The thermal conductivity of Functionally Graded Materials (FGMs) can be efficiently designed through topology optimization to obtain thermal meta-structures that actively steer the heat flow. Compared to conventional analytical design methods, topology optimization allows handling arbitrary geometries, boundary conditions and design requirements; and producing alternate designs for non-unique problems. Additionally, as far as the design of meta-structures is concerned, topology optimization does not need intuition-based coordinate transformation or the form invariance of governing equations, as in the case of transformation thermotics. We explore isogeometric density-based topology optimization in the continuous setting, which perfectly aligns with FGMs. In this formulation, the density field, geometry and solution of the governing equations are parameterized using non-uniform rational basis spline entities. Accordingly, the heat conduction problem is solved using Isogeometric Analysis. We design various 2D & 3D thermal meta-structures under different design scenarios to showcase the effectiveness and versatility of our approach. We also design thermal meta-structures based on architected cellular materials, a special class of FGMs, using their empirical material laws calculated via numerical homogenization.

Design for composite material additive manufacturing is governed by multiple process variables that can be computationally expensive to optimize. This is especially true when considering discrete variables, such as the material type to be used, which lead to a lot of possible solutions that have to be evaluated. Here, we propose a workflow for optimizing topology and fiber placement of 3D volumetric structures based on mechanical performance under multiple load cases and environmental impact. An eco-informed material selection from a set fibers and polymers is followed by a methodology to optimize the manufacturing setting. By performing these two steps sequentially, the number of input parameter sets to be tested is reduced in a combinatorial scale, along with the computational cost. The framework can be easily extended by adapting the analyses and holds significant promise for the design of additive manufactured sustainable structures.