Delamination is an important mode of failure in composite structures. This work describes two different cohesive layer models which can be used to predict the initiation and the growth of delamination. The first one designated as the UMAT model is based on a stress-strain relationship and has a small but finite thickness. The second model designated as the UEL model is constructed in terms of nodal forces and relative displacements and the initial thickness of the model is chosen as zero. It is demonstrated that both models are capable of predicting delamination initiation and can be used to identify the critical values of the modal components of strain energy release rate. However it turns out that the UMAT model is not able to predict large crack extensions as it has a tendency to form a "neck" and "lock" the crack tip.; Delamination under low velocity impact on composite laminates is investigated using the cohesive layer models in the light of published experimental results. It is found that the models are able to capture the trends in the impact velocity versus crack length relationships. There is a small but noticeable difference in the predictions of static and dynamic analyses and the initial crack length is seen to be a factor in the final crack lengths attained in the dynamic analysis.; The behavior of a compressed sandwich column with a suddenly triggered delamination between a facing sheet and core is studied. It is found that if the axial end-shortening exceeds a threshold value the delamination growth is rapid and unstable; within a matter of milliseconds, the entire facing sheet can be ripped apart from the core.; The dissertation concludes with an abbreviated study of a 3-D problem employing an extended version of UEL type element. The delamination is studied as a plate is compressed in a certain direction. It is seen that under static conditions the overall buckling interferes with delamination growth by promoting contact between delaminated surfaces. However when the overall bending is retrained the delamination grows rapidly in a direction transverse to the direction of compression.
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