Linear elastic properties derivation from microstructures representative of transport parameters

Abstract

It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.

Investigation of the effects of the microstructure on the sound absorption performance of polymer foams using a computational homogenization approach

“…As shown in Fig. 8, the membrane thickness has a significant influence on the effective elastic stiffness, which is in agreement with the work of Hoang et al [47]. Here, the influence of the thickness of the membranes is further stud-ied for thicknesses of the order of 1 µm, which is representative for flexible PU foams [3,48].…”

Opening and retraction of particulate soap films

“…In these applications, aqueous foams are often used as templates to obtain solid aerated materials. The stability of the liquid aqueous foam (fresh material) but also the mechanical and acoustical properties of the solid foam after drying, which depend especially on the fraction of open cells and the apertures sizes of the membranes [16,17], are affected by the presence of the particles. Understanding how the particles affect this aspects is challenging.…”

An Overview of Microstructural Approaches for Modelling and Improving Sound Proofing Properties of Cellular Foams: Developments and Prospects

“…The effective mechanical properties are obtained numerically for different solid foam models from finite element calculations and may be compared to values coming from experiments on real samples. The effective linear-elastic properties of the solid networks are determined by a finite element scheme operating on discretized representations of the structure; see [3] for further details. The material constituting the skeleton is assumed to be locally isotropic and linear-elastic; the elastic properties of the gaseous fluid phase are considered as negligible compared to the ones of the solid skeleton.…”

“…First, three-dimensional idealized geometry and transports provide most of the visco-thermal dissipative phenomena appropriate for modeling sound absorbing materials [2]. Second, the solid matrix is allowed to be deformed under small perturbations to account for the effective elastic properties; an essential feature for sound insulating simulations [3]. Direct extensions of this work could deal with an improvement of local geometry modeling (cell size elongation or degree of anisotropy, description of the struts and membranes by Plateau borders).…”

“…Thus, research activity in this area may reflect specific attention for a particular shape, from purely open cells [15] to situations where a variable closure rate of membranes was employed to reveal those microphysical effects associated with transport phenomena [16] and linear elasticity [3]. The link between micro and macro scales is provided by the theoretical results obtained from the homogenization of periodic structures' technique; indicating the boundary value problems to be solved at micro-scale, the structure of governing equations at macro-scale, and how the associated coefficients should be computed (macroscopic properties) [17]- [19].…”