13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- 2.2. 3D cohesive element insertion Embedding cohesive surfaces into complicated 3D microstructure meshes is not a trivial task. The biggest challenge lies in how to effectively deal with the changes in the 3D nodal and elemental connectivities due to the introduction of cohesive surfaces. An algorithm has been developed to automatically insert 3D cohesive elements along grain boundaries and within individual grains. The method generally includes the following steps: (1). Find the node set which will be duplicated. The set can be defined as nodes along grain boundaries or within arbitrary grains. (2). Sort out the target elements which include the node set, then duplicate the nodes and redistribute the updated node labels to the corresponding elements. Assign the same coordinates to the duplicated nodes as the virgin nodes. (3). Generate cohesive elements with consistent nodal ordering (clockwise or counter-clockwise) in adjacent element facets. The top and bottom facets are determined by calculating the surface normal. Either top or bottom face can be defined by a positive surface normal value. The key lies in keeping the pattern consistent. (4). Create different cohesive element sets. Sort out cohesive elements that belong to grains or grain boundaries so that different cohesive laws can be correctly assigned. Fig.2 Bilinear traction-separation law. Both cohesive elements along grain boundaries and within grains follow the bilinear traction-separation law as shown in Fig. 2. This law is derived from a potential which is a function of separation vector through a state variable defined as 2 2 n nc t tc . This variable describes the effective instantaneous state of mixed-mode separations. Here, n n Δ and 2 2 2 2 t p q = Δ Δ n n p Δ Δ n n q = Δ Δ n n denote, respectively, the normal and tangential components of Δ, with n being unit normal and p and q being two unit tangential vectors. Note that n, p and q are mutually perpendicular to each other and form a right-handed triad. nc is the critical normal separation at which the cohesive strength of an interface vanishes under conditions of pure normal
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