Supplementary Materials: Influence of Partially Debonded Interface on Elasticity of Syntactic Foam: A Numerical Study

摘要: For the mixed model, the meshes in the microspheres were made by first dividing the interfaces with a mesh density of 1/20 of the diameter of the microsphere. Then the volumetric meshes were made from the surface meshes by the automatic meshing algorithm provided by the Ansys. Since the wall thickness of the microsphere is thinner than the surface mesh density, the microspheres were meshed to have only two finite elements in the thickness direction (shown in Fig. 3a in the paper). Since each tetrahedral element had 4 integration points near its corners, there is only two or three integration points through the thickness direction of the microspheres in the mixed model. The validity of the finite elements used in the mixed model was checked by comparing with models having different types of finite elements meshes in the microspheres. Four different models were used for the comparison. Among them, three models used brick-type elements for the microspheres with 2, 4 and 6 layers in the thickness direction. The microspheres were meshed by 20-node brick elements (SOLID186, Ansys). In an additional model, the microspheres were discretized by two layers of 8-node solid-type multilayer elements (SOLSH190, Ansys). The finite element meshes of the different models are shown in Fig. S1. The elastic modulus of the models were obtained by applying 1% uniaxial tensile loads. The boundary conditions were the same as described in the paper. The debonding fraction was fixed for the all calculation by ζ= 0%(fully bonded). Table. S1 shows the elastic moduli obtained by the different models and their deviations from the mixed model used in …