Advanced finite element analyses to compute the J-integral for delaminated composite plates

This study concerns several possible ways of computing the J-integral in the cases of laminated composite plate structures containing delamination. On the one hand, two special types of plate finite element families are provided for advanced fracture mechanical analyses. On the other hand, a numerical algorithm is introduced also that utilizes results derived from solid element models built in commercial finite element software. In order to create plate elements, the first-order (FSDT) and the third-order shear deformation theories (TSDT) are applied with two equivalent single layers. A subparametric element family is created by using the Hermite interpolation with the FSDT that grants the continuity of the derivatives at the element borders. Besides, an isoparametric family is created also with the TSDT employing the Lagrange interpolation scheme. This paper aims to present the compact formulations of calculating the J-integral around the delamination fronts for both plate element families. The calculation of the J-integral is implemented as a matrix multiplication by taking advantage of the properties of plate transition elements. The models yield improved fracture mechanical analyses for delaminated composite plates with linear elastic material behaviour. In addition, computing the J-integral is not available in most commercial finite element software for laminated orthotropic materials, therefore, an appropriate algorithm is presented here for this purpose. To conclude, the models and algorithms are applied to two case studies and subjected to a comprehensive comparison with analytical and formerly used finite element solutions.

Automated summary

This study explores several methods for computing the J-integral in laminated composite plate structures with delamination. It introduces two special types of plate finite elements and a numerical algorithm. The study presents compact formulations for calculating the J-integral and applies matrix multiplication to take advantage of plate transition elements. The models and algorithms are applied to case studies and compared with analytical and previously used finite element solutions.