An Inverse Method for Analyzing Defects in Heterogeneous Materials

Evaluation of defects in heterogeneous materials, such as cellulose-fiber composites, can lead to methods for improving strength. Full-field displacement measurement techniques,

e.g.

, digital image correlation and electronic speckle pattern interferometry, provide useful information by which defects can be evaluated. Inverse Methods (IM) have been used to determine material properties from full-field displacement data. In homogenous materials, the resulting system of equations relating displacements with applied load and constitutive properties is overdetermined and is solved with traditional least squares methods. However, heterogeneous materials create an underdetermined system that cannot be addressed in the same way. Numerically simulated heterogeneous, orthotropic materials were evaluated in a 2-D finite element model, and the resulting nodal displacements were used as input to an IM algorithm. The algorithm determined local moduli, Ex and Ey, with errors, ranging from 9% to 20%. Errors in calculated Gxy were greater. Techniques for reducing error are provided. Simulations suggested IM can be an important tool in defect evaluation given full-field displacement measurements.