Title: ON THE ISSUE OF MULTISCALE ROBUSTNESS IN COMPUTATIONAL MECHANICS
1ON 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
2Alternative titles
- From Megastructure to Nanostructure analysis in
One Simulation Framework - From macro to micro insight of engineering
structure in one simulation framework without
submodelling
3Mathematical 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
4Engineering approach
- (is) Historically simplified with the aim to
shorten the time from idea to manufacturing,
construction or real time decision making
5Novel engineering approaches
- Nonsimplified engineering calculations, HEXA8,
450000 d.o.f., materially nonlinear, 4 iteration,
app. 5minutes, PCDualCore1.8MhZ, Software Straus7
Megastructure
6Numerical methods referring to different length
scales
FEM
MD
1 Schmauder S Computational Mechanics Annu.
Rev. Mater. Res. Vol.32, 2002, pp.43765
7From 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.
8Industrial 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
9Resent 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)
10Recent Citation List
- Cuomo M, Contrafatto L (2000)Â Stress rate for
elastoplastic models with internal variables
based on augmented Lagrangian regularization.
Intern. Journal of Solids and Structures 37
3935-3964 - Zoran Draškovic (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 ValentÃn (2004). Tensegrity
Structures and their Application to Architecture,
Queen's University, School of Architecture, Belfas
t, Northern Ireland - Icardi U, Atzori A (2004) Â Â 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
11Multiscale 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.
12New 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.
13Multiscale 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.
14Multiscale robustness test
- The necessary and sufficient solvability test
must be fulfilled regardless of geometrical
multiscale resolution of finite element
discretization.
15Motive
To develop reliable multiscale FE procedure for
solving engineering and bioengineering problems
that are complex in
- material,
- geometry,
- loading,
- scale of observations.
16Transient heat transfer in solids
17Elastostatics
18Present 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.
19Primal-mixed finite element approach in transient
heat transfer
Subscript p is for prescribed
Subscript v is for unknown variable
20Primal-mixed finite element approach in
elastostatics
Subscript p is for prescribed
Subscript v is for unknown variable
Initial stress/strain, Residual stress,
21Finite element family HC
22Reliability
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.
23Multiscale robustness
- Necessary conditions for solvability
- Sufficient conditions for solvability. Eigenvalue
analysis
24Eigenvalues 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.
26Fully 3D FE procedure
Present procedure is fully 3D per
- geometry
- loading
- constitutive relation
No dimensional reduction.
27Main 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.
28Full 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.
29Clamped square plate
30Clamped 3D Plate Full theory Case A
Full theory.
The stress concentration point is inside the
plate.
31Clamped 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.
32Clamped 3D Plate Displacement Convergence
33Clamped 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.
34Clamped plate FEA multiscale
35Plate with a hole (one quarter)
36Plate with a hole
37Plate with a hole
38Deformed configurations
39Long steel Coated Shaft
40Thermo-mechanical barrier coating
Five model problems with decreasing thickness of
coating and bond is examined.
41Convergence per decreasing of coating thickness
42Nuclear Reactor Core Primal Approach
False heat flux result in the first iteration per
time, Lower maximal heat flux result.
43Nuclear Reactor Core Primal-mixed Approach
44Execution time
45Molecular dynamics
46Nanoidentation- Bridging the scales
FE HC8/9
47Wind 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
48Failure assessment
49FE analysis
Delamination
Debonding
Crack
50Pressure load from CFD
Model without gear box
Model with gear box
51Full multiscale analysis
18789 dofs per displacement vector and stress
tensor 76.36 sec on the notebook 1.4GHz Intel
Pentium (R) 512MB RAM
52Aramide Composite Material
53Fiber Optic Sensor
Specimen size 12x105mmx7.3mm, Optic Sensor Core
d0.0625mm
54Rotary Pellet Plant Kiln Straus7
55Paper 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
56Paper in press
- ON A NEW FULLY 3D MULTIFIELD FINITE ELEMENT
APPROACH IN A SEMI-COUPLED THERMO-MECHANICAL
ANALYSIS - Dubravka Mijuca
57PRIMACY OF COMPUTATIONAL MECHANICS IN
COMPUTATIONAL SCIENCE
- The Mechanics exclusively give us insight in the
motion and deformation of particles of both
solids and fluids.
58Computational Mechanics Students
- Team while working on a NEC SX6i supercomputers
at Japan - Serbia Center for Simulation Science - www.center.bg.ac.yu/simulation/
59Reactor Engineering
With Prof. samu Motojima, Director General of
the NIFST NINS Japan and Prof. Milos Skoric from
the NIFS Japan Nikola Tesla Museum Belgrade
60Special 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
61AD ASTRA PER ASPERA