Phase Field Simulation of Brittle Fracture in Topology Optimized Multi-Phase Structures with Prescribed Mass and Structural Envelope Volume
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Topology optimization of multi-phase material with constraints on the volume of the structural envelope in addition to the mass yields structures with a graded porosity. The envelope constraint enforces global porosity fraction, with the optimizer deciding where the porous material is placed. We assess the failure behaviour of eight such structures with a phase field model for brittle fracture in which the local fracture toughness follows the local porosity, and compare them at identical mass with the solid and the fully porous structures following from mass constraint only. Two mass levels are considered, a light one in which solid material may fill 30 % of the design domain and a heavy one with 60 %. At equal mass the graded structures store between 4 and 20 % more elastic energy before a crack forms than the solid references and crack at an 8 to 15 % larger deformation, while their peak force lies within a few percent of the solid design. The fully porous reference, which is both softer and less crack resistant, falls short of the graded structures by a factor of three to four. The length scale over which the porosity may vary has a non-monotone influence on the fracture response.
