Wave propagation analysis in composite plate with clapping delamination based on spectral element method

The spectral element method is considered as a fast converging and computationally efficient numerical method for modelling propagating waves in composite structures. However, only simplified models for simulating damage either using additional mass, local changes in mechanical properties or separation of element nodes in the damage area are encountered in the literature. In our work, we propose to use contact traction at the damage interface in addition to nodes separation. Contact tractions are represented by Lagrange multipliers and are subject to frictionless sliding Karush-Kuhn-Tucker conditions to prevent the penetration of two composite layers. So far, this type of approach has been implemented in SEM for aluminium cracked structures. While the cracked structure is considered in a two-dimensional domain, clapping delamination in composite must be implemented in a three-dimensional space. The essence in determining the contact forces is to identify the gap between two layers for each time step. The element nodes of one surface, termed "slave", are projected onto another surface, termed "master". The gap is equal to the difference of the position vectors of each point, while according to KKT conditions, contact forces appear if the gap is less than zero.