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Title: ON THE ISSUE OF MULTISCALE ROBUSTNESS IN COMPUTATIONAL MECHANICS


1
ON THE ISSUE OF MULTISCALE ROBUSTNESS IN
COMPUTATIONAL MECHANICS
  • DUBRAVKA MIJUCA
  • Department of Mechanics, Faculty of Mathematics
  • University of Belgrade, SERBIA
  • dmijuca_at_matf.bg.ac.yu,
  • www.matf.bg.ac.yu/dmijuca

2
Alternative titles
  • From Megastructure to Nanostructure analysis in
    One Simulation Framework
  • From macro to micro insight of engineering
    structure in one simulation framework without
    submodelling

3
Mathematical Models to trace the displacements of
nanoparticles
  • Schrödinger most general
  • Bohr-Oppenheimer decoupled Schrödinger
  • Newtonian mechanics feasible to solve

Mijuca D, Mastilovic S (2005) A Novel One-To-One
Multiscale Approach to Computational Mechanics of
Materials, 1st International Workshop on
Nanoscience Nanotechnology IWON2005, November
1518, pp. 180-186
4
Engineering approach
  • (is) Historically simplified with the aim to
    shorten the time from idea to manufacturing,
    construction or real time decision making

5
Novel engineering approaches
  • Nonsimplified engineering calculations, HEXA8,
    450000 d.o.f., materially nonlinear, 4 iteration,
    app. 5minutes, PCDualCore1.8MhZ, Software Straus7

Megastructure
6
Numerical methods referring to different length
scales
FEM
MD
1 Schmauder S Computational Mechanics Annu.
Rev. Mater. Res. Vol.32, 2002, pp.43765
7
From Continuum to Nanomechanics
  • Contemporary computer hardware resources and new
    mathematical and software tools to handle large
    scale computing, open doors for richer FE
    theories in which reliability is not compromised
    even if the model problem analyzed requires
    consideration through geometrical scales from
    continuum to micro to nanomechanics.

8
Industrial Problems
  • New materials, as composite sandwiched plates
    with foam in its core, and functionally graded
    materials,
  • Analysis at higher temperatures (fire) when
    material properties drastically change,
  • Fully 3d reliable numerical procedure toward
    incompressibility 5.
  • Fiber-optic sensors in non-destructive testing
  • Coated bodies

9
Resent References
  • Mijuca D (2004) On hexahedral finite element
    HC8/27 in elasticity. Computational Mechanics
    33(6)466-480
  • Mijuca D, Mastilovic S (2005) A Novel One-To-One
    Multiscale Approach to Computational Mechanics of
    Materials, 1st International Workshop on
    Nanoscience Nanotechnology IWON2005, November
    1518, pp. 180-186
  • Mijuca D, Ziberna A and Medjo B (2006) A Novel
    Primal-Mixed Finite Element Approach for Heat
    Transfer in Solids, Computational Mechanics,
    on-line first DOI 10.1007/s00466-006-0034-0
  • Mijuca D (2006) On Dimensional Reduction in
    Multiscale, Finite Element and Atomistic,
    Analysis in Solid Mechanics, WSEAS Transactions
    On Applied And Theoretical Mechanics, Issue 1,
    Volume 1, pp.16-25,, ISSN 1991-8747
  • Mijuca D (2006) On Primal-Mixed formulation in
    Elasticity and Thermoelasticity, Monograph,
    Faculty of Mathematics University of Belgrade
    (2006)

10
Recent Citation List
  • Cuomo M, Contrafatto L (2000)  Stress rate for
    elastoplastic models with internal variables
    based on augmented Lagrangian regularization.
    Intern. Journal of Solids and Structures 37
    3935-3964
  • Zoran DraÅ¡kovic (2002)  Numerical Comparison of
    The Scalar, Pseudoinvariant And Invariant
    Approach In The Derivation Of Finite Element
    Equations Of Motion In Curvilinear
    Coordinates. FACTA UNIVERSITATIS, Series Mech.
    Vol.312, pp.351 - 357
  • Gómez Jáuregui Valentín (2004). Tensegrity
    Structures and their Application to Architecture,
    Queen's University, School of Architecture, Belfas
    t, Northern Ireland
  • Icardi U, Atzori A (2004)   Simple, efficient
    mixed solid element for accurate analysis of
    local effects in laminated and sandwich
    composites, Advances in Engineering Software 35,
    pp 843859,
  • V. A. Maksimyuk and I. S. Chernyshenko (2004)
    Mixed functionals in the theory of nonlinearly
    elastic shells. Volume 40, Number 11 / November,
     International Applied Mechanics, Springer New
    York ISSN 1063-7095 (Print) 1573-8582 (Online)
  • K.S. Chavan, B.P. Lamichhane and B.I. Wohlmuth
    (2005) Locking-Free Finite Element Methods For
    Linear Nonlinear Elasticity In 2d And 3d. (2005)
    Preprint SFB404 2005-13
  • Jim Wood (2005) D5603 - Procedural Benchmarks
    for Common Fabrication Details in Plate/Shell
    Structures, NAFEMS-FENet.
  • U. Icardi (2006) Layerwise mixed element with
    sublaminates approximation and 3D zig-zag field,
    for analysis of local effects in laminated and
    sandwich composites. International Journal for
    Numerical Methods in Engineering. on line first

11
Multiscale analysis
  • There is a growing need to develop systematic
    modeling and simulation approaches for multiscale
    and multimaterials model problems in mega and
    microstructures in order to provide the accurate
    data of the subregions of different geometric
    scales
  • about the state of stress,
  • defect structure,
  • thermo-mechanical performance.

12
New definition
  • The new definition of the multiscale robustness
    in computational mechanics, is introduced in
    order to support theoretical settings of
    multiscale analysis, that is bridging of
    simulation on atomistic scale with simulation on
    the scale of continuum mechanics, and vice versa.

13
Multiscale Robustness
  • Some finite element approach is multiscale robust
    if it retains its reliability regardless of the
    geometrical scale of the finite element used for
    the discretization of the material domain.

14
Multiscale robustness test
  • The necessary and sufficient solvability test
    must be fulfilled regardless of geometrical
    multiscale resolution of finite element
    discretization.

15
Motive
To develop reliable multiscale FE procedure for
solving engineering and bioengineering problems
that are complex in
  • material,
  • geometry,
  • loading,
  • scale of observations.

16
Transient heat transfer in solids
17
Elastostatics
18
Present FEM approach
  • primal-mixed FEM FEMIX HC8/27(MD/LJ)
  • multifield transient heat transfer /
    elastostatics,
  • semi-coupled physical fields (via temperature),
  • multiphisics,
  • multiscale,
  • Coordinate independent
  • full scale, three-dimensional in geometry,
    physical lows and constitutive relations,
  • bridged by semi-coupling (via displacement) with
    simulation on atomistic level
  • Residual stress input straightforwardly enabled.

19
Primal-mixed finite element approach in transient
heat transfer
Subscript p is for prescribed
Subscript v is for unknown variable
20
Primal-mixed finite element approach in
elastostatics
Subscript p is for prescribed
Subscript v is for unknown variable
Initial stress/strain, Residual stress,
21
Finite element family HC
22
Reliability
The proposed hexahedral finite element HC8/27
passes low and high order convergence and
efficiency tests in transient heat transfer and
elastostatic analyses, that is, it is
  • solvable,
  • stable,
  • accurate and efficient,

Shortly it is reliable.
23
Multiscale robustness
  • Necessary conditions for solvability
  • Sufficient conditions for solvability. Eigenvalue
    analysis

24
Eigenvalues for different one finite element
configurations
25
(Why not) Dimensional Reduction
Dimensional reduction (geometrical
simplification) is one of two generic techniques
for physical problem idealization
  • Solid bodies with one or two axial dimensions
    much smaller than other, are traditionally
    examined by plate, shell or beam theories.

26
Fully 3D FE procedure
Present procedure is fully 3D per
  • geometry
  • loading
  • constitutive relation

No dimensional reduction.
27
Main flaws of dimensional reduction
  • Aspect-ratio restriction.
  • Transitional error between FE of different
    dimensionalities.
  • Inappropriate in analysis of coated bodies
  • Inappropriate in multiscale analysis (narrow
    finite elements)
  • Error in the place and intensity of maximal
    stress results.

28
Full scale analysis vs. simplified
  • Beam, Plate and Shell theories can be also
    simulated by the Full 3d approaches.
  • If we enter dimensional reduction assumptions in
    the present full scale FE approach, the app.
    solution will converge theirs target results.

29
Clamped square plate
30
Clamped 3D Plate Full theory Case A
Full theory.
The stress concentration point is inside the
plate.
31
Clamped 3D Plate Plane theory Constraints Case
B
Transversal shear stresses are suppressed on the
physical boundaries in order to simulate the
plate theory.
The stress concentration point is on the clamped
edge.
32
Clamped 3D Plate Displacement Convergence
33
Clamped 3D Plate Conclusions
  • Unrealistic neglecting of the transverse shear
    stress component, minimize shear stress influence
    which softness the finite element solution, so
    it may instantly undergo apparently higher
    deflections.
  • Transversal shear stress component can not be
    neglected, because it smears the real stress
    picture, in which stress concentration point is
    inside the plate in the vicinity of clamped edge,
    and not on the clamped edge itself.
  • In addition, the maximal stress result is lower
    than one obtained by the plate theory assumptions.

34
Clamped plate FEA multiscale
35
Plate with a hole (one quarter)
36
Plate with a hole
37
Plate with a hole
38
Deformed configurations
39
Long steel Coated Shaft
40
Thermo-mechanical barrier coating

Five model problems with decreasing thickness of
coating and bond is examined.
41
Convergence per decreasing of coating thickness
42
Nuclear Reactor Core Primal Approach
False heat flux result in the first iteration per
time, Lower maximal heat flux result.
43
Nuclear Reactor Core Primal-mixed Approach
44
Execution time
45
Molecular dynamics
46
Nanoidentation- Bridging the scales
FE HC8/9
47
Wind turbine rotor blade design
  • Vesta turbine design
  • Layered composite
  • The blade is of glass fibre/epoxy matrix
    pre-pregs
  • The gear box is made of fibre/epoxy
  • The adhesive is made of epoxy
  • External load gravitational, CFD

48
Failure assessment
49
FE analysis
Delamination
Debonding
Crack
50
Pressure load from CFD
Model without gear box
Model with gear box
51
Full multiscale analysis
18789 dofs per displacement vector and stress
tensor 76.36 sec on the notebook 1.4GHz Intel
Pentium (R) 512MB RAM
52
Aramide Composite Material
53
Fiber Optic Sensor
Specimen size 12x105mmx7.3mm, Optic Sensor Core
d0.0625mm
54
Rotary Pellet Plant Kiln Straus7
55
Paper in press
  • ON ADVANCED HSL SOLUTION ROUTINES IN PRIMAL-MIXED
    FEA THERMO-MECHANICAL ANALYSIS
  • Iain Duff (President of SIAM) , Dubravka Mijuca

Computational Science and Engineering
Department, Atlas Centre, Rutherford Appleton
Laboratory, Oxon OX11 0QX Faculty of
Mathematics, University of Belgrade, Studentski
trg 16, 11000 Belgrade, Serbia
56
Paper in press
  • ON A NEW FULLY 3D MULTIFIELD FINITE ELEMENT
    APPROACH IN A SEMI-COUPLED THERMO-MECHANICAL
    ANALYSIS
  • Dubravka Mijuca

57
PRIMACY OF COMPUTATIONAL MECHANICS IN
COMPUTATIONAL SCIENCE
  • The Mechanics exclusively give us insight in the
    motion and deformation of particles of both
    solids and fluids.

58
Computational Mechanics Students
  • Team while working on a NEC SX6i supercomputers
    at Japan - Serbia Center for Simulation Science
  • www.center.bg.ac.yu/simulation/

59
Reactor Engineering
With Prof. samu Motojima,  Director General of
the NIFST NINS Japan and Prof. Milos Skoric from
the NIFS Japan Nikola Tesla Museum Belgrade
60
Special Session Finite element simulation of the
high risk constructions, experiences andproblems
2nd WSEAS International Conference on APPLIED and
THEORETICAL MECHANICS (MECHANICS '06), Venice,
Italy, November 20-22, 2006. www.worldses.org/conf
erences/2006/venice/mechanics
61
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