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Article Dans Une Revue Physical Review Letters Année : 2019

Focusing and Mode Separation of Elastic Vector Solitons in a 2D Soft Mechanical Metamaterial

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Soft mechanical metamaterials can support a rich set of dynamic responses, which, to date, have received relatively little attention. Here, we report experimental, numerical, and analytical results describing the behavior of an anisotropic two-dimensional flexible mechanical metamaterial when subjected to impact loading. We not only observe the propagation of elastic vector solitons with three components-two translational and one rotational-that are coupled together, but also very rich direction-dependent behaviors such as the formation of sound bullets and the separation of pulses into different solitary modes. Ongoing advances in digital manufacturing technologies are enabling fabrication of systems with an unprecedented level of compositional and structural complexity [1-3]. This remarkable control of geometry has stimulated major advances in the design of mechanical metamaterials-designer matter with unique mechanical properties that are dictated by their engineered structure [4,5]. While initial efforts in the field have focused on systems with unusual linear properties, such as negative Poisson's ratio [6-8], negative stiffness [9,10], and negative thermal expansion [11,12], large deformation and nonlinearities have been recently embraced as a means toward new functionalities, including programmability [13], energy absorption [14], and shape transformation [15]. Moreover, it has been shown that highly deformable mechanical metamaterials can be designed to support the propagation of a variety of nonlinear waves with large displacement amplitudes [16-19], providing a convenient platform to study non-linear wave physics. However, to date the investigation of the nonlinear dynamic response of flexible metamaterials has been limited to one-dimensional (1D) systems. Here, we investigate the nonlinear dynamic response of a 2D flexible mechanical metamaterial comprising a periodic arrangement of squares connected at their vertices by thin ligaments [18,20,21]. Remarkably, our experiments and analyses reveal that several new physical phenomena emerge when subjecting the structure to low-energy impacts. First, our system supports the propagation of elastic vector solitons with three polarization components-two transla-tional and one rotational. Second, we investigate the effect of the anisotropy of the medium on the 2D nature of the soliton and find that such anisotropy plays a crucial role, leading to rich new nonlinear effects. For example, for propagation at 45°from the symmetry axis, a distinct focusing effect is observed. The pulse does not spread along either direction, suggesting that sound bullets may exist in our system. Moreover, we find that for most other propagation angles the wave separates into two distinct solitary modes, each following a principal direction of symmetry. While 2D nonlinear elastic waves have been previously studied in granular media [22-25], the monolithicity and printability of our system allow facile control of the architecture, and hence control of the system's nonlinear dynamic response, providing a powerful platform to explore, visualize, and engineer new wave phenomena. We start by studying experimentally the response of a 2D circular sample with 30 squares along its diameter when excited with an impactor [see Fig. 1(a)]. Our sample is fabricated out of polydimethylsiloxane using direct ink writing, an extrusion-based 3D printing approach [26].
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hal-02325883 , version 1 (22-10-2019)



Bolei Deng, Chengyang Mo, Vincent Tournat, Katia Bertoldi, Jordan R Raney. Focusing and Mode Separation of Elastic Vector Solitons in a 2D Soft Mechanical Metamaterial. Physical Review Letters, 2019, 123 (2), ⟨10.1103/PhysRevLett.123.024101⟩. ⟨hal-02325883⟩
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