A phase-field-based graded-material topology optimization with stress constraint

In this paper, a phase-field approach for structural topology optimization for a 3D-printing process which includes stress constraints and potentially multiple materials or multiscales is analyzed. First-order necessary optimality conditions are rigorously derived and a numerical algorithm which implements the method is presented. A sensitivity study with respect to some parameters is conducted for a two-dimensional cantilever beam problem. Finally, a possible workflow to obtain a 3D-printed object from the numerical solutions is described and the final structure is printed using a fused deposition modeling (FDM) 3D printer.