24.2.3 Different Cross-Section Areas Across an Interface This study is focused on the interface in the transmission bar. There are two kinds of change in the interface; one is the change of cross-sectional area and the other is the change of material. Both of them can produce reflection. To identify the cross-interface bond force, a composite coefficient c should be identified. Shown below is the calculation of the coefficient. It begins with finding the bond force c1 between the two cross-sectional areas or the two materials. Similarly, the bond force c2 can be identified. Since they should be equal to each other, the composite coefficient can then be identified. The bond force on c1 is f1 ¼c1 u3 u1 x3 x1 The bond force on c2 is f2 ¼c2 u2 u3 x2 x3 Since f ¼f1 ¼f2 ¼c u2 u1 x2 x1 c ¼ 1 1 c1 x3 x1 x2 x1 þ 1 c2 x2 x3 x2 x1 (24.6) The effect due to different materials can also be identified accordingly. Simulation results match well with experiment results. Hence, the technique in finding the interface bond is validated. Fig. 24.3 Peridynamic simulation of wave propagation in a simple bar 198 T. Jia and D. Liu
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