In crystalline materials, the ordinary elastic moduli are replaced by cijkl, a fourth order tensor with eighty one elements. It appears that the most general material has eighty one elastic moduli, but this number is reduced because cijkl has the following symmetries:
(i) Cjikl = Cijkl
(ii) Cijlk = Cijkl
(iii) Cklij = Cijkl
How many elastic moduli does the most general material actually have?