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A higher-order layerwise model is proposed to determine stress intensity factors using virtual crack closure technique for single-edge-crack aluminum plates with patch repairs. The present method is based on p -convergent approach and adopts the concept of subparametric elements. In assumed displacement fields, strain-displacement relations and three-dimensional constitutive equations of layers are obtained by combination of two- and one-dimensional shape functions. Thus, it allows independent implementation of p -refinement for in-plane and transversal displacements. In the proposed elements, the integrals of Legendre polynomials and Gauss-Lobatto technique are employed to interpolate displacement fields and to implement numerical quadrature, respectively. For verification of the present model, not only single-edge-crack plates but also V-notch aluminum plates are first analyzed. For patched aluminum plate with behavior of complexity, the accuracy and simplicity of the present model are shown with comparison of the results with previously published papers using the conventional three-dimensional finite elements based on h -refinement.

Implementation of Virtual Crack Closure Technique for Damaged Composite Plates Using Higher-Order Layerwise Model