I'm working in a iterative method with piezoelectric composites. During the implementation (in MATLAB) I work with the piezolectric components in a single matrix, reduced to a vector by the Hill algebra. However, I'm having problems because of the different orders of the components values. I know there is a way to normalize all the values, but it can't be by dividing the whole matrix by the same number, so, if anybody can help me I will appreceite it. You answer here or write me to naecita [at] gmail.com
Thanks.
When you perform
When you perform normalization, you need to make sure that the energy or electric enthalpy will remain the same unit. Hence the right normalization scheme can be achieved by diving the electric field by a big number to make it of similar magnitude as the mechanical strain. And then multipy that big number to the corresponding material constants to ensure the energy remains the same.
Piezoelectric coefficients
Helen,
It's not so much a normalization as a change in units. Instead of using elastic constants (c's) in N/m^2, use GPa. The piezoelectric coefficients (e's) remain as C/m^2. Instead of using dielectric permittivities as C/Vm use nC/Vm. By doing this, the elastic constants will be of order ~100, piezoelectric constants ~10, and permittivities ~10. Then strains remain the same, stresses are in GPa, electric displacements are in C/m^2, and electric fields are in GV/m.
Hope this helps.
Chad