ON A RELIABLE FINITE ELEMENT APPROACH IN MULTISCALE MULTIMATERIAL SOLID THERMO- MECHANICS
D. Mijuca
Abstract
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.
