ATILA can take into account the active materials' full anisotropy. The definition of a piezoelectric or magnetostrictive material can use up to 82 coefficients (163 coefficients if you define a lossy material) that describe the stiffness tensor, the piezomagnetic or piezoelectric tensor, the magnetic or dielectric tensor, and all the coupling factors. The example in Figure 18 shows the coefficient matrix of magnetostrictive materials.
To complete the description of the active materials, you must also define a polarization direction. The polarization direction of a material corresponds to the crystal easy magnetostriction direction for a magnetostricitve material, and to the poling direction for a piezoelectric material.
Usually, defining a uniform polarization direction in the active materials is sufficient; but some active materials have radial, and even spherical polarization directions. ATILA can take these polarizations into account For example, piezoceramic hemispheres can be assembled in pairs to form a sphere (Figure 19), and used as hydrophones and sonar transponders for <->hydro-surveying, underwater location and communications.
Figure 20 shows a cutaway view of the hollow piezoelectric sphere used in a hydrophone. The mesh we used in the computation represents only 1/24th of the sphere. We added fluid elements in order to solve the solid/fluid problem. The sphere's inner side is grounded.
Figure 21 shows the electrical potential in the piezoelectric material.
ATILA also displays the 3D pressure field in the fluid elements, as
shown in Figure 22.
ATILA is a very powerful program that will help you model anisotropic materials and uniform, cylindrical, and spherical polarizations.
