arXiv subjects

Xiaoming Mao

Publications and source records attributed to Xiaoming Mao.

At least 37 records · Page 2Linked to original sources

arXiv2023

Backscattering-free edge states below all bands in two-dimensional auxetic media

Unidirectional and backscattering-free propagation of sound waves is of fundamental interest in physics, and highly sought-after in engineering. Current strategies utilize topologically protected chiral edge modes in bandgaps, or complex mechanisms involving active constituents or nonlinearity. Here we propose a new class of passive, linear, one-way edge states based on spin-momentum locking of Rayleigh waves in two-dimensional media in the limit of vanishing bulk modulus, which provides $100\%$ unidirectional and backscattering-free edge propagation at a broad range of frequencies instead of residing in gaps between bulk bands. We further show that such modes are characterized by a new topological winding number that is analogous to discrete angular momentum eigenvalues in quantum mechanics. These passive and backscattering-free edge waves have the potential to enable a new class of phononic devices in the form of lattices or continua that work in previously inaccessible frequency ranges.

cond-mat.soft↗

arXiv2023

Geometrically frustrated self-assembly of hyperbolic crystals from icosahedral nanoparticles

Geometric frustration is a fundamental concept in various areas of physics, and its role in self-assembly processes has recently been recognized as a source of intricate self-limited structures. Here we present an analytic theory of the geometrically frustrated self-assembly of regular icosahedral nanoparticle based on the non-Euclidean crystal {3, 5, 3} formed by icosahedra in hyperbolic space. By considering the minimization of elastic and repulsion energies, we characterize prestressed morphologies in this self-assembly system. Notably, the morphology exhibits a transition that is controlled by the size of the assembled cluster, leading to the spontaneous breaking of rotational symmetry.

cond-mat.soft↗

arXiv2023

Rationalizing Euclidean Assemblies of Hard Polyhedra from Tessellations in Curved Space

Entropic self-assembly is governed by the shape of the constituent particles, yet a priori prediction of crystal structures from particle shape alone is non-trivial for anything but the simplest of space-filling shapes. At the same time, most polyhedra are not space-filling due to geometric constraints, but these constraints can be relaxed or even eliminated by sufficiently curving space. We show using Monte Carlo simulations that the majority of hard Platonic shapes self-assemble entropically into space-filling crystals when constrained to the surface volume of a 3-sphere. As we gradually decrease curvature to "flatten" space and compare the local morphologies of crystals assembling in curved and flat space, we show that the Euclidean assemblies can be categorized either as remnants of tessellations in curved space (tetrahedra and dodecahedra) or non-tessellation-based assemblies caused by large-scale geometric frustration (octahedra and icosahedra).

cond-mat.soft↗

arXiv2022

Assur graphs, marginally jammed packings, and reconfigurable metamaterials

Isostatic frames are mechanical networks that are simultaneously rigid and free of self-stress states, and is a powerful concept in understanding phase transitions in soft matter and designing of mechanical metamaterials. Here we analyze substructures of isostatic frames, by generalizing ``Assur graphs'' to the torus and examine them in physical systems. We show that the contact network of marginally jammed packings approach torus Assur graphs in the thermodynamic limit, and demostrate how Assur graphs offer a new design principle for mechanical metamaterials in which motion and stress can propagate in reconfigurable pathways, while rigidity of the entire structure is maintained.

cond-mat.soft↗

arXiv2022

Stress-stress Correlations Reveal Force Chains in Gels

We investigate the spatial correlations of microscopic stresses in soft particulate gels, using 2D and 3D numerical simulations. We use a recently developed theoretical framework predicting the analytical form of stress-stress correlations in amorphous assemblies of athermal grains that acquire rigidity under an external load. These correlations exhibit a pinch-point singularity in Fourier space leading to long-range correlations and strong anisotropy in real space, which are at the origin of force-chains in granular solids. Our analysis for the model particulate gels at low particle volume fractions demonstrates that stress-stress correlations in these soft materials have characteristics very similar to those in granular solids and can be used to identify force chains. We show that the stress-stress correlations can distinguish floppy from rigid gel networks and the intensity patterns reflect changes in shear moduli and network topology, due to the emergence of rigid structures during solidification.

cond-mat.soft↗

arXiv2022

Stress focusing and damage protection in topological Maxwell metamaterials

Advances in the field of topological mechanics have highlighted a number of special mechanical properties of Maxwell lattices, including the ability to focus zero-energy floppy modes and states of self-stress (SSS) at their edges and interfaces. Due to their topological character, these phenomena are protected against perturbations in the lattice geometry and material properties, which makes them robust against the emergence of structural non-idealities, defects, and damage. Recent computational work has shown that the ability of Maxwell lattices to focus stress along prescribed SSS domain walls can be harnessed for the purpose of protecting other regions in the bulk of the lattice from detrimental stress concentration and, potentially, inhibiting the onset of fracture mechanisms at stress hot spots such as holes and cracks. This property provides a powerful, geometry-based tool for the design of lattice configurations that are robust against damage and fracture. In this work, we provide a comprehensive experiment-driven exploration of this idea in the context of realistic structural lattices characterized by non-ideal, finite-thickness hinges. Our experiments document the onset of pronounced domain wall stress focusing, indicating a remarkable robustness of the polarization even in the presence of the dilutive effects of the structural hinges. We also demonstrate that the polarization protects the lattice against potential failure from defected hinges and cracks in the bulk. Finally, we illustrate numerically the superiority of SSS domain walls compared to other trivial forms of reinforcements.

cond-mat.mtrl-sci↗

arXiv2022

Omnimodal topological polarization of bilayer networks: analysis in the Maxwell limit and experiments on a 3D-printed prototype

Periodic networks on the verge of mechanical instability, called Maxwell lattices, are known to exhibit zero-frequency modes localized to their boundaries. Topologically polarized Maxwell lattices, in particular, focus these zero modes to one of their boundaries in a manner that is protected against disorder by the reciprocal-space topology of the lattice's band structure. Here, we introduce a class of mechanical bilayers as a model system for designing topologically protected edge modes that couple in-plane dilational and shearing modes to out-of-plane flexural modes, a paradigm that we refer to as omnimodal polarization. While these structures exhibit a high-dimensional design space that makes it difficult to predict the topological polarization of generic geometries, we are able to identify a family of mirror-symmetric bilayers that inherit the in-plane modal localization of their constitutive monolayers whose topological polarization can be determined analytically. Importantly, the coupling between the layers results in the emergence of omnimodal polarization, whereby in-plane and out-of-plane edge modes localize on the same edge. We demonstrate these theoretical results by fabricating a mirror-symmetric, topologically polarized kagome bilayer consisting of a network of elastic beams via additive manufacturing and confirm this finite-frequency polarization via finite element analysis and laser-vibrometry experiments.

cond-mat.soft↗

arXiv2022

Soft mechanical metamaterials with transformable topology protected by stress caching

Maxwell lattice metamaterials possess a rich phase space with distinct topological states featuring mechanically polarized edge behaviors and strongly asymmetric acoustic responses. Until now, demonstrations of non-trivial topological behaviors from Maxwell lattices have been limited to either monoliths with locked configurations or reconfigurable mechanical linkages. This work introduces a transformable topological mechanical metamaterial (TTMM) made from a shape memory polymer and based on a generalized kagome lattice. It is capable of reversibly exploring topologically distinct phases of the non-trivial phase space via a kinematic strategy that converts sparse mechanical inputs at free edge pairs into a biaxial, global transformation that switches its topological state. Thanks to the shape memory effect, all configurations are stable even in the absence of confinement or a continuous mechanical input. Topologically-protected mechanical behaviors, while robust against structural (with broken hinges) or conformational defects (up to ~55% mis-rotations), are shown to be vulnerable to the adverse effects of stored elastic energy from prior transformations (up to a ~70% reduction in edge stiffness ratios, depending on hinge width). Interestingly, we show that shape memory polymer's intrinsic phase transitions that modulate chain mobility can effectively shield a dynamic metamaterial's topological response (with a 100% recovery) from its own kinematic stress history, an effect we refer to as "stress caching".

cond-mat.mtrl-sci↗

arXiv2022

Synthetically Non-Hermitian Nonlinear Wave-like Behavior in a Topological Mechanical Metamaterial

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, non-reciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a new regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials, and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly exceeding conventional elasticity.

cond-mat.soft↗

arXiv2022

Multistable Topological Mechanical Metamaterials

Concepts from quantum topological states of matter have been extensively utilized in the past decade in creating mechanical metamaterials with topologically protected features, such as one-way edge states and topologically polarized elasticity. Maxwell lattices represent a class of topological mechanical metamaterials that exhibit distinct robust mechanical properties at edges/interfaces when they are topologically polarized. Realizing topological phase transitions in these materials would enable on-and-off switching of these edge states, opening unprecedented opportunities to program mechanical response and wave propagation. However, such transitions are extremely challenging to experimentally control in Maxwell topological metamaterials due to mechanical and geometric constraints. Here we create a Maxwell lattice with bistable units to implement synchronized transitions between topological states and demonstrate dramatically different stiffnesses as the lattice transforms between topological phases both theoretically and experimentally. By combining multistability with topological phase transitions, for the first time, this metamaterial not only exhibits topologically protected mechanical properties that swiftly and reversibly change, but also offers a rich design space for innovating mechanical computing architectures and reprogrammable neuromorphic metamaterials. Moreover, we design and fabricate a topological Maxwell lattice using multi-material 3D printing and demonstrate the potential for miniaturization via additive manufacturing. These design principles are applicable to transformable topological metamaterials for a variety of tasks such as switchable energy absorption, impact mitigation, wave tailoring, neuromorphic metamaterials, and controlled morphing systems.

physics.app-ph↗

arXiv2022

Band theory and boundary modes of high-dimensional representations of infinite hyperbolic lattices

Periodic lattices in hyperbolic space are characterized by symmetries beyond Euclidean crystallographic groups, offering a new platform for classical and quantum waves, demonstrating great potentials for a new class of topological metamaterials. One important feature of hyperbolic lattices is that their translation group is nonabelian, permitting high-dimensional irreducible representations (irreps), in contrast to abelian translation groups in Euclidean lattices. Here we introduce a general framework to construct wave eigenstates of high-dimensional irreps of infinite hyperbolic lattices, thereby generalizing Bloch's theorem, and discuss its implications on unusual mode-counting and degeneracy, as well as bulk-edge correspondence in hyperbolic lattices. We apply this method to a mechanical hyperbolic lattice, and characterize its band structure and zero modes of high-dimensional irreps.

cond-mat.mes-hall↗

arXiv2021

Topological Flexural Modes in Polarized Bilayer Lattices

Topological lattices have recently generated a great deal of interest based on the unique mechanical properties rooted in their topological polarization, including the ability to support localized modes at certain floppy edges. The study of these systems has been predominantly restricted to the realm of in-plane mechanics, to which many topological effects are germane. In this study, we stretch this paradigm by exploring the possibility to export certain topological attributes to the flexural wave behavior of thin lattice sheets. To couple the topological modes to the out-of-plane response, we assemble a bilayer lattice by stacking a thick topological kagome layer onto a thin twisted kagome lattice. The band diagram reveals the existence of modes whose out-of-plane character is controlled by the edge modes of the topological layer, a behavior elucidated via simulations and confirmed via laser vibrometer experiments on a bilayer prototype specimen. These results open an alternative direction for topological mechanics whereby flexural waves are controlled by the in-plane topology, leading to potential applications for flexural wave devices with engineered polarized response.

physics.app-ph↗

arXiv2021

Prestressed elasticity of amorphous solids

Prestress in amorphous solids bears the memory of their formation, and plays a profound role in their mechanical properties, from stiffening or softening elastic moduli to shifting frequencies of vibrational modes, as well as directing yielding and solidification in the nonlinear regime. Here we develop a set of mathematical tools to investigate elasticity of prestressed discrete networks, which disentangles the effects from disorder in configuration and disorder in prestress. Applying these methods to prestressed triangular lattices and a computational model of amorphous solids, we demonstrate the importance of prestress on elasticity, and reveal a number of intriguing effects caused by prestress, including strong spatial heterogeneity in stress-response unique to prestressed solids, power-law distribution of minimal dipole stiffness, and a new criterion to classify floppy modes.

cond-mat.soft↗

arXiv2021

Frustrated Self-Assembly of Non-Euclidean Crystals of Nanoparticles

Self-organized complex structures in nature, e.g. viral capsids, hierarchical biopolymers, and bacterial flagella, offer efficiency, adaptability, robustness, and multi-functionality. Can we program the self-assembly of three-dimensional (3D) complex structures with simple building blocks, and reach similar or higher level of sophistication in engineered materials? Here we present an analytic theory of tetrahedral nanoparticles (NPs) self-assembling in 3D space, where unavoidable geometrical frustration combined with competing attractive and repulsive inter-particle interactions lead to controllable, high-yield, and enantiopure self-assembly of helicoidal ribbons. This theory, based on crystal structures in non-Euclidean space, predicts morphologies that exhibit qualitative agreement with experimental observations. We expect that this theory will offer a general framework for the self-assembly of simple polyhedral building blocks into complex morphologies with new material capabilities such as tunable optical activity, essential for multiple emerging technologies.

cond-mat.soft↗

arXiv2021

Topological Floppy Modes in Epithelial Tissues

Recent advances in topological mechanics have revealed unusual phenomena such as topologically protected floppy modes and states of self-stress that are exponentially localized at boundaries and interfaces of mechanical networks. In this paper, we explore the topological mechanics of epithelial tissues, where the appearance of these boundary and interface modes could lead to localized soft or stressed spots and play a role in morphogenesis. We consider both a simple vertex model (VM) governed by an effective elastic energy and its generalization to an active tension network (ATN) which incorporates active adaptation of the cytoskeleton. By analyzing spatially periodic lattices at the Maxwell point of mechanical instability, we find topologically polarized phases with exponential localization of floppy modes and states of self-stress in the ATN when cells are allowed to become concave, but not in the VM.

cond-mat.soft↗

arXiv2021

Collective Motility, Mechanical Waves, and Durotaxis in Cell Clusters

Epithelial cell clusters often move collectively on a substrate. Mechanical signals play a major role in organizing this behavior. There are a number of experimental observations in these systems which await a comprehensive explanation. These include: the internal strains are tensile even for clusters that expand by proliferation; the tractions on the substrate are often confined to the edges of the cluster; there can exist density waves within the cluster; clusters can exhibit collective durotaxis when individual cells show no effect; and for cells in an annulus there is a transition between expanding clusters with proliferation and the case where cells fill the annulus and rotate around it. We formulate a mechanical model to examine these effects. We use a molecular clutch picture which allows "stalling" -- inhibition of cell contraction by external forces. Stalled cells are passive from a physical point of view and the un-stalled cells are active. By attaching cells to the substrate and to each other, and taking into account contact inhibition of locomotion, we get a simple picture for many of these findings as well as predictions that could be tested. SI text/figures included, SI movies at https://rice.box.com/s/xiy3mwsfj3203lfu7pk0udfklexcgsew

physics.bio-ph↗

arXiv2021

Fractional solitons in non-Euclidian elastic plates

We show that minimal-surface non-Euclidean elastic plates share the same low-energy effective theory as Haldane's dimerized quantum spin chain. As a result, such elastic plates support fractional excitations, which take the form of charge-$1/2$ solitons between degenerate states of the plates, in strong analogy to their quantum counterpart. These fractional solitons exhibit properties similar to fractional excitations in quantum fractional topological states, including deconfinement and braiding, as well as unique new features such as holographic properties and diode-like nonlinear response, demonstrating great potentials for applications as mechanical metamaterials.

cond-mat.soft↗

arXiv2021

Correlated rigidity percolation in fractal lattices

Rigidity percolation (RP) is the emergence of mechanical stability in networks. Motivated by the experimentally observed fractal nature of materials like colloidal gels and disordered fiber networks, we study RP in a fractal network. Specifically, we calculate the critical packing fractions of site-diluted lattices of Sierpiński gaskets (SG's) with varying degrees of fractal iteration. Our results suggest that although the correlation length exponent and fractal dimension of the RP of these lattices are identical to that of the regular triangular lattice, the critical volume fraction is dramatically lower due to the fractal nature of the network. Furthermore, we develop a simplified model for an SG lattice based on the fragility analysis of a single SG. This simplified model provides an upper bound for the critical packing fractions of the full fractal lattice, and this upper bound is strictly obeyed by the disorder averaged RP threshold of the fractal lattices. Our results characterize rigidity in ultra-low-density fractal networks.

cond-mat.soft↗