13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- them. The finite thickness interface elements are used to connect shell elements belonging to adjacent sublaminates, see Fig. 1b. Thus the laminates could be considered as sandwich shells stacked by shell elements and the interface elements. In this way, the intralaminar and interlaminar damages could be considered separately with both kinds of elements. Figure 1. (a) 3D solid model (b) 3D shell model The interface element consists of eight rigid beams and a zero thickness cohesive element. The master node of a rigid beam is used to connect external shell node, and its slave node is used to connect internal cohesive element node. The rigid beams transfer the translational and rotational movements of the shell nodes to the internal cohesive element (Fig. 2). Interlaminar fracture takes place at the internal cohesive elements. Although being composed of discrete rigid beams and cohesive element, the interface element presents itself as a solid one in which DOFs of the internal nodes have been eliminated by deduction of its kinematic formulae. There will be no additional DOFs are required in the FE models except those of shell elements. The interface element has been implemented in the commercial FE code ABAQUS [7] via its user element subroutine (UEL). Newton-Cotes full integration scheme is adopted. Figure 2. Schematic of the connection of shell elements and interface element 2.2. Interface element formulation In the interface element, the relation of the nodal displacements between master and slave nodes of the ith (i=1,…,8) rigid beam can be given as: S δi M i i u = t u (i=1,…, 8) (1) where ( ) T M MMMMxMyMz = , , , , , i i i i i i i u v w θ θ θ u and ( ) T S S S S Sx Sy Sz = , , , , , i i i i i i i u v w θ θ θ u are the displacement vectors at master and slave nodes of ith rigid beam respectively. δi t is the displacement transformation matrix of the two nodes: ( ) ( ) ( ) δi 1 0 0 0 - - - 0 1 0 - - 0 - 0 0 1 - - - 0 = 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 i i i i S M S M i i i i S M S M i i i i S M S M z z y y z z x x y y x x ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ t (2) Solid Elements Cohesive Elements (a) Debonded Region (b) z y x Shell Elements Interface Elements Master node Shell Element Slave node Cohesive Element Sublaminate Shell Element Sublaminate Rigid Beam thickness=0
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