells

Abstract

The generalized method of cells (GMC) is demonstrated to be a viable micromechanics tool for predicting the deformation and failure response of laminated composites with and without notches subjected to tensile and compressive static loading. Given the axial [0], transverse [90], and shear [+45/−45] response of a carbon/epoxy (IM7/977-3) system, the unnotched and notched behavior of three multidirectional layups (1) Layup 1: [0,45,90,−45]2S, (2) layup 2: [60,0,-60]3S, (3) layup 3: [30,60,90,−30,−60]2S) are predicted under both tensile and compressive static loading. Matrix nonlinearity is modeled in two ways. The first assumes all nonlinearity is due to anisotropic progressive damage of the matrix only, which is modeled, using the multiaxial mixed mode continuum damage model (MMCDM) within GMC. The second utilizes matrix plasticity coupled with brittle final failure based on the maximum principle strain criteria to account for matrix nonlinearity and failure within NASA's multiscale framework (FEAMAC). Both MMCDM and plasticity models incorporate brittle strain and stress based failure criteria for the fiber. Upon satisfaction of this criterion, the fiber properties are immediately reduced to a nominal value. The constitutive response for each constituent (fiber/matrix) is characterized using a combination of vendor data and the axial, transverse and shear response of unnotched laminates. Then, the capability of the multiscale methodology is assessed, by performing blind predictions of the mentioned notched and unnotched composite laminates response under tensile and compressive loading. Tabulated data along with the detailed results (i.e. stress–strain curves as well as damage evolution states at various ratios of strain to failure) for all laminates are presented.