On a small scale you could model up the exact geometry of this sandwich composite with outer sheets along with the inner core of bottle caps. It would scale poorly though as you go beyond just having a tiny sample. In a small way this is good because as you scale up the size of your analyzed sample it becomes an okay assumption to model the core bottle cap region as a homogeneous orthotropic material rather than the exact discrete geometry. The key behind going from the modeled geometric representation to a homogeneous approximation is calculating what the material properties are that will represent it.
To do this you can use a Simulation to calculate meta-material properties. This idea of calculating a meta-material only works when the sheet size is larger than the individual specific geometry of the bottle caps.
In order to calculate the meta-material properties you would make a modeled square of your sheet (20x20 bottle caps; large enough that localized geometry behaviors average out), apply the materials to the bottle caps and outer sheets, fixture one end, and pull the the other end with an arbitrary constant load and see what the displacement is from that loading. With the known load and calcualted displacement you can calculate what the Elastic Modulus is for X/Y directions (in-plane directions). To get the Z direction (normal to sheet direction) you would likely need to pattern the 20x20 bottle cap sheet several times in the Z-direction and, again apply a tension load in that direction to find another calculated displacement.
From all this you calculate the specific orthotropic properties of the "bottle cap" material that can replace those bottle caps in the specific orientation you tested/constructed them in. This would allow for you to analyze larger scale objects without taking days for the solver to complete.