I am studying the effective material property of a double-layered perforation (Fig. 1). The perforation rate is different on the two layers, which are connected via arrays of pillars. Both perforation and pillars are closer packed in y-direction (the beam length direction) than the x-direction (the beam width direction) to render an anisotropic in plane material property. Fig. 1 (b) shows a unit cell of such a periodic perforation.
(a) (b)
Fig. 1, (a) a double-layered perforation (b) the unit cell of the double-layered perforation.
The effective material property of a single layer perforation is well established. Its orthotropic symmetry has rendered the effective compliance matrix to have the form in Fig. 2 (b).
(a) (b)
Fig. 2, (a) a unit cell of a single layer perforation. (b) effective compliance matrix for the single layer perforation.
Although the symmetry of the double-layered perforation (point group 2mm) is slightly different from the single perforation symmetry (point group mmm), they both belongs to the orthohombic class. My question is: can the double-layered perforation be equivalented to be a homogeneous anisotropic material with the compliance matrix in Fig. 2 (b)? Is the fact that the perforation gets only one period in the thickness direction makes the effective elastic tensor form different? What will be the form?