On a new 3D primal-mixed finite element approach for thermal stress analysis of multi-layered geometrically multiscale structures

This paper presents a new reliable fully three-dimensional time efficient primal-mixed finite element approach with continuous primal and dual variables in geometrically multiscale thermoelasticity. The semi-coupling between thermal and mechanical physical fields is achieved straightforwardly via essential boundary condition per stress, and without consistency error. The direct sparse solver and matrix scaling routine are used for the solution of resulting large scale indefinite systems of linear equations. It will be shown that present solid finite element HC8/27 passes the first and the second stability condition (inf-sup test) for highly distorted finite elements with aspect ratio up to 7 orders of magnitude, for both, compressible and nearly incompressible materials. A number of pathological benchmark model problems, with material interfaces or coatings, with geometrical scale resolutions up to 8 orders of magnitude and aspect ratio of finite elements up to 7 orders of magnitude, are examined to test the robustness and execution times. It is shown that by rapid varying of spatial scale over local heterogeneities, the singularity of stress is captured without oscillation. It is shown that, if needed, present approach can simulate the simplified theories, as beam and plate theories, if the same restrictions on the stress tensor components are imposed. The new definition of multiscale reliability is given.