JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition - 64

modelling

Multiscale thermomechanical
modelling of closed-cell materials
Requirements for lighter-weight structures and material
savings are driving a search for multifunctional materials
with optimized mechanical, thermal and acoustic properties.

By
D. Baillis, laMCos, iNsa-lyoN,
CNRs UMR 5259, P.M. MiChaUD, R. CoqUaRD,
EC2Ms, W. RaMBaUD, CRyosPaCE, R. DENDiEvEl,
siMaP, CNRs, GRENoBlE iNP, UNivERsité JosEPh
FoURiER, l. ChazEaU, MatEis, iNsa DE lyoN, CNRs
UMR 5510

he design of the cryogenic storage tanks for the future
Ariane 5 and Ariane 6 launchers (new generation)
makes use of an innovative strategy to meet new
requirements for lighter-weight structures and material
savings, and to improve the tank performance. The Ariane
5 cryogenic storage tanks are thermally insulated by lowdensity closed-cell foams that are bonded to the tank. These
closed-cell materials are under high thermomechanical stress.
The tank design must take into account not only thermal
insulation requirements (holding the temperature of the
liquid gas inside the tanks), but also mechanical strength
requirements (internal pressure, compression, bending, and
buckling stability). The challenge is to find the closed-cell
materials with the best thermal and mechanical performance
for the specific application. To reach this objective, you have
to understand and model the thermomechanical behaviour

Fig. 1: Diagram of the multiscale modelling approach

64 jec composites magazine / No88 April 2014

of insulating closed-cell polymer foams. This means analysing
the influence of the material microstructure (cell size), the
density, and the nature of the solid phase on their thermal
and mechanical properties. A multiscale modelling approach
is proposed (Figure 1).

Three levels of scale
This approach is based on three levels of scale. At the local
phase scale (a few microns), the knowledge of the thermomechanical properties of the foam's solid phase is sought.
Then the behaviour at the mesoscopic scale of a few cells (a
few millimetres) is predicted using a realistic model of the
foam structure (by X-ray tomography). This finite element
model is subjected to a thermomechanical load to provide the
necessary input parameters for building a behaviour model
at the macroscopic scale (a few centimetres) for the design of
structures like the Ariane V launcher. The current resolution
of tomographs limits the method's use when the characteristic size of the architecture is about the same or smaller than
the resolution. Also, if the architecture imposes an excessively
low resolution, it limits the size of the volume for analysis.
Therefore, it is necessary to find a more flexible complementary tool to offset these drawbacks. This has advantages: the
ability to model a larger volume of material and to perform
useful parametric analyses, especially in optimization processes. A Voronoi-type structural model is an alternative that
allows determining the right size for representative elementary volumes (REV) and validating the thermal and mechanical
models based on X-ray tomography. It also allows analysing
the influence of cell irregularity and of their more or less ran-

JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition