Progressive Failure of a Unidirectional Fiber-reinforced Composite Using the Method of Cells: Discretization Objective Computational Results

Abstract

The smeared crack band theory is implemented within the generalized method of cells and high-fldelity generalized method of cells micromechanics models to capture progressive failure within the constituents of a composite material while retaining objectivity with respect to the size of the discretization elements used in the model. An repeating unit cell containing 13 randomly arranged flbers is modeled and subjected to a combination of transverse tension/compression and transverse shear loading. The implementation is verifled against experimental data (where available), and an equivalent flnite element model utilizing the same implementation of the crack band theory. To evaluate the performance of the crack band theory within a repeating unit cell that is more amenable to a multiscale implementation, a single flber is modeled with generalized method of cells and high-fldelity generalized method of cells using a relatively coarse subcell mesh which is subjected to the same loading scenarios as the multiple flber repeating unit cell. The generalized method of cells and high-fldelity generalized method of cells models are validated against a very reflned flnite element model. Micromechanics techniques can be employed to model the individual constituents within a composite material. Typically, a repeating unit cell (RUC) in the composite microstructure is identifled, and analysis is performed on that RUC assuming periodic boundary conditions. The response of a point in a continuum is determined assuming an inflnite array of the RUCs. However, representative volume element (RVE) methodologies exist which incorporate applying non-periodic boundary conditions to a subvolume that accurately represents the composite microstructure. The RVE is meant to represent the actual microstructure of the continuum, and the size of the features of the microstructure is preserved. Micromechanics can be utilized to provide the homogenized composite stifiness, or they can be used to model damage and failure within the constituents. If utilized for the latter, the global mechanisms can arise through the natural evolution and interaction of the mechanisms in the constituents of the micromechanics model. Numerous micromechanical frameworks exist that encompass analytical, semi-analytical, and numerical techniques. An expansive review of many micromechanics theories is given in Ref. 1. In this work, a continuum damage model (CDM) is implemented within the generalized method of cells (GMC), high-fldelity generalized method of