Elastic properties of shaped porous materials : …...Elastic properties of shaped porous materials...

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Elastic properties o and modelling François-Xavier Bécot1 1 , MATELYS – Research La 7 rue des Maraîchers, Bât F-69120 Vaulx-en-Velin, F Keywords: Porous, elastic, I-INCE Classification of S Under certain conditions, p to satisfy architecture cons increase the material perfor For instance, wedge shape frequencies. It was earlier could be reproduced by rep them being modelled using Figure 1 : Model of a 1 [email protected] of shaped porous materials : exp Luc Jaouen, Fabien Chevillotte ab t B France , vibration, double porosity Subject Number: 43.55.Ev, 43.55.Pe EXTENDED ABSTRACT porous materials used for noise abatement ne strains as for corrugated sheets. Moreover, it rmance. e is used to increase the sound absorption p demonstrated that the performances of this t presenting the wedge as a series of perforated g the double porosity theory [1] (see Figure 1) an anechoic wedge by a series of perforated periments eed to be shaped t may be used to properties at low type of materials d layers, each of ). d layers [1].

Transcript of Elastic properties of shaped porous materials : …...Elastic properties of shaped porous materials...

Page 1: Elastic properties of shaped porous materials : …...Elastic properties of shaped porous materials : experiments and modelling François-Xavier Bécot1 1, Luc Jaouen, Fabien Chevillotte

Elastic properties of shaped porous materials : experiments and modelling

François-Xavier Bécot11, Luc Jaouen, Fabien ChevillotteMATELYS – Research Lab7 rue des Maraîchers, Bât BF-69120 Vaulx-en-Velin, France Keywords: Porous, elastic,

I-INCE Classification of Subject Number:

Under certain conditions, porous materials used f

to satisfy architecture constrains as for corrugated sheets. Moreover, it may be used to

increase the material performance.

For instance, wedge shape is used to increase the sound absorption properties at low

frequencies. It was earlier demonstrated that the performances of this type of materials

could be reproduced by representing the wedge as a series of perforated layers, each of

them being modelled using the double porosity theory [1] (see Figure 1).

Figure 1 : Model of an anechoic wedge by a series of perforated layers [

1 [email protected]

Elastic properties of shaped porous materials : experiments

, Luc Jaouen, Fabien Chevillotte

Research Lab 7 rue des Maraîchers, Bât B

Velin, France

elastic, vibration, double porosity

INCE Classification of Subject Number: 43.55.Ev, 43.55.Pe

EXTENDED ABSTRACT

Under certain conditions, porous materials used for noise abatement need to be shaped

to satisfy architecture constrains as for corrugated sheets. Moreover, it may be used to

increase the material performance.

For instance, wedge shape is used to increase the sound absorption properties at low

es. It was earlier demonstrated that the performances of this type of materials

could be reproduced by representing the wedge as a series of perforated layers, each of

ed using the double porosity theory [1] (see Figure 1).

odel of an anechoic wedge by a series of perforated layers [

Elastic properties of shaped porous materials : experiments

or noise abatement need to be shaped

to satisfy architecture constrains as for corrugated sheets. Moreover, it may be used to

For instance, wedge shape is used to increase the sound absorption properties at low

es. It was earlier demonstrated that the performances of this type of materials

could be reproduced by representing the wedge as a series of perforated layers, each of

ed using the double porosity theory [1] (see Figure 1).

odel of an anechoic wedge by a series of perforated layers [1].

Page 2: Elastic properties of shaped porous materials : …...Elastic properties of shaped porous materials : experiments and modelling François-Xavier Bécot1 1, Luc Jaouen, Fabien Chevillotte

This analytical model was proved to be numerically efficient compared to purely

numerical approaches (e.g. finite elements), allowing for fast and reliable predictions

[1,2] (see Figure 2). It was also proved that this model could be coupled to an image

source model to predict the sound field inside an anechoic room to detect possible

discrepancies from the free field assumption [2].

Figure 2 : Results of the analytical simulation of the sound absorption under plane

wave at normal incidence for an anechoic wedge [1].

As per the elastic properties, “wavy” shaped materials are known to present interesting

decoupling properties for undesired vibrational levels. For instance, concrete slab

underlayers are known to enable higher compression performances compared to the

same material having a flat surface (see Figure 3).

Figure 1 : Examples of a shaped porous materials used for vibration insulation.

Page 3: Elastic properties of shaped porous materials : …...Elastic properties of shaped porous materials : experiments and modelling François-Xavier Bécot1 1, Luc Jaouen, Fabien Chevillotte

While the analytical model

instance above), the prediction of

open question. Therefore, this paper proposes to investigate a numerical model based on

a two-scale micro-macro approach.

The first stage consists in predicting the intrinsic elastic properties

From a series of numerical tests for both compression and shear stress, the full elasticity

matrix is retrieved, enabling to calculate the Young’s modulus and the Poisson’s ratio

[3] (see Figure 4).

Figure 2 : Numerical compression amatrix (bottom)

Once these intrinsic parameters retrieved, the second stage of the model consis

shaping numerically the porous materials and applying the stress under consideration

using a similar approach as in the first stage. At the second stage however, the retrieved

parameter is the stiffness of the shaped porous material. It should be hig

this is not an intrinsic property as it is associated with the prescribed material thickness

and the value of the heel and of the tip of the “wave”.

The validation of this approach is carried out at the two considered stages. The

predicted intrinsic properties are validated against measurement of the Young’s

modulus and Poisson’s ratio carried out using a quasi

core (unshaped) material [4]. The stiffness of the shaped material is then evaluated both

for compression and bending motion and compared to the numerical predicted values.

Results are presented for various shape geometries and several nature of the porous

substrate. In particular, the tested porous cores comprise fibrous and chipped materials

as well as visco-elastic foams.

This work enables to prototype virtually the elastic properties of shaped porous

materials as an alternative to less efficient trial and error tests.

While the analytical modelling of the acoustic properties is largely documented (see for

instance above), the prediction of the elastic properties of this type of material is still an

open question. Therefore, this paper proposes to investigate a numerical model based on

macro approach.

The first stage consists in predicting the intrinsic elastic properties of the porous core.

From a series of numerical tests for both compression and shear stress, the full elasticity

matrix is retrieved, enabling to calculate the Young’s modulus and the Poisson’s ratio

ompression and shear stresses (top) enabling to recover the (bottom). Illustrations extracted from the ScalingCell software

(http://scalingcell.matelys.com/).

Once these intrinsic parameters retrieved, the second stage of the model consis

shaping numerically the porous materials and applying the stress under consideration

using a similar approach as in the first stage. At the second stage however, the retrieved

parameter is the stiffness of the shaped porous material. It should be hig

this is not an intrinsic property as it is associated with the prescribed material thickness

and the value of the heel and of the tip of the “wave”.

The validation of this approach is carried out at the two considered stages. The

ntrinsic properties are validated against measurement of the Young’s

modulus and Poisson’s ratio carried out using a quasi-static compression method on the

core (unshaped) material [4]. The stiffness of the shaped material is then evaluated both

ssion and bending motion and compared to the numerical predicted values.

Results are presented for various shape geometries and several nature of the porous

substrate. In particular, the tested porous cores comprise fibrous and chipped materials

elastic foams.

This work enables to prototype virtually the elastic properties of shaped porous

materials as an alternative to less efficient trial and error tests.

ing of the acoustic properties is largely documented (see for

the elastic properties of this type of material is still an

open question. Therefore, this paper proposes to investigate a numerical model based on

of the porous core.

From a series of numerical tests for both compression and shear stress, the full elasticity

matrix is retrieved, enabling to calculate the Young’s modulus and the Poisson’s ratio

to recover the full elasticity

. Illustrations extracted from the ScalingCell software

Once these intrinsic parameters retrieved, the second stage of the model consists in

shaping numerically the porous materials and applying the stress under consideration

using a similar approach as in the first stage. At the second stage however, the retrieved

parameter is the stiffness of the shaped porous material. It should be highlighted that

this is not an intrinsic property as it is associated with the prescribed material thickness

The validation of this approach is carried out at the two considered stages. The

ntrinsic properties are validated against measurement of the Young’s

static compression method on the

core (unshaped) material [4]. The stiffness of the shaped material is then evaluated both

ssion and bending motion and compared to the numerical predicted values.

Results are presented for various shape geometries and several nature of the porous

substrate. In particular, the tested porous cores comprise fibrous and chipped materials

This work enables to prototype virtually the elastic properties of shaped porous

Page 4: Elastic properties of shaped porous materials : …...Elastic properties of shaped porous materials : experiments and modelling François-Xavier Bécot1 1, Luc Jaouen, Fabien Chevillotte

REFERENCES [1] Bécot, F.-X. and Jaouen, L. and Gourdon, E., Applications of the Dual Porosity

Theory to Irregularly Shaped Porous Materials, Acta Acustica united with Acustica,

Vol. 94 (5), pp. 715-724 (2008)

[2] Bécot, F.-X. and Schneider, S. and Jaouen, L., Prediction of the sound field in

anechoic rooms : comparison of two different approaches, In Proceedings of Euronoise /

Acoustics'08, Paris, France (2008)

[3] Hoang, M. T. and Bonnet, G. and Luu, H. T. and Perrot, C., Linear elastic properties

derivation from microstructures representative of transport parameters, J. Ac. Soc. Am.,

Vol. 135 (6), pp. 3172-3185 (2014)

[4] Langlois, C. and Panneton, R. and Atalla, N., Polynomial relations for quasi-static

mechanical characterization of isotropic poroelastic materials, J. Ac. Soc. Am., Vol. 110

(6), pp. 3032-3040 (2001)