PSI - Issue 41

Efstathios E. Theotokoglou et al. / Procedia Structural Integrity 41 (2022) 361–371 Efstathios E.Theotokoglou/ Structural Integrity Procedia 00 (2022) 000–000

365

5

5. Material model In all the cases that we have considered in this study the rule of mixtures (Belarbi, et al., (2022)), (Tran, et al., (2019)) has been used in order to obtain the effective material properties. In our study only the Young’s modulus is considered as function of the spatial coordinates, whereas the Poisson’s ratio as constant.The material model for the configuration with the ceramic core is (Belarbi, et al., (2022)).   ( ) m c m c P z P P P V    (12) The material model for the configuration with the metal core is (Do, et al., (2020)), (Tran, et al., (2019)).   ( ) c m c m P z P P P V    (13) where P is the material property and V is the volume fraction, (m) and (c) represent metal and ceramic respectively. For the models considered in our study the volume fraction for each layer is given by (Belarbi, et al., (2022)), (Do, et al., (2020)).

p

p

  

  

y h   

y h h h  













(14)

(1)

(2) V 1,

(3)

V

,

1 2 y h h  ,

2 3 y h h ,

V

,

3 4 y h h  ,



 



1

4

 

2 1 h h

  

3 4

where (p) is the volume fraction index.

Figure 2 Variation of the Young’s modulus through the height of the beam for a) ceramic core and b) metal core

In Figure 2 appears the variation through the y axis of the elastic moduli of the core and the face sheets for the different indexes of the volume fraction and for the discontinuous cases (Section 4). 6. Validation of the Finite element model In order to validate our Finite element code, we have considered 2 cases. In the first one we examined a sandwich beam with a ceramic core and FGM face sheets (Figure 1). In the second case we examined a cantilever beam presented in Figure 3.