Institute of Fundamental Technological Research

Although the elastic properties of porous materials depend mainly on the volume fraction of pores, the details of pore distribution within the material representative volume are also important and may be the subject of optimisation. To study their effect, experimental analyses were performed on samples made of a polymer material with a predefined distribution of spherical voids, but with various porosities due to different pore sizes. Three types of pore distribution with cubic symmetry were considered and the results of experimental analyses were confronted with mean-field estimates and numerical calculations. The mean-field ‘cluster’ model is used in which the mutual interactions between each of the two pores in the predefined volume are considered. As a result, the geometry of pore distribution is reflected in the anisotropic effective properties. The samples were produced using a 3D printing technique and tested in the regime of small strain to assess the elastic stiffness. The digital image correlation method was used to measure material response under compression. As a reference, the solid samples were also 3D printed and tested to evaluate the polymer matrix stiffness. The anisotropy of the elastic response of porous samples related to the arrangement of voids was assessed. Young’s moduli measured for the additively manufactured samples complied satisfactorily with modelling predictions for low and moderate pore sizes, while only qualitatively for larger porosities. Thus, the low-cost additive manufacturing techniques may be considered rather as preliminary tools to prototype porous materials and test mean-field approaches, while for the quantitative and detailed model validation, more accurate additive printing techniques should be considered. Research paves the way for using these computationally efficient models in optimising the microstructure of heterogeneous materials and composites.

Pore configuration, Anisotropy, Elasticity, Micro-mechanics, Additive manufacturing

An assembly of additively-manufactured modules to form two-dimensional networks of labyrinthine slits results in a sound absorber with extremely high tortuosity and thereby a relatively low frequency quarter wavelength resonance. Fully analytical modelling is developed for the generic design of such composite acoustic panels, allowing rapid exploration of various specific designs. In addition to labyrinthine channels in a non-porous solid skeleton, a case is also considered where the skeleton has microporosity such that its permeability is very much lower than that due to the labyrinthine channels alone. The analytical modelling is verified by numerical calculations, as well as sound absorption measurements performed on several 3D printed samples of modular composite panels. The experimental validation required overcoming the non-trivial difficulties related to additive manufacturing and testing samples of extreme tortuosity. However, due to the two-dimensionality and modularity of the proposed design, such absorbers can possibly be produced without 3D printing by assembling simple, identical modules produced separately. The experimental results fully confirmed the theoretical predictions that significant sound absorption, almost perfect at the peak, can be achieved at relatively low frequencies using very thin panels, especially those with double porosity.

Sound absorption,Extreme tortuosity,Double porosity,Acoustic composites,Additive manufacturing

The potential usefulness of relatively simple pore microstructures such as parallel, identical, inclined slits for creating broadband sound absorption has been argued through analytical models. In principle, such microstructures could be realised through budget additive manufacturing. However, validation of the analytical predictions through normal incidence impedance tube measurements on finite layers is made difficult by the finite size of the tube. The tube walls curtail the lengths of inclined slits and, as a result, prevent penetration of sound through the layer. As well as demonstrating and modelling this effect, this paper explores two manufacturing solutions. While analytical and numerical predictions correspond well to absorption spectra measured on slits normal to the surface, discrepancies between measured and predicted sound absorption are noticed for perforated and zigzag slit configurations. For perforated microgeometries this is found to be the case with both numerical and analytical modelling based on variable length dead-end pores. Discrepancies are to be expected since the dead-end pore model does not allow for narrow pores in which viscous effects are important. For zigzag slits it is found possible to modify the permeability used in the inclined slit analytical model empirically to obtain reasonable agreement with data.

slitted sound absorber, additive manufacturing, microstructure-based modelling

Closed-cell metal foams are lightweight and durable materials resistant to high temperature and harsh conditions, but due to their fully closed porosity they are poor airborne sound absorbers. In this paper a classic method of drilling is used for a nearly closed-cell aluminium foam to open its porous interior to the penetration of acoustic waves propagating in air, thereby increasing the wave energy dissipation inside the pores of the perforated medium. The aim is to investigate whether it is possible to effectively approximate wave propagation and attenuation in industrial perforated heterogeneous materials with originally closed porosity of irregular shape by means of their simplified microstructural representation based on computer tomography scans. The applied multi-scale modelling of sound absorption in foam samples is confronted with impedance tube measurements. Moreover, the collected numerical and experimental data is compared with the corresponding results obtained for perforated solid samples to demonstrate a great benefit coming from the presence of an initially closed porous structure in the foam.

closed-cell metal foams, perforation, sound absorption, microstructure effects, dissipated powers

This work investigates a porous composite with modifiable micro-geometry so that its ability to absorb noise can be accommodated to different frequency ranges. The polymeric skeleton of the composite has a specific periodic structure with two types of pores (larger and smaller ones) and two types of channels (wide and narrow ones), and each of the large pores contains a small steel ball. Depending on the situation, the balls block different channels that connect the pores, and therefore alter the visco-inertial phenomena between the saturating air and solid skeleton which take place at the micro-scale level and are responsible for the dissipation of the energy of acoustic waves penetrating the porous composite. All this is studied numerically using advanced dual-scale modelling, and the results are verified by the corresponding experimental tests of 3D-printed samples. Particular attention is paid to the prototyping and additive manufacturing of such adaptive porous composites.

porous composite, adaptive sound absorber, microstructure-based modelling, additive manufacturing

The purpose of this work is to check if additive manufacturing technologies are suitable for reproducing porous samples designed for sound absorption. The work is an inter-laboratory test, in which the production of samples and their acoustic measurements are carried out independently by different laboratories, sharing only the same geometry codes describing agreed periodic cellular designs. Different additive manufacturing technologies and equipment are used to make samples. Although most of the results obtained from measurements performed on samples with the same cellular design are very close, it is shown that some discrepancies are due to shape and surface imperfections, or microporosity, induced by the manufacturing process. The proposed periodic cellular designs can be easily reproduced and are suitable for further benchmarking of additive manufacturing techniques for rapid prototyping of acoustic materials and metamaterials.

porous materials, designed periodicity, additive manufacturing, sound absorption

Selective laser sintering and binder jetting are two additive manufacturing technologies that use loose powder as a feedstock. In the case of binder jetting, the printout walls are essentially permeable and need to be additionally impregnated to be fully air-tight. The permeability of sintered objects, on the other hand, can be controlled to some extent by the amount of laser energy, among other things, provided to the exposed layer. Exploring these two technologies, several single- and double-porosity samples were additively manufactured, examined and acoustically measured in an impedance tube. Moreover, the normal incidence sound absorption spectra resulting from these structures were predicted employing multi-scale methods. The values of porosity and permeability of permeable printed materials were determined and utilised in the applied modelling. It is observed that making the skeleton microporous and permeable enables effective sound absorption even in primitive 3D printed acoustic treatments.

The low frequency peaks in the absorption spectra of layers of conventional porous materials correspond to quarter wavelength resonances and the peak frequencies are determined essentially by layer thickness. If the layer cannot be made thicker, the frequency of the peak can be lowered by increasing the tortuosity of the material. Modern additive manufacturing technologies enable exploration of pore network designs that have high tortuosity. This paper reports analytical models for pore structures consisting of geometrically complex labyrinthine networks of narrow slits resembling Greek meander patterns. These networks offer extremely high tortuosity in a non-porous solid skeleton. However, additional enhancement of the low frequency performance results from exploiting the dual porosity pressure diffusion effect by making the skeleton microporous with a significantly lower permeability than the tortuous network of slits. Analytical predictions are in good agreement with measurements made on two samples with the same tortuous slit pattern, but one has an impermeable skeleton 3D printed from a photopolymer resin and the other has a microporous skeleton 3D printed from a gypsum powder.

sound absorption, high tortuosity, dual porosity, 3D printed materials

Materials with open porosity are known to absorb sound very well. However, their efficiency in acoustic absorption and insulation is sometimes restricted to specific frequency ranges. It is possible to circumvent this drawback by designing a porous microstructure that can be modified on the fly and thereby enabling the change in its crucial geometrical parameters like tortuosity that influence the intensity of viscous energy dissipation phenomena taking place on a micro scale. A prototype of such a material consisting of relocatable small steel balls embedded in a periodic rigid skeleton is devised and additively manufactured in separate pieces in the stereolithography technology. The balls are inserted into proper places manually. The full sample is then assembled and its acoustic characteristics are determined computationally and experimentally using dual-scale, unit-cell analyses and impedance tube measurements, respectively. The resulting material is shown to possess two extreme spectra of normal incidence sound absorption coefficient and transmission loss that are dependent on the particular position of balls inside the microstructure. In consequence, acoustic waves from a much larger frequency range can be effectively absorbed or insulated by a relatively thin material layer compared to a similar design without movable balls.

sound absorption, sound transmission, modifiable porous microstructure, additive manufacturing

Low-frequency sound absorption by thin rigid porous hard-backed layers is enhanced if the geometrical tortuosity is increased. Increasing tortuosity increases the fluid flow path length through the porous layer thereby increasing the effective thickness. In turn, this reduces the effective sound speed within the layer and the frequency of the quarter wavelength layer resonance. One way of increasing tortuosity is through rectangular labyrinthine channel perforations. In addition to the tortuosity of the porous matrix, the bulk tortuosity value is influenced by the channel widths, lengths, and number of folds. A sample with an impervious skeleton and a sample in which the solid skeleton is perforated with oblique cylindrical holes evenly spaced in a rectangular pattern have been fabricated using conventional methods and an additive manufacturing technology, respectively. The sound absorption spectra resulting from these structures have been predicted analytically as well as numerically and compared with normal incidence impedance-tube measurements.

Designs with uniformly distributed slits normal or inclined to the incident surface exhibit a great potential because of their simplicity and good acoustical performance. However, production of materials of this sort is challenging as the required fabrication precision is very high. This paper deals with additive manufacturing, modeling, and impedance tube testing of a few slitted geometries and their variations, including cases where the dividing walls between slits are perforated. They were designed to be producible with current 3D printing technology and provide reliable measurements using standardized equipment. The normal incidence sound absorption curves predicted analytically and numerically were verified experimentally. It is observed that such simple configurations may lead to absorption properties comparable to porous acoustic treatments with more complex microstructure. The good agreement between the predictions and measurements supports the validity of the multi-scale modeling employed.

Despite very good mechanical and physical properties such as lightness, rigidity and high thermal conductivity, closed-porosity metal foams alone are usually poor acoustic treatments. However, relatively low production cost weighs them in many applications in favour of their open-cell equivalents. In the present paper, this attractive and popular material is subject to consideration from the point of view of the improvement of its sound absorption characteristics. A classic method of perforation is proposed to open the porous interior of the medium to the penetration of acoustic waves and therefore enhance the dissipation of their energy. The interaction between the perforation diameter and closed-cell microstructure as well as its impact on the overall sound absorption of a similar foam were already studied in 2010 by Chevillotte, Perrot and Panneton, so these topics are not discussed much in this work. On the other hand, the objective here is to investigate if one can efficiently approximate the wave propagation phenomenon in real perforated heterogeneous materials with closed porosity of irregular shape by means of their simplified three-dimensional representation at the micro-level. The applied multi-scale modelling of sound absorption was confronted with measurements performed in an impedance tube. Moreover, as expected, numerical and experimental comparisons with relevant perforated solid samples show great benefit coming from the presence of a porous structure in the foam, although it was initially closed.

With a rapid development of modern Additive Manufacturing Technologies it seems inevitable that they will sooner or later serve for production of specific porous and meta-porous acoustic treatments. Moreover, these new technologies are already being used to manufacture original micro-geometric designs of sound absorbing media in order to test microstructure-based effects, models and hypothesis. In the view of these statements, this work reports differences in acoustic absorption measured for porous specimens which were produced from the same CAD-geometry model using several additive manufacturing technologies and 3D-printers. A specific periodic unit cell of open porosity was designed for the purpose. The samples were measured acoustically in the impedance tube and also subjected to a thorough microscopic survey in order to check their quality and look for the discrepancy reasons.

Sound absorption, Additive Manufacturing Technologies

Recent investigations show that the normal incidence sound absorption in 3D-printed rigid porous materials is eminently underestimated by numerical calculations using standard models. In this paper a universal amendment to the existing mathematical description of thermal dispersion and fluid flow inside rigid foams is proposed which takes account of the impact of the additive manufacturing technology on the acoustic properties of produced samples. The porous material with a motionless skeleton is conceptually substituted by an equivalent fluid with effective properties evaluated from the Johnson-Champoux-Allard-Pride-Lafarge model. The required macroscopic transport parameters are computed from the microstructural solutions using the hybrid approach. A cross-functional examination of the quality (shape consistency, representative surface roughness, etc.) of two periodic specimens obtained from additive manufacturing processes is additionally performed in order to link it to the results of the multiscale acoustic modelling. Based on this study, some of the transport parameters are changed depending on certain quantities reflecting the actual quality of a fabricated material. The developed correction has a considerable influence on the predicted value of the sound absorption coefficient such that the original discrepancies between experimental and numerical curves are significantly diminished.

Rigid porous material, Additive manufacturing, Sound absorption

The purpose of this work is to present and investigate the concept of adaptive sound absorbers, that is, periodic porous media with modifiable micro-geometry, so that their ability of sound absorption or insulation can be changed in various frequency ranges. To demonstrate this concept, a simple periodic porous micro-geometry with small bearing balls inside pores is proposed. By a simple positioning of the periodic porous sample the gravity force is used for the small balls to close some of the windows linking the pores, changing in that way the flow path inside pores, which entails significant modifications of the relevant parameters of permeability and tortuosity. Also the viscous characteristic length is changed, while the porosity as well as the thermal characteristic length remain unchanged. Nevertheless, such significant changes of some crucial transport parameters strongly affect the overall acoustic wave propagation in the porous medium. All this is studied using an advanced dual-scale modelling as well as experimental testing of 3D-printed specimens.

A composite additively manufactured material for controlled sound absorption is proposed. The operation of the material is based on its changeable microgeometry with steel balls that modify propagation of acoustic waves when subject to an external magnetic field. Both numerical predictions and experimental verification is provided.

sound absorption, porous material, multiscale modelling, coupled problem

An acoustical characterisation of additively manufactured rigid slitted structures is considered. A set of six JCAL microstructural parameters is deduced from dynamic density and bulk modulus obtained from normal incidence surface acoustic impedance experimental data. The results show that the characteristic lengths are the most difficult to characterise.