the linear constitutive equation describes piezo behavior. See wiki. But I can find an example in which linear relationship may not satisfy. Given a piezo disk wih polarization in thickness direction and upper and bottom surface as electrodes. I just short circuit the up and bottom surface and put it freely on the table. In such a condition, E=0 in the piezo no doubtly, stress T=0 also, because I do not put any force on it. Then from constitutive equation P=0. But not forget there is spontaneous polarization in disk, so P should not be zero, it has a initial value! Ok, can we say the linear constitutive equation is wrong?