ON A RELIABLE FINITE ELEMENT APPROACH IN MULTISCALE MULTIMATERIAL SOLID THERMO- MECHANICS

This paper presents an original time efficient primal-mixed finite element approach in the geometrically multiscale solid thermo-mechanics. It will be shown that present finite element HC8/27 passes 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. 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. A number of pathological benchmark model problems, with material interfaces or coating, 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 reliability. A new definition of multiscale reliability is given. It will be shown how dimensional reduction theories can drastically deteriorate the place and intensity of maximal stress results, which can lead to a premature structure failure. In addition, bridging of continuum (finite element) and atomistic (molecular dynamics) mechanics is more accurate if continuum approach is based on a reliable fully three-dimensional numerical approach, mainly because it prevails spurious results and enables extension of the continuum region deep toward the atomistic scale.