13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- deformation ( 0 t ). Similarly, tc is the critical tangential separation at which the cohesive strength of an interface vanishes under conditions of pure shear deformation ( 0 n ). max T represents the maximum traction that the cohesive element can sustain before damage initiates. Fig.3 Effect of mesh tie constraint on the calculated J values. 2.3. Generation of mesh tie constraint Calculation of the J-integral in the homogenized region requires a closed contour. It would very difficult to define contours if the homogenized region is meshed with unstructured elements. To solve the problem, two regions of mesh are used. An unstructured tetrahedral mesh is used for the microstructure region and a structured tetrahedral mesh is used for the homogenized region. It would be extremely challenging to create a transitional region that connects the two types of meshes. Instead, the mesh tie constraint in ABAQUS is used. This constraint requires no conformity of node connection between the two regions. It circumvents the problem with acceptable accuracy. As illustrated for a 2D problem in Fig. 3, there is only a very minor difference between the J values for cases with and without the mesh tie constraint. It should be noted that iso2mesh cannot generate perfect microstructure meshes with smooth exterior surfaces and sharp vertices as shown in Fig. 4. If the two regions cannot be seamlessly attached, the energy loss caused by the gap will significantly influence the accuracy of calculation. We innovatively develop an algorithm to generate a shell mesh which is around the unsmoothed microstructure block to ensure proper node and element connectivity. The two regions are successfully assembled using the mesh tie constraint as illustrated in Fig. 5.
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