Heat Transfers and Solid Mechanics in Microarchitectured Materials Using Periodic Homogenization
Microarchitectured materials are generally made of different compounds bound at the microscopic level using a periodic pattern. This results in a macroscopic material with new properties arising from each of the individual compound properties and the way the microarchitecture binds them. The periodic microstructure can then be optimized to obtain specific macroscopic material properties, but attention must be paid to the microstructure response, such as hot spots in heat transfers or mechanical stresses in structural mechanics. Using a finite element analysis to forecast such behaviors is often computationally challenging due to the abundance of geometrical details, leading to a large number of degrees of freedom to solve for. Modelers must then rely on more sophisticated numerical methods.
This paper studies the use of the periodic homogenization method in heat transfers and solid mechanics. This method has the advantage to be built upon a well-established mathematical basis. The initial problem is reformulated into two-scale finite element problem. At the microstructure-scale, unitary stimulations of the material are performed in order to characterize homogenized properties of the material. At the part-scale, homogenized temperature or displacement fields are solved. Each of these steps requires to solve far less degrees of freedom than the initial problem. Ultimately, both results are combined by relocation in order to get an accurate prediction of the local temperature, conductive fluxes, displacement and mechanical stresses.
