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Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

SEMINAIRE ROBERVAL

Modeling of multi-scale and multi-physical properties

• f acoustic materials

Camille Perrot

Laboratoire Modélisation et Simulation Multi Echelle (MSME), UMR 8208 CNRS Université Paris-Est Marne-la-Vallée

4 Juin 2015

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

OUTLINE

• I. Administrative overview
• II. Overview of research activities
• III. Scientific focus on modeling real porous media
• IV. Conclusion and future works

Outline

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

OUTLINE

• I. Administrative overview
• II. Overview of research activities
• III. Scientific focus on modeling real porous media
• IV. Conclusion and future works

Outline

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• I. ADMINISTRATIVE OVERVIEW

A) Short CV

38 years old Education:

• Doctorat in Acoustics and PhD in Mechanical Engineering (2002-2006)

Prepared at ENTPE [FR] and Université de Sherbrooke [QC, CA] Title: “Micro-structure and acoustical macro-behavior: Approach by reconstruction of a representative elementary cell” Advisors:Pr. R. Panneton [CA]

• Dr. X. Olny (co-advisor) [FR], Pr. J.-L. Guyader (co-advisor) [FR]
• Master in Acoustics, Université Lyon 1, France (2002)
• Bachelor in Applied Physics, Université Lille 1, France (2001)

Professional experience: 2007 – 2008 - Postdoctoral researcher, Dpt. of Mech. Eng., Sherbrooke 2008 – … - Assistant professor (UPEM)

Curriculum Vitae

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• I. ADMINISTRATIVE OVERVIEW

B) Publications and Services

• 12 papers in international referred journals
• 1 chapter of book
• 8 conferences given at the invitation of the organization committee in an

international congress

• 15 referred communications in international or national conferences

Publications University Services

• Head of a master’s program specialized in project engineering, 2013-…
• Responsible for the 1st academic year at the ESIPE school of engineering, 2010-…
• Mentor for one or two students in engineering each year (ESIPE), 2008-…

Awards

• Eligible for the research and doctoral supervision grants (PEDR), 2014-2017.

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• I. ADMINISTRATIVE OVERVIEW

C) Supervised students

Supervised doctoral students

Supervised students

2009 – 2012: Minh Tan HOANG

Co-advised with G. Bonnet [20%] “Multi-scale and multi-physics modeling of the acoustical behavior of porous media: Application to the optimization of industrial foams”. Financial Support: ANRT - Cifre Faurecia.

Corresponding publications: 4 paper, 1 chapter of book, 10 communications.

2013 – 2016: Hoang Tuan LUU

Co-advised with R. Panneton (QC) [50%] and V. Monchiet (FR) [15%] “Multi-scale modeling of acoustic dissipation in technical textiles made of natural hollow fibers” – Joint PhD Program Fr-Qc. Financial support: NSERC and FQRNT CA (100%).

Corresponding publications: 1 paper, 1 communication.

2014 – 2017: Mu HE

Co-advised with V. Monchiet [15%] “Microstructure and acoustic properties of fibrous media: A deterministic multi-scale approach”. Financial support: ADEME (50%), CSTB (25%), ISOVER (25%).

Supervised Master students: 15 Master students

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• I. ADMINISTRATIVE OVERVIEW

D) Contracts

• 2009 – 2012: Collaborative research contract with FAURECIA (PI)

Contracts

“Multi-scale and multi-physics modeling of the acoustical behavior of porous media: Application to the optimization of industrial foams”

• 2010 – 2012: Collaborative research contract with LAFARGE (PI)

“Acoustic properties of porous gypsum materials”

• 2014 – 2017: Collaborative research contract with CSTB and ISOVER (PI)

“Microstructure and acoustic properties of fibrous media: A deterministic multi-scale approach”

• 2014 – 2017: Scientific responsible for the acoustic part of ANR MatEtPro ProMap

ANR: French National Research Agency MatEtPro: Materials and Process for Performing Products “ProMap - Optimizing functional properties of particulate foams” Collaboration with: Navier, Paris 7 University, Saint-Gobain Research

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

OUTLINE

• I. Administrative overview
• II. Overview of research activities
• III. Scientific focus on modeling real porous media
• IV. Conclusion and future works

Outline

Multi-scale properties of acoustic materials

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Camille PERROT, Habilitation defense, Université Paris-Est Marne-la-Vallée, December 11, 2014

• II. OVERVIEW OF RESEARCH

ACTIVITIES

1) Determination from local geometry models of the acoustical macro-behavior of real porous media

• Problem statement: determination of the acoustical properties of metallic foams

by axial X-ray micro-computed tomography and numerical analysis

• Difficulties:

 Identification of the REV  Bridging the gap between a qualitative and quantitative description of the morphology (reconstruction artifacts)  Frequency-dependent phenomena (descretization of the boundary layer)

• Fig. 2.1 Main steps of the reconstruction process by X-ray axial µCT

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• II. OVERVIEW OF RESEARCH

ACTIVITIES

1) Determination from local geometry models of the acoustical macro-behavior of real porous media

• Fig. 2.2 Results summary

Results:  Identification of PUCs representative

• f purely geometrical macroscopic

parameters  Computation of the dynamic bulk modulus from random walkers (3D)  Computation of the dynamic viscous permeability (2D)  Reconstruction of the frequency- dependent acoustic behavior

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• II. OVERVIEW OF RESEARCH

ACTIVITIES

2) Relations between microstructures and properties of sound absorbers

• Purpose: devising micro-/macro relations, from the numerical tools and modeling

techniques previously developed

• Fig. 2.2 Effect of the throat size in the range [20 µm – 210 µm] on the sound absorption coefficient

 Absorption level  Selectivity  Weight reduction

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• II. OVERVIEW OF RESEARCH

ACTIVITIES

3) Modeling of heterogeneous poroelastic materials with a broad distribution of pore sizes

• Fig. 2.3 Velocity field magnitude [LF] (left) and electric field magnitude [HF] (right) for a porosity of 0.8.

Black is zero, white is maximum. [Martys and Garboczi, PRB (1992)].

• Problem statement: How to identify a representative volume element for

heterogeneous poroelastic materials (PUC) ?

• Difficulties: The fluid flow paths are not the same according to frequency.

 Critical path ideas might be useful to tackle this problem

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

OUTLINE

• I. Administrative overview
• II. Overview of research activities
• III. Scientific focus on modeling real porous media
• IV. Conclusion and future works

Outline

Multi-scale properties of acoustic materials

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Camille PERROT, Habilitation defense, Université Paris-Est Marne-la-Vallée, December 11, 2014

• III. SCIENTIFIC FOCUS

A) Transport properties

• Context: determination of the acoustical properties from the microstructure
• A long standing problem: [Rayleigh, 1945 (2nd Ed.); Zwikker and Kosten, 1949;

Attenborough, 1982; Allard and Atalla, 2009 (2nd Ed)]

• Aim. Get insight into the microstructure of real porous media and understand

how it collectively dictates their macro-scale acoustic properties.

• Method:

 Determine a unit cell suitable for representing the local geometry of a porous medium.  Solve the partial differential equations in such a cell to obtain the parameters governing the physics at the upper scale.

Introduction

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

A) Transport properties

Direct static characterization of foam samples

Microstructure characterization: characteristic shape measurements

• FIG. 3.1 Typical micrographs of real foam samples: (a) R1, (b) R2, (c) R3.

 Measurement of cell shape characteristics such as the average

numbers of edges per face

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

A) Transport properties

Direct static characterization of foam samples

Microstructure characterization: characteristic size measurements

• FIG. 3.2 Ligament length distributions: R1 (left), R2 (middle), R3 (right).

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

A) Transport properties

Direct static characterization of foam samples

Direct determination of porosity and static permeability

Porosity measurement after Baranek and Champoux et al.

Porosity Permeability

Measurement of the permeability (or static airflow resistivity) following ISO 9053.

Microstructure

(-) φ ( ) k

2

m

R1 0.98 ± 0.01 2.60 ± 0.08 ×10-9 R2 0.97 ± 0.01 2.98 ± 0.14 ×10-9 R3 0.98 ± 0.01 4.24 ± 0.29 ×10-9

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

A) Transport properties

Numerical estimates of the transport properties from a 3D Periodic Unit Cell (PUC)

1) Defining the local geometry model

• Fig. 3.3 Basic 3D periodic foam model geometry

 Algebraic equations linking micro- to macro- geometric properties

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

A) Transport properties

Numerical estimates of the transport properties from a 3D Periodic Unit Cell (PUC)

2) Scaling the unit cell

exp

2

• r

L φ   →    

exp

• p

BET

S



r →

• h

d

k D k = ×

• Fig. 3.4 1/4th of the reconstructed foam sample period R1.

Low-frequency scaled velocity field k*0xx [x 10-9 m2]

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

A) Transport properties

Results on asymptotic transport properties obtained from FE

Table 2.1 A comparison between computed and measured macroscopic parameters Figure 3.5 A typical SEM image of the foam sample (microstructure R1)

Foams Method

(-) φ ' (µm) Λ ( ) k

2

m (-) α (µm) Λ (-)

∞

α ( ) k '

2

m ' α0

R1 Computations 506 1.22 297 1.02 5.01×10-9 1.13 Measurements 0.98 2.60×10-9 Characterization (a) 440 129 1.12 8.30×10-9

(a) model based calibration

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

A) Transport properties

Implementing a missing ingredient: solid films or membranes

Figure 3.6 Solid film implementation using an iterative algorithm on δ from a 3D

• pen cell model and corresponding sound absorbing behavior

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

B) Elastic properties

• Aim. Relate pore structure to both transport and elastic properties on the basis of

easily measured single properties of porous materials (with and without membrane).  Sound absorption and sound transmission loss of the poroelastic materials

Introduction

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

B) Elastic properties

Materials and Methods

Figure 3.7 Geometrical characteristics of two solid foam samples, H1 (top) and H2 (bottom)

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

B) Elastic properties

Materials and Methods

Effective mechanical properties

• Obtained numerically for two different solid foam models from FE calculations

and compared to experiments.

• Hypothesis:

 The material constituting the skeleton is locally isotropic and linear elastic.  Elastic properties of the gaseous fluid phase negligible.

• Method:

 Apply two macroscopic external strains on the cube that bound the solid foam model: a tensile strain and a shear strain.  Estimation of the elastic moduli through volume and orientation averaging.

Multi-scale properties of acoustic materials

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Camille PERROT, Habilitat Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015 ion defense, Université Paris-Est Marne-la-Vallée, December 11, 2014

• III. SCIENTIFIC FOCUS

B) Elastic properties

Materials and Methods

Figure 3.8 Numerical experiments allowing to identify the elastic constants C11, C12, C44.

( )

12 1 2 2 1

E E e e e e = ⊗ + ⊗    

11 1 1

E E e e = ⊗  

(A) Tensile strain numerical experiment: (B) Shear strain numerical experiment:

(a) the displacement field (μm); (b) the stress field σ11(N/m2); (c) the stress field σ22 (N/m2) (a) the displacement field (μm); (b) the stress field σ12 (N/m2)

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

B) Elastic properties

Results and Discussion

Geometrical and transport macroscopic properties

• Rather good agreement with experimental data when standard deviations are

taken into account

• Model insensitive to polydispersity of the throat size
• Very low permeability combined with vibrations affect the experimental

estimation of Λ’ Table 3.2 Macroscopic parameters: Comparison between computational and experimental results (least favorable case, H2)

Foam Method

φ

Λ’ (μm) k0 (×10-10 m2) Λ (μm) α∞ k0’ (×10-10 m2) H2 Computation 179 ± 46 53 ± 9 2.40 ± 0.55 48 ± 26 Measurements 0.97 ± 0.01 2.56 ± 0.60 Characterization 424 ± 92 13 ± 6 1.58 ± 0.64 53 ± 16

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

B) Elastic properties

Results and Discussion

Analysis of the representativity of the microstructure from SEM images

 Large relative proportion of small interconnexions explain why, in the single throat size model, its viscous characteristic length Λ is overestimated

Figure 3.9 Distribution of interconnexion or window sizes for foam samples H2

2 2

2 (X) . (X)

Vp S

dV dS

∞ ∞

Λ =

∫ ∫

v v

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

B) Elastic properties

Results and Discussion

Discussion on the relative influence of membrane closure rate and thickness

• The effects of membrane thickness and closure rate appear as having a

stronger weight on the overall response compared to the effect of cross section shape and cross sectional variation (especially when φ and k0 uncertainties are taken into account)

• This justify the use of the proposed idealized unit cell
• Unit cells also representative of independently measured effective linear

poroelastic properties?

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

B) Elastic properties

Results and Discussion

Linear elastic properties

 Note a low sensitivity of the Young’s modulus with preconstraint for H1.

Figure 3.10 The Young’s modulus E measured from compression testing

exp 1

( ) 5.4 kPa E H

τ →

=

exp 2

( ) 14.4 kPa E H

τ →

=

max exp 1 0.035

( ) 17.7 kPa E H

τ =

=

max exp 2 0.05

( ) 122.7 kPa E H

τ =

=

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

B) Elastic properties

Results and Discussion

Linear elastic properties

Figure 3.11 Comparison between non-dimensional experimental and numerical quasi-static Young’s moduli

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

B) Elastic properties

Results and Discussion

Figure 3.12 Sound transmission loss of a poroelastic foam sample, H2 (least favorable case)

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• III. SCIENTIFIC FOCUS

C) Developing foams

Developing acoustically effective foams via cellular structure

Numerical experiments at macro-scale

Foam

φ

' Λ (μm) σ (N.m-4.s) Λ (μm) α∞

• 10

2 0 ' ( 10

m ) k × (Pa) E Insulating (H1b) 0.95 127 40 000 52 1.3 20 13 333 Absorbing (H2b) 0.95 188 40 000 62 2 52 40 000

Targeted poroelastic parameters

Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

C) Developing foams

Guidelines for the translation of the targeted poroelastic parameters into a feasible cellular structure

• k0 - homothetic transformations
• α∞ - Membrane effect
• E - Control the quantity of “urethane” bounds

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• III. SCIENTIFIC FOCUS

C) Developing foams

Design procedure linking cellular structure with poroelastic parameters

Modification of the testing instruction in the iterative algorithm

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

OUTLINE

• I. Administrative overview
• II. Overview of research activities
• III. Scientific focus on modeling real porous media
• IV. Conclusion and future works

Outline

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• IV. CONCLUSION

A) Main conclusions

A continuity between microstructure, properties and manufacturing of poroelastic foams has begun to emerge

Main conclusions (1/2)

• A unified set of transport and elastic calculations has ben carried out
• The tetrakaidecahedron is an appropriate 3D local geometry to achieve long-

wavelength acoustics simulations

• A simply open cell geometry is generally not a sufficient feature (membranes)
• Two simple characteristic lengths of the microstructure, the pore and throat

size may describe a wide class of disordered materials (experience)

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• IV. CONCLUSION

A) Main conclusions

A continuity between microstructure, properties and manufacturing of poroelastic foams has begun to emerge

Main conclusions (2/2)

• Corresponding models, although perfectly ordered, fairly representative of 3

distinct classes of transports when compared to measurements

• Reasonable to account for the tiny apertures (polydisperse interconnections)
• Scaled elastic properties of the modeled microstructures fall relatively close to

the expected values (low density soft polyurethane foams)

• The above results can be used to support the development of light weighted

acoustically effective foams

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• IV. CONCLUSION

B) Ongoing and Future works

Ongoing work

 Collaboration with the Centre for Mathematical Morphology from MINES ParisTech

Random vs idealized geometries

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• IV. CONCLUSION

B) Ongoing and Future works Modeling Plateau borders Viscous velocity field, potential velocity field, low frequency temperature field Improvement of the prediction (H2)

 Collaboration with Navier Laboratory (ProMAP project)

Recent advances in pore-morphology-based simulations

Multi-scale properties of acoustic materials

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Camille PERROT, Séminaire Roberval, université de Technologie Compiègne, 4 juin 2015

• IV. CONCLUSION

B) Ongoing and Future works

 Collaboration with Université de Sherbrooke (PhD Thesis, Hoang Tuan LUU)

Fibrous media

Future works

 Collaboration with J. Guilleminot and V. Monchiet

A stochastic approach to micro-/macro modeling

• Modeling and identification
• Multifunctional optimization (including cross-property relations)