Adaptive modelling of delamination growth using isogeometric continuum shell elements

Paper in proceeding, 2017

As a means to decrease the complexity and size of numerical models for the simulation of progressive failure in composite laminates, and thereby also the computational time required for the simulations, we here propose an adaptive continuum shell element model based on the concept of Isogeometric Analysis. The concept based is based on the approach presented by Hosseini et al. [1], but in contrast to their work, in which delamination interfaces are predefined, we here address the need to handle successive introduction of new discontinuities in an automated fashion. The formulation adopts T-spline basis functions for the discretisation of the shell mid-surface, whereas a higher-order B-spline functions are used for the interpolation in the thickness direction. A discontinuity can be incorporated in this latter function by so-called knot-insertion to account for ply interfaces (weak discontinuities) and delaminations (strong discontinuities). In order to automatically enhance the element, various stress-based criteria using element local improved interlaminar stresses can be used. However, for such a stress based approach, the prediction of the through-thickness variation of out-of-plane stress components needs to be improved if a coarse shell approximation is used (the so-called lumped state explained below). For this purpose, we propose and demonstrate the capability of a reconstruction technique based on the classical strategy of integrating the momentum balance equations. Due to the nature of the isogeometric analysis approximation and its higher order displacement smoothness over element edges, this reconstruction can be performed element-wise. This possibility to do an element-wise reconstruction is a strength compared to traditional shell elements, based on Lagrange approximations for the displacement field, for which displacement approximation derivatives (and thereby stresses) are non-smooth. In this way, the isogeometric continuum element can be used in an even more efficient fashion, allowing for the detailed analysis of large, thin-walled composite structures.