Topology optimization considering static failure theories for ductile and brittle materials

This research develops a stress-based topology optimization method (STOM) that considers various static failure criteria, including those from the maximum shear stress theory, the distortion energy theory, the ductile Coulomb–Mohr theory, the brittle Coulomb–Mohr theory, and the modified Mohr theory for ductile and brittle materials. Due to some theoretical and numerical challenges, the above static failure theories have not been implemented in topology optimization. By substituting failure formulas that are non-differentiable with respect to the stress components and design variables with differentiable approximation formulas, it is possible to utilize these failure criteria to design mechanical structures that minimize mass.

► It is the first time to consider static failure theories in topology optimization.
► Nonsymmetric designs can be found with different compression and tensile strengths.
► The differentiability of static failure theories is addressed.
► Two and three dimensional problems are considered for stress based design.