A common framework for three micromechanics approaches to analyze elasto-plastic deformations of fiber-reinforced composites

Three micromechanics approaches (method of cells, Fourier series analysis, and transformation field analysis) are formulated so that the final expressions relating the local sub-cell strain to the homogenized macro-strain in a unit cell are similar, although the three techniques and assumptions made to deduce them are different. This allows for a direct comparison of the three methods, and, more importantly, enables one to use the same algorithm for solving equations after the strain concentration and the strain transformation matrices have been determined from the three methods. Elastic constants found from the three approaches compare well with each other, and with those experimentally found. The micromechanics approaches are embedded in a finite element scheme to study elasto-plastic deformations of fiber-reinforced composites. The three sets of the axial stress-axial strain curves are found to correlate well with each other, and with the experimental ones. We use these micromechanics approaches to determine strains in each sub-cell from the macro-strains (i.e., dehomogenize global strains into local strains), find stresses in each constituent or sub-cell, and then employ the micromechanics technique to find macro-stresses (Le., homogenize stresses) and stiffnesses.