4. Generalities

This macro-command is used to calculate the equivalent thermal conduction and thermoelastic properties for periodic structures by a homogenization method.

In the general case, this type of operation cannot be automated, because the definition of the periodicities is linked to the structure to be treated.

In order to achieve an automated procedure, it is necessary to restrict the use of CALC_MATE_HOMOaux basic cells with a parallelepiped pattern, so that the pairs of faces facing each other are trivial to identify. This has no impact on structures with rectangular steps, but on the other hand it requires finding a periodic pattern with rectangular steps in other situations (for a hexagonal step see the test cases hplv105c or hplv106)

In addition, in order to take advantage of symmetries, the use of CALC_MATE_HOMO is restricted to basic cells that are also symmetric with respect to the 3 axes: this leads to an orthotropic equivalent material. The mesh thus corresponds to the first octant of the base cell \(\left(x\ge 0\phantom{\rule{0.5em}{0ex}};\phantom{\rule{0.5em}{0ex}}y\ge 0\phantom{\rule{0.5em}{0ex}};\phantom{\rule{0.5em}{0ex}}z\ge 0\right)\). This choice leads to an orthotropic equivalent material, and to the absence of flexion-membrane coupling for homogenized plates.