Multiscale Analysis of Transverse Cracking in Cross-Ply Laminated Beams Using the Layerwise Theory

A finite element model based on the layerwise theory is developed for the analysis of transverse cracking in cross-ply laminated beams. The numerical model is developed using the layerwise theory of Reddy, and the von Kármán type nonlinear strain field is adopted to accommodate the moderately large rotations of the beam. The finite element beam model is verified by comparing the present numerical solutions with the elasticity solutions available in the literature; an excellent agreement is found. The layerwise beam model is then used to investigate the influence of transverse cracks on material properties and the response in cross-ply laminates using a multiscale approach. The multiscale analysis consists of numerical simulations at two different length scales. In the first scale, a mesoscale, a systematic procedure to quantify the stiffness reduction in the cracked ply is proposed exploiting the laminate theory. In the second scale, a macroscale, continuum damage mechanics approach is used to compute homogenized material properties for a unit cell, and the effective material properties of the cracked ply are extracted by the laminate theory. In the macroscale analysis, a beam structure under a bending load is simulated using the homogenized material properties in the layerwise finite element beam model. The stress redistribution in the beam according to the multiplication of transverse cracks is taken into account and a prediction of sequential matrix cracking is presented.