A consistent and stable quadrature scheme for Galerkin meshfree methods for applications in nonlinear solid mechanics.
Abstract not provided.
Bishop, Joseph E.↗
SEARCH · Engineering Papers
Results for “nonlinear mechanics”
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Analysis of a ratcheting mechanism via nonlinear reduced-order modeling and probabilistic multi-fidelity surrogate modeling
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Najera-Flores, David Aaron [Sandia National Labora↗
Statistical mechanics and pressure of composite multimoded weakly nonlinear optical systems
Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear-wave settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to interactions between different frequencies and polarizations. The purpose of this work is to develop a thermodynamic theory that takes into account the synergistic action of multiple components. We find that the type of the nonlinearity involved can have important implications in the thermalization process and, hence, can lead to different thermal equilibrium conditions. Importantly, we derive closed-form expressions for the actual optomechanical pressure that is exerted on the system. In particular, the total optomechanical pressure is the sum of the partial pressures due to each component. Our results can be applied to a variety of weakly nonlinear optical settings such as multimode fibers, bulk waveguides, photonic lattices, and coupled microresonators. We present two specific examples, where two colors interact in a one-waveguide array with either a cubic or quadratic nonlinearity.
Efremidis, Nikolaos K. (ORCID:0000000298300268)↗
Multiple Degradation Mechanisms in Reinforced Concrete Structures, Modeling and Risk Analysis
The overarching goal of this project is to complement ongoing Department of Energy (DOE) Light Water Reactor Sustainability (LWRS)-funded Grizzly concrete modeling development efforts by providing improved multi-physics models for incorporation into the Grizzly and BlackBear codes. Objectives of this work identified at the outset of this project include: 1. Coupling between mechanical damage and transport processes. The mechanical damage will be characterized by nonlinear mechanical constitutive models appropriate for concrete used in nuclear power plants (NPPs). 2. Improved representation of the coupling among the transport process, building on the current moisture and thermal transport models in Grizzly. The parameters for coupling among heat and mass transport in the multi-physics model will be experimentally determined. 3. Coupling among different scale levels of concrete constituents, fine and coarse aggregates, cement paste, hydration products, and pore structure. 4. Probabilistic analysis of the random nature of the heterogeneous concrete structure and the environmental factors (ambient temperature and humidity) and their multiple effects on concrete deterioration. 5. Benchmark verification, validation and uncertainty quantification of the thermo-hygro- chemo-mechanical (THCM) concrete formulation. The end goal of this work was to provide a comprehensive and robust simulation capability that can be applied at the engineering scale for analysis of realistic deterioration scenarios in NPP concrete structures.
36 MATERIALS SCIENCE↗
The role of collective elasticity on activated structural relaxation, yielding, and steady state flow in hard sphere fluids and colloidal suspensions under strong deformation
In this work, we theoretically study the effect of external deformation on activated structural relaxation and aspects of the nonlinear mechanical response of glassy hard sphere fluids in the context of elastically collective nonlinear Langevin equation theory. This microscopic force-based approach describes activated relaxation as a coupled local–nonlocal event involving caging and longer range collective elasticity, with the latter becoming more important and ultimately dominant with increasing packing fraction under equilibrium conditions. The central new question we address is how this physical picture of activated relaxation, and the relative importance of local caging vs collective elasticity physics, depends on external deformation. Theoretical predictions are presented for deformation-induced enhancement of mobility, the onset of relaxation speed up at remarkably low values of stress, strain, or shear rate, apparent power law thinning of the steady state structural relaxation time and viscosity, a non-vanishing activation barrier in the shear thinning regime, an apparent Herschel–Bulkley form of the rate dependence of the steady state shear stress, exponential growth of different measures of a dynamic yield or flow stress with the packing fraction, and reduced fragility and dynamic heterogeneity under deformation. The results are contrasted with experiments and simulations, and qualitative or better agreement is found. An overarching conclusion is that deformation strongly reduces the importance of longer range collective elastic effects relative to the local caging aspect for most, but not all, physical questions, with deformation-dependent fragility and dynamic heterogeneity phenomena being qualitatively sensitive to collective elasticity. Overall, nonlinear rheology is predicted to be a more local problem than quiescent structural relaxation, albeit with deformation-modified activated processes still important.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Programmable soft valves for digital and analog control
In soft devices, complex actuation sequences and precise force control typically require hard electronic valves and microcontrollers. Existing designs for entirely soft pneumatic control systems are capable of either digital or analog operation, but not both, and are limited by speed of actuation, range of pressure, time required for fabrication, or loss of power through pull-down resistors. Using the nonlinear mechanics intrinsic to structures composed of soft materials—in this case, by leveraging membrane inversion and tube kinking—two modular soft components are developed: a piston actuator and a bistable pneumatic switch. These two components combine to create valves capable of analog pressure regulation, simplified digital logic, controlled oscillation, nonvolatile memory storage, linear actuation, and interfacing with human users in both digital and analog formats. Three demonstrations showcase the capabilities of systems constructed from these valves: 1) a wearable glove capable of analog control of a soft artificial robotic hand based on input from a human user’s fingers, 2) a human-controlled cushion matrix designed for use in medical care, and 3) an untethered robot which travels a distance dynamically programmed at the time of operation to retrieve an object. This work illustrates pathways for complementary digital and analog control of soft robots using a unified valve design.
42 ENGINEERING↗
Application of the Schwarz alternating method for the coupling of nonlinear solid mechanics-based and fluids-based full order models to nonlinear reduced order models
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Barnett, Joshua Lamar↗
Mechanical Roles of Polysaccharide Assembly and Interactions in Plant Cell Walls
Plants synthesize polysaccharide-based primary cell walls that possess unique microstructures and mechanical properties to accommodate plant growth and provide protection. Here, it remains challenging to assess the role of polysaccharide organization and interactions in the mechanical behavior of primary cell walls owing to their complex microstructure and highly nonlinear mechanical responses. Employing a coarse-grained molecular dynamics model developed for onion epidermal walls, this work explores the conditions under which polysaccharide assembly and interactions might play a significant role in primary cell wall mechanics. Cellulose–cellulose adhesion plays a dominant role in the wall load-bearing capacity, but when cellulose–cellulose adhesion was disrupted computationally, cellulose–xyloglucan adhesion could influence the wall load-bearing capacity. Contrary to the common concept that xyloglucans mechanically tether well-separated cellulose microfibrils, xyloglucans functioned in this case as interfibrillar adhesives capable of transmitting tensile forces between cellulose microfibrils. Our findings may inform design criteria of new materials inspired by plant cell walls.
59 BASIC BIOLOGICAL SCIENCES↗
Measurement of the Static Nonlinear Third-Order Elastic Moduli of Rocks: Problems and Applicability
The third-order elastic (TOE) model has been used to describe the widely observed nonlinear mechanical behaviors of earth materials. In addition to linear elastic constants ( λ , μ ), three nonlinear elastic moduli ( A , B , C ) are required for isotropic rocks. Contrary to previous research on dynamic TOE moduli, this study followed the protocol to measure strain and stress under uniaxial and hydrostatic compressive tests statically, which were later used to invert for the full set of TOE moduli for four standard rock types with differing pore structures of a porous oolitic limestone, quartz-rich sandstones, and a dense crystalline basalt. The applicability of the TOE model to characterize nonlinearity depends on the fulfillment of path-independence and small-strain assumptions. Using the measured static TOE moduli, the finite element model demonstrates that the stress in the vicinity of the wellbore is more amplified than the stress in the linear elastic case, which leads to a wider zone of rock failure around the wellbore. Due to the long-standing discrepancy between static and dynamic moduli, the rarely reported full set of static TOE moduli is necessary and will benefit future research in understanding the effect of rock nonlinearity on geophysical and geomechanical applications, such as long-term safe storage of CO 2 and generating process of geohazards.
58 GEOSCIENCES↗
Optical tweezer measurements of asymptotic nonlinearities in complex fluids
This article presents micro-medium-amplitude oscillatory shear (μMAOS), a method to measure the frequency-dependent micromechanical properties of soft materials in the asymptotically nonlinear regime using optical tweezers. For this work, we have developed a theoretical framework to extract these nonlinear mechanical properties of the material from experimental measurements and also proposed a physical interpretation of the third-order nonlinearities measured in single-tone oscillatory tests. We validate the method using a well-characterized surfactant solution of wormlike micelles, and subsequently employ this technique to demonstrate that the cytoplasm of a living cell undergoes strain softening and shear thinning when locally subjected to weakly nonlinear oscillatory deformations.
59 BASIC BIOLOGICAL SCIENCES↗
Plasmonic Nonlinear Energy Transfer Enhanced Second Harmonic Generation Nanoscopy
Nonlinear optical response is a fingerprint of various physicochemical properties of materials related to symmetry, including crystallography, interfacial configuration, and carrier dynamics. However, the intrinsically weak nonlinear optical susceptibility and the diffraction limit of far-field optics restrict probing deep-subwavelength-scale nonlinear optics with measurable signal-to-noise ratio. Here, we propose an alternative approach toward efficient second harmonic generation (SHG) nanoscopy for SHG-active sample (zinc oxide nanowire; ZnO NW) using an SHG-active plasmonic nanotip. Our full-wave simulation suggests that the experimentally observed high near-field SHG contrast is possible when the nonlinear response of ZnO NW is enhanced and/or that of the tip is suppressed. Here, this result suggests possible evidence of quantum mechanical nonlinear energy transfer between the tip and the sample, modifying the nonlinear optical susceptibility. Further, this process probes the nanoscale corrosion of ZnO NW, demonstrating potential use in studying various physicochemical phenomena in nanoscale resolution.
36 MATERIALS SCIENCE↗
Mechanical Resonant Sensing of Spin Texture Dynamics in a 2D Antiferromagnet
Abstract The coupling between the spin degrees of freedom and macroscopic mechanical motions, including striction, shearing, and rotation, has attracted wide interest with applications in actuation, transduction, and information processing. Experiments so far have established the mechanical responses to the long‐range ordered or isolated single spin states. However, it remains elusive whether mechanical motions can couple to a different type of magnetic structure, the non‐collinear spin textures, which exhibit nanoscale spatial variations of spin (domain walls, skyrmions,etc.) and are promising candidates to realize high‐speed computing devices. Here, collective spin texture dynamics is detected with nanoelectromechanical resonators fabricated from 2D antiferromagnetic (AFM) MnPS 3 with 10 −9 strain sensitivity. By examining radio frequency mechanical oscillations under magnetic fields, new magnetic transitions are identified with sharp dips in resonant frequency. They are attributed to collective AFM domain wall motions as supported by the analytical modeling of magnetostriction and large‐scale spin‐dynamics simulations. Additionally, an abnormally large modulation in the mechanical nonlinearity at the transition field infers a fluid‐like response due to ultrafast domain motion. The work establishes a strong coupling between spin texture and mechanical dynamics, laying the foundation for electromechanical manipulation of spin texture and developing quantum hybrid devices.
Chemistry↗
Bayesian inference in band excitation scanning probe microscopy for optimal dynamic model selection in imaging
The universal tendency in scanning probe microscopy (SPM) over the last two decades is to transition from simple 2D imaging to complex detection and spectroscopic imaging modes. The emergence of complex SPM engines brings forth the challenge of reliable data interpretation, i.e., conversion from detected signals to descriptors specific to tip–surface interactions and subsequently to material’s properties. In this work, we implemented a Bayesian inference approach for the analysis of the image formation mechanisms in band excitation SPM. Compared to the point estimates in classical functional fit approaches, Bayesian inference allows for the incorporation of extant knowledge of materials and probe behavior in the form of corresponding prior distribution and return the information on the material functionality in the form of readily interpretable posterior distributions. We explore the nonlinear mechanical behaviors spatially in a classical ferroelectric material, PbTiO 3 . We observe the non-trivial evolution of the Duffing stiffness term and the nonlinearity of the sample surface, determine spatial clustering of the nonlinear response, and perform a Landau analysis on predicting the nonlinear coefficient, which indicates that ferroelectric behavior can be a cause of the observed results. These observations suggest that the spectrum of anomalous behaviors at the ferroelectric domain walls may be broader than previously believed and can extend to non-conventional mechanical properties in addition to static and microwave conductance.
36 MATERIALS SCIENCE↗
Limits on Mode Coherence in Pulsating DA White Dwarfs Due to a Nonstatic Convection Zone
The standard theory of pulsations deals with the frequencies and growth rates of infinitesimal perturbations in a stellar model. Modes which are calculated to be linearly driven should increase their amplitudes exponentially with time; the fact that nearly constant amplitudes are usually observed is evidence that nonlinear mechanisms inhibit the growth of finite amplitude pulsations. Models predict that the mass of convection zones in pulsating hydrogen-atmosphere (DAV) white dwarfs is very sensitive to temperature (i.e., M CZ α T –90 eff ), leading to the possibility that even low-amplitude pulsators may experience significant nonlinear effects. In particular, the outer turning point of finite-amplitude g-mode pulsations can vary with the local surface temperature, producing a reflected wave that is out of phase with what is required for a standing wave. This can lead to a lack of coherence of the mode and a reduction in its global amplitude. In this paper we show that: (1) whether a mode is calculated to propagate to the base of the convection zone is an accurate predictor of its width in the Fourier spectrum, (2) the phase shifts produced by reflection from the outer turning point are large enough to produce significant damping, and (3) amplitudes and periods are predicted to increase from the blue edge to the middle of the instability strip, and subsequently decrease as the red edge is approached. Furthermore, this amplitude decrease is in agreement with the observational data while the period decrease has not yet been systematically studied.
79 ASTRONOMY AND ASTROPHYSICS↗
Multiscale modeling-enabled design of multifunctional composites
This study aims to create a comprehensive model that considers multiple scales and physics for predicting the electromechanical behavior of fiber-reinforced composites enhanced with barium titanate (BaTiO3). In our earlier work, we have demonstrated that depositing BaTiO3 microparticles of 200-nm-diameter, on fiber surfaces during fiber-reinforced composite fabrication enhances mechanical strength, passive self-sensing, and energy harvesting properties. The key is to carefully control the microparticle concentration to prevent agglomeration. Since the particles are micron-sized, understanding how agglomeration affects the composites' electromechanical properties is crucial for guiding such multifunctional materials’ design. This study introduces a micromechanics-based approach to explore the impact of microparticle dispersion on the bulk composites' electromechanical properties. Insights gained from this investigation are applied in experiments, enabling accurate predictions of mechanical and self-sensing responses in BaTiO3-enhanced fiber-reinforced composites. Micro-level findings from this computational approach can be integrated into larger continuum models to comprehensively capture the electromechanical behavior of the composite structures at bulk scale. The proposed model is validated by comparing predictions with experimental results, accounting for the nonlinear mechanical and electromechanical behaviors of constituent materials. Consequently, this computational model serves as a digital platform for efficiently designing multifunctional composites.
Gupta, Sumit↗
Strongly nonlinear wave propagation in elasto-plastic metamaterials: Low-order dynamic modeling
Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are often prohibitively expensive at scales of interest. Prior studies have therefore utilized low-order effective medium models, such as discrete mass-spring lattices, to capture essential properties in the long-wavelength limit. While models of this type have been successfully implemented for a wide variety of nonlinear elastic systems, they have predominantly considered dynamics depending only on the instantaneous kinematics of the lattice, neglecting history-dependent effects, such as wear and plasticity. Here, to address this limitation, the present study develops a lattice-based modeling framework for nonlinear elastic metamaterials undergoing plastic deformation. Due to the history- and rate-dependent nature of plasticity, the framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than an elastic system of comparable size. We demonstrate the method using several models inspired by classical lattice dynamics and continuum plasticity theory and explore means to obtain empirical plasticity models for general geometries, thereby gaining insight into the influence of microstructural plasticity on effective material performance, which can be used to improve the design of nonlinear mechanical metamaterials.
Dynamic simulation↗
A solvable model of a nonlinear extension of quantum mechanics
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. Here, we hope that this simple example will elucidate some of the issues of interpreting nonlinear generalization of quantum mechanics that have been put forth to resolve questions about quantum measurement theory.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Large-scale harmonic balance simulations with Krylov subspace and preconditioner recycling
The multi-harmonic balance method combined with numerical continuation provides an efficient framework to compute a family of time-periodic solutions, or response curves, for large-scale, nonlinear mechanical systems. The predictor and corrector steps repeatedly solve a sequence of linear systems that scale by the model size and number of harmonics in the assumed Fourier series approximation. In this paper, a novel Newton–Krylov iterative method is embedded within the multi-harmonic balance and continuation algorithm to efficiently compute the approximate solutions from the sequence of linear systems that arise during the prediction and correction steps. Further, the method recycles, or reuses, both the preconditioner and the Krylov subspace generated by previous linear systems in the solution sequence. A delayed frequency preconditioner refactorizes the preconditioner only when the performance of the iterative solver deteriorates. The GCRO-DR iterative solver recycles a subset of harmonic Ritz vectors to initialize the solution subspace for the next linear system in the sequence. The performance of the iterative solver is demonstrated on two exemplars with contact-type nonlinearities and benchmarked against a direct solver with traditional Newton–Raphson iterations.
97 MATHEMATICS AND COMPUTING↗