## 1 Introduction  
A dark soliton is an envelope soliton that has the form of a density dip with a phase jump across its density minimum. This localized waveform is supported on the top of a stable continuous wave background. Since dark solitons are fundamental nonlinear excitations of a universal model, the defocusing nonlinear Schrodinger (NLS) equation, they have been studied extensively in diverse branches of physics. These include chiefly nonlinear optics [1] and Bose-Einstein condensates [2], but also discrete mechanical systems [3], thin magnetic films [4], complex plasmas [5], water waves [6], and so on. The interest of dark solitons arises from the fact that--since they are composite objects, consisting of a background wave and a soliton--they have a number of interesting properties that may find important applications. Indeed, as compared to the bright solitons (which are governed by the focusing NLS equation), they can be generated by a thresholdless process, are less affected by loss and background noise, and are more robust against various perturbations [1, 2]. In addition, in optics, dark solitons have potential applications, e.g., in inducing steerable waveguides in optical media, or for ultradense wavelength-division-multiplexing [1]. Recently, important nonlinear effects--including higher harmonic generation [7, 8, 9], self-demodulation [10, 11], and soliton formation [12, 13, 14, 15, 16], and others--have attracted much attention in acoustics, and especially in the context of acoustic metamaterials; these are periodic structures--thus featuring dispersion--which are characterized by negative effective parameters, i.e., negative mass density [17] and negative bulk modulus [18]. Usually, such metamaterials are acoustic waveguides loaded with resonators, presenting strong dispersion around the resonance frequency and Braggband [19; 20]. Dissipation naturally plays a key role in such structures, especially in super-absorbing sound materials [21; 22] (see also work in Refs. [23; 24]). The combination of dispersion and dissipation [20; 23; 25; 26; 27] has mainly been investigated in the linear regime; nevertheless, the additional effect of nonlinearity, which is naturally introduced at high acoustic levels has not been studied in detail in acoustic metamaterials. This is also the case of studies on acoustic solitons of various types--pulse-like [12; 13] and envelope bright ones [12; 14]. As far as dark solitons are concerned, they were predicted to occur in acoustic waveguides loaded with an array with Helmholtz resonators [12], while the effect of dissipation was neglected. To the best of our knowledge, the dissipation-induced dynamics of dark solitons in acoustic metamaterials, has not been investigated so far. In this work, we analytically and numerically study envelope dark solitons in a one-dimensional (1D) acoustic metamaterial composed of a waveguide featuring a periodic array of side holes. Based on the transmission line (TL) approach, which is widely used in acoustics [28; 29; 30; 31; 32], we model this system by a nonlinear dynamical lattice with losses. In the continuum approximation, the latter leads to a nonlinear, dispersive and dissipative wave equation. Employing the multiple scales perturbation method, we derive an effective defocusing nonlinear Schrodinger (NLS) equation which supports dark soliton solutions. The effect of dissipation is also taken into regard, and is studied analytically by means of perturbation theory for solitons [33]. Numerical simulations, at the level of the nonlinear lattice model, are also performed showing a very good agreement with the analytical predictions relying on the NLS picture. The methodology of this work paves the way for relevant studies in double-negative acoustic metamaterials. The paper is structured as follows. In Section 2, we introduce our setup, derive the 1D nonlinear lattice model, and study the linear properties of the system.