Design of Thermal Metamaterials using Isogeometric Structural Optimization

Scientists are interested in controlling how heat moves to increase heat transfer effi-
ciency, create thermal analogs to electronic devices (like diodes and capacitors) and
propose innovative applications like thermal computing and thermal communication.
They use special materials called thermal metamaterials that have unique structures
and thermal properties. The usual method to design such thermal metamaterials
involves a transformation theory, but it has limitations, like difficulty in handling
complex design and manufacturing constraints due to its analytical nature. It also lacks
generality as it requires case-dependent intuition-based coordinate transformations.
To overcome these issues, we’re creating a versatile tool that uses numerical methods
to design any thermal metamaterial with specific goals. Specifically, we exploit struc-
tural optimization, a numerical optimization method that can intelligently distribute
constituent materials (the thermal metamaterials) to achieve their best performance
based on the specified goal. In this thesis, we exploit structural optimization methods
that can intelligently distribute constituent materials (of the thermal metamaterials)
to achieve the best-required performance. Later, to broaden the design scope, we also
propose the utilization of Functionally Graded Materials (FGMs), which allows access
to an entire spectrum of thermal conductivity covered by the conductivities of the
constituents. We’re also exploring Functionally Graded Materials for a broader design
range. Our research has shown that this approach can efficiently design various thermal
metamaterials, like concentrators and cloaks, without needing any intuition-based
information or case-specific mathematical formulation. These methods are robust in
handling different shapes and conditions, and they can be adapted to manufacturing
requirements. The proposed methods are flexible for future improvements, like dealing
with nonlinearities and time-dependent responses.