Minimizing the maximum von Mises stress of elastic continuum structures using topology optimization and additively manufactured functionally graded materials

The rising cost of natural resources and environmental concerns motivate systematic design and manufacture of more efficient structures. For that purpose, topology optimization has been appealing, as well as working on an enlarged design space to include multi-material solutions. The resulting optimal designs can be materialized using multi-material additive manufacturing. In the present framework, multi-material printed parts or layouts can be envisaged as having better strength properties than single-material counterparts. The maximum von Mises stress is minimized inside a design domain through topology changes and material selection. The selected composite material model encompasses either the classical arrange of two discrete materials with sharp interfaces, or their mixture controlled by the volume fraction of each base material to generate a Functionally Graded Material (FGM). An optimized continuous variation of properties makes the FGM appealing to mitigate stress concentrations. To adequately capture the physics of mixtures considering the FGM's mechanical properties, one uses the RAMP interpolation scheme within the Hashin-Shtrikman bounds. A set of plane stress benchmarks are proposed. It is shown that considerably lower stress peaks on the evaluated structures can be obtained on the account of introducing more than one solid phase, specifically in the case of FGM solutions.