Multiscale analysis of thermal problems in heterogeneous materials with Direct FE2 method

Abstract

AbstractMultiscale thermal analysis is motivated by efficient modeling of complex microstructural response (nonlinear conduction, transient conduction, coupled thermomechanics, etc.) without resorting to fully resolved simulations, direct numerical simulation (DNS). It is typically conducted with an FE method that couples two levels of finite element simulations in a nested manner. This article presents a Direct FE method for modeling heat transfer problems in heterogeneous solids. The proposed method is developed based on the same theoretical framework as the FE method, namely downscaling and upscaling rules. However, the scale transitions are achieved through temperature/nodal thermal force in Direct FE rather than temperature gradient/heat flux in common FE implementations. The two‐level simulations can be solved in a monolithic scheme where the macroscopic and microscopic DOFs are coupled through multi‐point constraints. This feature allows an easy implementation in standard FE packages without resorting to repeated transfer of data between two scales. For transient thermal problems, the implementation provides an option to either incorporate or exclude thermal inertial effects and heat generation at the microscale. The performance of the Direct FE is demonstrated by several numerical examples including coupled thermal‐mechanical analysis and transient heat conduction, and the results are compared with DNSs.