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Free Material Optimization (FMO), a branch of topology optimization, in whichthe design variables are the full constitutive tensors, can provide the mostgeneral form of the design problems. Considering the microstructure composed ofisotropic materials, the constitutive tensors are yet positive definite andsymmetric. On the other hand, it has been reported that the symmetry of thisconstitutive tensor can be broken in appearance by considering other physicalphenomena. In the present study, we focus on the thermal Hall effect, which isexplained as the phenomena that induces the temperature gradient orthogonal toa given temperature gradient across a solid when a magnetic field is applied tothe solid. This effect makes the thermal conductivity tensor asymmetric andjustifies extending the space of the constitutive tensors to be an asymmetricdomain. We propose the FMO for asymmetric constitutive tensors, parameterizingthe design space so that the physically available property could be naturallysatisfied. Several numerical experiments are provided to show the validity andthe utility of the proposed method.

Free material optimization of thermal conductivity tensors with asymmetric components