Constrained Versions of the Free Material Design Methods and Their Applications in 3D Printing

The paper deals with the free material design and its constrained versions constructed by imposing: (a) cubic symmetry (cubic material design, CMD), (b) isotropy with: (b1) independent bulk and shear moduli (isotropic material design, IMD), and (b2) fixed Poisson’s ratio (Young’s modulus design, YMD). In the latter case the Young modulus is the only design variable. The moduli are viewed as non-negative, thus allowing for the appearance of void domains within the design domain. The paper shows that all these methods (CMD, IMD, YMD) reduce to two mutually dual problems: