Harnessing transition waves to realize deployable structures.

Transition waves that sequentially switch bistable elements from one stable configuration to another have received significant interest in recent years not only because of their rich physics but also, for their potential applications, including unidirectional propagation, energy harvesting, and mechanical computation. Here, we exploit the propagation of transition waves in a bistable one-dimensional (1D) linkage as a robust mechanism to realize structures that can be quickly deployed. We first use a combination of experiments and analyses to show that, if the bistable joints are properly designed, transition waves can propagate throughout the entire structure and transform the initial straight configuration into a curved one. We then demonstrate that such bistable linkages can be used as building blocks to realize deployable three-dimensional (3D) structures of arbitrary shape.

Temporal Evolution of Erosion in Pore Networks: From Homogenization to Instability.

We study the dynamics of flow networks in porous media using two and three dimensional pore-network models. We consider a class of erosion dynamics for a single phase flow with no deposition, chemical reactions, or topology changes assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show that depending on the erosion law, the flow may become uniform and homogenized or become unstable and develop channels. By defining an order parameter capturing these different behaviors we show that a phase transition occurs depending on the erosion dynamics. Using a simple model, we identify quantitative criteria to distinguish these regimes and correctly predict the fate of the network, and discuss the experimental relevance of our result.

Harnessing Mechanical Deformation to Reduce Spherical Aberration in Soft Lenses.

Mechanical deformation has recently emerged as a promising platform to realize optical devices with tunable response. While most studies to date have focused on the tuning of the focal length, here we use a combination of experiments and analyses to show that an applied tensile strain can also largely reduce spherical aberration. We first demonstrate the concept for a cylindrical elastomeric lens and then show that it is robust and valid over a range of geometries and material properties. As such, our study suggests that large mechanical deformations may provide a simple route to achieve the complex profiles required to minimize aberration and realize lenses capable of producing images of superior quality.

Experimental Demonstration of an Ultrabroadband Nonlinear Cloak for Flexural Waves.

Broadband cloaking of flexural waves is a major challenge since the governing equation is not form invariant under coordinate transformations. We fabricate a flexural cloaking structure using only a single material composed of homogeneous and isotropic layers, and then present experimental evidence of the first near-ideal broadband cloak in thin plates. The 3D-printed structure is shown to effectively disguise an object over a broad frequency range (2 kHz-11 kHz). The proposed cloak has potential applications in shielding sensors and sensitive components from vibrations in bridges, automobiles, and aircraft.

Complex Deformation in Soft Cylindrical Structures via Programmable Sequential Instabilities.

The substantial deformation exhibited by hyperelastic cylindrical shells under pressurization makes them an ideal platform for programmable inflatable structures. If negative pressure is applied, the cylindrical shell will buckle, leading to a sequence of rich deformation modes, all of which are fully recoverable due to the hyperelastic material choice. While the initial buckling event under vacuum is well understood, here, the post-buckling regime is explored and a region in the design space is identified in which a coupled twisting-contraction deformation mode occurs; by carefully controlling the geometry of our homogeneous shells, the proportion of contraction versus twist can be controlled. Additionally, bending as a post-buckling deformation mode can be unlocked by varying the thickness of our shells across the circumference. Since these soft shells can fully recover from substantial deformations caused by buckling, then these instability-driven deformations are harnessed to build soft machines capable of a programmable sequence of movements with a single actuation input.

Mesh-based GNN surrogates for time-independent PDEs.

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of requiring long-range exchange of information across the computational domain for obtaining accurate predictions. In the context of graph neural networks (GNNs), this calls for deeper networks, which, in turn, may compromise or slow down the training process. In this work, we present two GNN architectures to overcome this challenge-the edge augmented GNN and the multi-GNN. We show that both these networks perform significantly better than baseline methods, such as MeshGraphNets, when applied to time-independent solid mechanics problems. Furthermore, the proposed architectures generalize well to unseen domains, boundary conditions, and materials. Here, the treatment of variable domains is facilitated by a novel coordinate transformation that enables rotation and translation invariance. By broadening the range of problems that neural operators based on graph neural networks can tackle, this paper provides the groundwork for their application to complex scientific and industrial settings.

Inverse Design of Mechanical Metamaterials with Target Nonlinear Response via a Neural Accelerated Evolution Strategy.

Materials with target nonlinear mechanical response can support the design of innovative soft robots, wearable devices, footwear, and energy-absorbing systems, yet it is challenging to realize them. Here, mechanical metamaterials based on hinged quadrilaterals are used as a platform to realize target nonlinear mechanical responses. It is first shown that by changing the shape of the quadrilaterals, the amount of internal rotations induced by the applied compression can be tuned, and a wide range of mechanical responses is achieved. Next, a neural network is introduced that provides a computationally inexpensive relationship between the parameters describing the geometry and the corresponding stress-strain response. Finally, it is shown that by combining the neural network with an evolution strategy, one can efficiently identify geometries resulting in a wide range of target nonlinear mechanical responses and design optimized energy-absorbing systems, soft robots, and morphing structures.

Broadband Bending of Flexural Waves: Acoustic Shapes and Patterns.

Directing and controlling flexural waves in thin plates along a curved trajectory over a broad frequency range is a significant challenge that has various applications in imaging, cloaking, wave focusing, and wireless power transfer circumventing obstacles. To date, all studies appeared controlling elastic waves in structures using periodic arrays of inclusions where these structures are narrowband either because scattering is efficient over a small frequency range, or the arrangements exploit Bragg scattering bandgaps, which themselves are narrowband. Here, we design and experimentally test a wave-bending structure in a thin plate by smoothly varying the plate's rigidity (and thus its phase velocity). The proposed structures are (i) broadband, since the approach is frequency-independent and does not require bandgaps, and (ii) capable of bending elastic waves along convex trajectories with an arbitrary curvature.

Broadband cloaking of flexural waves.

The governing equation for elastic waves in flexural plates is not form invariant, and hence designing a cloak for such waves faces a major challenge. Here, we present the design of a perfect broadband cloak for flexural waves through the use of a nonlinear transformation in the region of the cloak and by matching term by term the original and transformed equations and also assuming a prestressed material with body forces. For a readily achievable flexural cloak in a physical setting, we further present an approximate adoption of our perfect cloak under more restrictive physical constraints. Through direct simulation of the governing equations, we show that this cloak, as well, maintains a consistently high cloaking efficiency over a broad range of frequencies. The methodology developed here may be used for steering waves and designing cloaks in other physical systems with non-form-invariant governing equations.