A priori determination of the elastic and acoustic responses of periodic poroelastic materials Sagar Deshmukh, Ankush Borkar, Alankar Alankar, Shankar Krishnan, Sripriya Ramamoorthy ⇑ Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India article info Article history: Received 2 October 2019 Received in revised form 31 March 2020 Accepted 26 May 2020 abstract Designed periodic foam structures have the potential for achieving predictable acoustic performance. For foam structures that have small strand thickness and made of low-modulus material, rigid-porous assumption may be inaccurate owing to strong fluid-structure coupling. The goal of this study is to design and predict the elastic and acoustic responses of periodic poroelastic structures. Three surface based and one truss based unit cell configurations are considered for study. Elastic properties of these unit-cell con- figurations are estimated using the homogenization approach and validated experimentally. The pre- dicted elastic properties are used along with the predicted five microscopic Johnson-Champoux-Allard (JCA) parameters for estimating the response of periodic foam structures using the Biot-UP formulation. Parametric study reveals that the effect of structural modes on acoustic absorption coefficient increases with increase in porosity as well as with decrease in pore size. A soft porous periodic lattice sample is fabricated and its predicted absorption coefficient as well as sound-induced displacement response are experimentally validated. The approach presented here will be useful to design soft periodic foam struc- tures for desired structural and acoustic response, and to control the effect of structural modes on acous- tic response. Ó 2020 Elsevier Ltd. All rights reserved. 1. Introduction Foams are known for their ability to combine various properties such as high stiffness with low weight, high compression strength combined with energy absorption, broadband noise absorption and heat dissipation [1]. Owing to such properties, they are proposed for structural applications requiring load-bearing features, for light-weight and impact-absorbing structures in vehicles, vibration and sound absorption, for heat exchangers, and in medical devices. For example, sandwich panels with foam core are a promising can- didate in the aerospace industry to design structures with high strength combined with low weight [2]. Foaming process used to manufacture stochastic foams involves bubbling, stirring and solidification of the molten metal. It is very difficult to carry out these processes in a fully controlled environ- ment. Stochastic foams therefore possess certain degree of irregu- larities such as inhomogeneity, cell wall corrugation (which could result in cell wall collapse on its neighbour), and porosity variation [3]. These irregularities in stochastic foams lead to variations in mechanical, thermal as well as acoustic properties due to their strong dependency on cellular structure [4–7]. Classical work by Gibson and Ashby [1] proposes a simple power law relationship (Eq. 1) between the stochastic foam relative density and elastic modulus. E  E ¼ C q  q  n ð1Þ In Eq. (1), the value of noften lies in the range 2<n < 3 in case of bending dominated loading conditions, which suggests that even a small variation in relative density can result in significant change in the effective properties of these structures [5]. In order to reduce these irregularities, periodic lattice materials [5,8,9] have been pro- posed in the past few years. Strut based periodic structures made of octet [10], cubic [11], diamond [11,12], and Kelvin configurations are widely being studied for their mechanical properties [5,13]. Fur- thermore, owing to the several advantages of surface based geome- tries such as high surface area to volume ratio, pore connectivity, ease of functional grading (porosity or pore density grading) [14] in comparison to the strut based lattice structure, periodic minimal surfaces are being investigated by researchers for mechanical, ther- mal, medical, and aerospace applications [14–18]. Recently, the design of periodic lattice structures was presented for acoustic applications [7,19]. Three different surface based unit cell structures were designed and fabricated to achieve predictable acoustic performance via estimation of five microscopic Johnson- Champoux-Allard (JCA) parameters [7]. Their advantage lies in https://doi.org/10.1016/j.apacoust.2020.107455 0003-682X/Ó 2020 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: ramamoor@iitb.ac.in (S. Ramamoorthy). Applied Acoustics 169 (2020) 107455 Contents lists available at ScienceDirect Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust