Thermal–mechanical metamaterial analysis and optimization using an Abaqus plugin

This paper demonstrates how commercial finite element software and optimization algorithms can be combined to fully explore the design space of thermal-mechanical metamaterials to reveal trends and new insight. This is achieved by developing an Abaqus plugin (EasyPBC) that automates the application of periodic boundary conditions and computes effective elastic and thermal expansion properties for 2D
and 3D problems. Abaqus is then linked to an optimizer to fully explore the design space and optimal trade-off between thermal and mechanical properties for two example metamaterials. The first example is a auxetic 2D star shaped metamaterial, where the proposed approach is used to create a design envelope for Poisson’s ratio and thermal expansion coefficient by solving a series of constrained optimization problems. The second example is a 3D metamaterial based on an octet truss, with additional members to expand the design space. A multi-objective optimization problem is solved to find the optimal trade-off between Young’s modulus and thermal expansion coefficient in a prescribed direction. The results of both examples expand our knowledge about the range of properties for these metamaterials, and designs for optimal trade-off between thermal and mechanical properties.