A two-level optimization procedure for material characterization of composites using two symmetric angle-ply beams

A two-level optimization procedure for determining elastic constants E₁, E₂, G₁₂, and ν₁₂ of laminated composite materials using measured axial and lateral strains of two symmetric angle-ply beams with different fiber angles subjected to three-point-bending testing is presented. In the first-level optimization process, the theoretically and experimentally predicted axial and lateral strains of a [(45°/−45°)₆]_s beam are used to construct the strain discrepancy function which is a measure of the sum of the squared differences between the experimental and theoretical predictions of the axial and lateral strains. The identification of the material constants is then formulated as a constrained minimization problem in which the best estimates of shear modulus and Poisson's ratio of the beam are determined to make the strain discrepancy function a global minimum. In the second-level optimization process, shear modulus and Poisson's ratio determined in the first level of optimization are kept constant and Young's moduli of the second angle-ply beam with fiber angles different from 45° are identified by minimizing the strain discrepancy function established at this level of optimization. The suitability of the proposed procedure for material characterization of composite materials has been demonstrated by means of a number of examples.