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Some topographies in plate structures can hide cracks and make it difficult to monitor damage growth. This is because topographical features convert homogeneous structures to heterogeneous one and complicate the wave propagation through such structures. At certain points destructive interference between incident, reflected and transmitted elastic waves can make those points insensitive to the damage growth when adopting acoustics based structural health monitoring (SHM) techniques. A newly developed nonlinear ultrasonic (NLU) technique called sideband peak count – index (or SPC-I) has shown its effectiveness and superiority compared to other techniques for nondestructive testing (NDT) and SHM applications and is adopted in this work for monitoring damage growth in plate structures with topographical features. The performance of SPC-I technique in heterogeneous specimens having different topographies is investigated using nonlocal peridynamics based peri-ultrasound modeling. Three types of topographies – “X” topography, “Y” topography and “XY” topography are investigated. It is observed that “X” and “XY” topographies can help to hide the crack growth, thus making cracks undetectable when the SPC-I based monitoring technique is adopted. In addition to the SPC-I technique, we also investigate the effectiveness of an emerging sensing technique based on topological acoustic sensing. This method monitors the changes in the geometric phase; a measure of the changes in the acoustic wave’s spatial behavior. The computed results show that changes in the geometric phase can be exploited to monitor the damage growth in plate structures for all three topographies considered here. The significant changes in geometric phase can be related to the crack growth even when these cracks remain hidden for some topographies during the SPC-I based single point inspection. Sensitivities of both the SPC-I and the topological acoustic sensing techniques are also investigated for sensing the topographical changes in the plate structures. 

A newly developed Nonlinear Ultrasonic (NLU) technique called sideband peak count-index (or SPC-I) measures the degree of nonlinearity in materials by counting the sideband peaks above a moving threshold line – larger the SPC-I value, higher is the material nonlinearity. In various published papers, the SPC-I technique has shown its effectiveness in Structural Health Monitoring (SHM) applications. However, the effects of different types of nonlinear phenomenon on the sideband peak generation is yet to be investigated in depth. This work addresses this knowledge gap and investigates the effects of different types of nonlinearity on the SPC-I technique. Three types of nonlinearities (material nonlinearity, structural nonlinearity and contact nonlinearity) are investigated separately through numerical modeling. Numerical modeling results show that the sideband peak values do not increase proportional to the input signal strength thus indicating nonlinear response, and different types of nonlinearities affect the SPC-I measurements differently. For the experimental verification a composite plate with impact-induced damage is considered for investigating the material nonlinearity and structural nonlinearity while a linear elastic aluminum plate is used to examine the contact nonlinearity between the transducers and the plate. The trends observed in the experimental observations matched the numerical model predictions. Monitoring damage growth in topographical structures – formed by inserting different materials in a matrix material is also investigated. In addition to the SPC-I technique an emerging acoustic parameter – “geometric phase change” based on the topological acoustics is also adopted for sensing damage growth in the topographical structures. The performance of SPC-I and topological acoustic sensing techniques as well as the Spectral Amplitude Difference (SAD) parameter for sensing the damage growth in topographical structures are compared and discussed. 

We investigate a one-dimensional discrete binary elastic superlattice bridging continuous models of superlattices that showcase a one-way propagation character, as well as the discrete elastic Su–Schrieffer–Heeger model, which does not exhibit this character. By considering Bloch wave solutions of the superlattice wave equation, we demonstrate conditions supporting elastic eigenmodes that do not satisfy the translational invariance of Bloch waves over the entire Brillouin zone, unless their amplitude vanishes for a certain wave number. These modes are characterized by a pseudo-spin and occur only on one side of the Brillouin zone for a given spin, leading to spin-selective one-way wave propagation. We demonstrate how these features result from the interplay of the translational invariance of Bloch waves, pseudo-spins, and a Fabry–Pérot resonance condition in the superlattice unit cell. 

We review the notion of “phase bit” or “phi-bit” in externally driven nonlinear acoustic metamaterials. Phi-bits are classical analogues of quantum bits, which open pathways to promising and validated modes of initializing, operating, and measuring information. Acoustic metamaterials offer ways to compute information using phase that should compare favorably with state-of-the-art quantum systems without suffering from quantum fragility. 

We present a sensing modality using the geometric phase of acoustic waves propagating in an underwater environment. We experimentally investigate the effect of scattering by a small subwavelength perturbation on a flat submerged surface. We represent the state of an acoustic field in the unperturbed and perturbed cases as multidimensional vectors. The change in geometric phase is obtained by calculating the angle between those vectors. This angle represents a rotation of the state vector of the wave due to scattering by the perturbation. We perform statistical analysis to define a signal-to-noise ratio to quantify the sensitivity of the geometric phase measurement and compare it to magnitude based measurements. This geometric phase sensing modality is shown to have higher sensitivity than the magnitude based sensing approach. 

Bone mineralization is critical to maintaining tissue mechanical function. The application of mechanical stress via exercise promotes bone mineralization via cellular mechanotransduction and increased fluid transport through the collagen matrix. However, due to its complex composition and ability to exchange ions with the surrounding body fluids, bone mineral composition and crystallization is also expected to respond to stress. Here, a combination of data from materials simulations, namely density functional theory and molecular dynamics, and experimental studies were input into an equilibrium thermodynamic model of bone apatite under stress in an aqueous solution based on the theory of thermochemical equilibrium of stressed solids. The model indicated that increasing uniaxial stress induced mineral crystallization. This was accompanied by a decrease in calcium and carbonate integration into the apatite solid. These results suggest that weight-bearing exercises can increase tissue mineralization via interactions between bone mineral and body fluid independent of cell and matrix behaviours, thus providing another mechanism by which exercise can improve bone health. This article is part of a discussion meeting issue ‘Supercomputing simulations of advanced materials’. 

We experimentally navigate the Hilbert space of two logical phi-bits supported by an externally driven nonlinear array of coupled acoustic waveguides by parametrically changing the relative phase of the drivers. We observe sharp phase jumps of approximately 180° in the individual phi-bit states as a result of the phase tuning of the drivers. The occurrence of these sharp phase jumps varies from phi-bit to phi-bit. All phi-bit phases also possess a common background dependency on the drivers’ phase. Within the context of multiple time scale perturbation theory, we develop a simple model of the nonlinear array of externally driven coupled acoustic waveguides to shed light on the possible mechanisms for the experimentally observed behavior of the logical phi-bit phase. Finally, we illustrate the ability to experimentally initialize the state of single- and multiple- phi-bit systems by exploiting the drivers’ phase as a tuning parameter. We also show that the nonlinear correlation between phi-bits enables parallelism in the manipulation of two- and multi-phi-bit superpositions of states. 

Abstract Dynamical simulations of an externally harmonically driven model granular metamaterial composed of four linearly and nonlinearly coupled granules show that the nonlinear normal mode can be expressed in a linear normal mode orthonormal basis with time dependent complex coefficients. These coefficients form the components of a state vector that spans a 2 2 dimensional Hilbert space parametrically with time. Local π jumps in the phase of these components occurring periodically are indicative of topological features in the manifold spanned by the geometric phase of the vibrational state of the metamaterial. We demonstrate that these topological features can be exploited to realize high sensitivity mass sensor. The effect of dissipation on sensitivity is also reported. Nonlinear granular metamaterials with very low dissipation could serve as mass sensors with considerable sensitivity to small mass changes via large changes in geometric phase. 

Abstract The Controlled-NOT (CNOT) gate is the key to unlock the power of quantum computing as it is a fundamental component of a universal set of gates. We demonstrate the operation of a two-bit C-NOT quantum-like gate using classical qubit acoustic analogues, called herein logical phi-bits. The logical phi-bits are supported by an externally driven nonlinear acoustic metamaterial composed of a parallel array of three elastically coupled waveguides. A logical phi-bit has a two-state degree of freedom associated with the two independent relative phases of the acoustic wave in the three waveguides. A simple physical manipulation involving the detuning of the frequency of one of the external drivers is shown to operate on the complex vectors in the Hilbert space of pairs of logical phi-bits. This operation achieves a systematic and predictable C-NOT gate with unambiguously measurable input and output. The possibility of scaling the approach to more phi-bits is promising.