Mechanisms of near-linear elastic deformation behavior in a binary metastable [beta]-type Ti-Nb allo
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Guo, Shun↗
SEARCH · Engineering Papers
Results for “Linear elasticity”
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Mechanics-modified equilibrium potential for linear-elastic electrode materials
The interfacial hydrostatic stress of the working electrode, not its surface-normal stress, is a more general and widely applicable stress descriptor to use for the mechanics-modified equilibrium potential Δ U .
Jung, Taeho [Department of Chemical and Biomolecul↗
Comparison of linear-elastic fracture and elastic-plastic fracture of ferritic steels in gaseous hydrogen
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San Marchi, Christopher William↗
Peridynamics and linear elastic fracture mechanics
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Silling, Stewart A.↗
Propagation of elastic waves in a flexomagnetic solid
Flexomagnetism is the coupling between magnetism and strain gradients and is a technologically relevant phenomenon. We present a theory of elastic wave propagation in a linear elastic flexomagnetic material with microstructure and strain gradient elastic interactions. The expressions of frequency, phase velocity, and group velocity of longitudinal and transverse waves are derived and are shown to depend on the flexomagnetic coefficient and microstructure. We also show that the effect of flexomagnetism and microstructure can lead to some interesting phenomena in wave propagation, which are not observed in classical linear elasticity theory of waves. Specifically, in contrast to classical linear elastic materials, where wave propagation is non-dispersive, flexomagnetic materials with microstructure can exhibit both normal and abnormal dispersion. It is also noteworthy that, in flexomagnetic materials with gradient elasticity, the phase velocities of transverse waves can exceed those of longitudinal waves, which is atypical in classical elasticity. Furthermore, waves can also attenuate for a certain range of wavenumbers that depend on the flexomagnetic coefficient and microstructural parameters. Finally, we explore the possibility of waves exhibiting zero group velocity modes, where waves are non-propagating but have strong local energy confinement, negative group velocity modes, where the wave packet moves in the opposite direction to that of wave propagation, and the phenomenon of wave freezing, where a propagating wave stops in space without diffusing or spreading.
Ghosh, Swarnava [ORNL] (ORCID:0000000338005264)↗
Non-linear elastic-plastic behavior of the invert glass lithium phosphorous oxynitride (LiPON)
Micro and nano-scale mechanical behavior of network/ionic glasses is dictated by their composition and the number of constraints per structural unit. From this perspective, the glass LiPON presents the opportunity for enhancement of the microscale ductility due to its rather unconstrained orthophosphate structure. Here, we use instrumented nanoindentation with different tip geometries to investigate the mechanical response of LiPON glass. The results reveal that the elastic modulus of LiPON is not constant and depends on pressure. With the method utilizing spherical nanoindentation and continuous stiffness measurement (CSM) we determine the yield point of LiPON. We propose the Drucker-Prager type of yield criterion for LiPON and estimate its yield stress in compression as 2.4 GPa. There exists another stress threshold, however, around 490 MPa, at which the elastic deformation becomes non-linear, and this can be mistaken for the yield stress.
Constitutive model↗
A Low-Rank QTT-based Finite Element Method for Elasticity Problems
We present an efficient and robust numerical algorithm for solving the linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve the linear elasticity problem on a computational domain that is more general than a square. By integrating Z-ordering and subdomain concatenation, our method substantially decreases memory usage and achieves a notable reduction in rank compared to established Finite Element implementations like the FEniCS platform. This efficiency is maintained while still guaranteeing exponential convergence with respect to the number of degrees of freedom. This performance gain, however, requires a fundamental rethinking of how core finite element operations are implemented. This includes changes to mesh discretization, node and degree of freedom ordering, stiffness matrix and internal nodal force assembly, and the execution of algebraic matrix-vector operations. In this work, we discuss all these aspects in detail and assess the method’s performance in the numerical approximation of three representative test cases.
97 MATHEMATICS AND COMPUTING↗
Multiscale analysis in solids with unseparated scales: fine-scale recovery, error estimation, and coarse-scale adaptivity
There are several engineering applications in which the assumptions of homogenization and scale separation may be violated, in particular, for metallic structures constructed through additive manufacturing. Instead of resorting to direct numerical simulation of the macroscale system with an embedded fine scale, an alternative approach is to use an approximate macroscale constitutive model, but then estimate the model-form error using a posteriori error estimation techniques and subsequently adapt the macroscale model to reduce the error for a given boundary value problem and quantity of interest. Here, we investigate this approach to multiscale analysis in solids with unseparated scales using the example of an additively manufactured metallic structure consisting of a polycrystalline microstructure that is neither periodic nor statistically homogeneous. As a first step to the general nonlinear case, we focus here on linear elasticity in which each grain within the polycrystal is linear elastic but anisotropic.
42 ENGINEERING↗
Range and strength of mechanical interactions of force dipoles in elastic fiber networks
Mechanical forces generated by myosin II molecular motors drive diverse cellular processes, most notably shape change, division and locomotion. These forces may be transmitted over long range through the cytoskeletal medium – a disordered, viscoelastic network of biopolymers. The resulting cell size scale force chains can in principle mediate mechanical interactions between distant actomyosin units, leading to self-organized structural order in the cell cytoskeleton. Inspired by such force transmission through elastic structures in the cytoskeleton, we consider a percolated fiber lattice network, where fibers are represented as linear elastic elements that can both bend and stretch, and the contractile activity of myosin motors is represented by force dipoles. Then, by using a variety of metrics, we show how two such contractile force dipoles interact with each other through their mutual mechanical deformations of the elastic fiber network. As a prelude to two-dipole interactions, we quantify how forces propagate through the network from a single anisotropic force dipole by analyzing clusters of nodes connected by highly strained bonds, as well as through the decay rate of strain energy with distance from a force dipole. We show that predominant fiber bending screens out force propagation, resulting in reduced and strongly network configuration-dependent dipole interactions. On the other hand, stretching-dominated networks support longer-ranged inter-dipole interactions that recapitulate the predictions of linear elasticity theory. By characterizing the differences between tensile and compressive force propagation in the fiber network, we show how inter-dipole interaction depends on the dipoles’ mutual separation and orientation. The resulting elastic interaction energy may mediate a force between multiple distant dipoles, leading to their self-organization into ordered configurations. In conclusion, this provides a potential pathway for active mechanical force-driven structural order in elastic biopolymer networks.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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↗
Experimental Investigation of Low-Frequency Distributed Acoustic Strain-Rate Responses to Propagating Fractures
Summary Low-frequency distributed acoustic sensing (LF-DAS) responds to strain changes due to far-field fracture propagation. To better understand the LF-DAS response to fracture propagation, we performed laboratory-scale hydraulic fracture experiments with embedded optical strain sensors. The objectives of this research are to generate hydraulic fractures of known geometry, measure the strain response along the embedded fiber-optic cable comparable to LF-DAS measurements, and use the results to inform the interpretation of field-derived LF-DAS data. The experiments were conducted in unconfined transparent cubic blocks with a dimension of 8 in. on each side. The block was made of transparent epoxy to visualize the fracture propagation. Fiber-optic sensing cables were embedded in the block at different distances to the source of injection. We injected dyed water through an injection tubing to generate a transverse, radial fracture along an initial flaw. An optical interrogator recorded the response of offset fiber Bragg grating (FBG) strain sensors normal to the plane of the fracture. The strain data were visualized on a waterfall plot, akin to visualizations of field-derived LF-DAS data. Dimensional analysis was used to scale the laboratory results to field conditions. We compared the evolution of the strain response at the fiber-optic cable, injection pressure, and rate with known fracture geometry. The measured strains were compared with Sneddon’s (1946) linear elastic solution for a penny-shaped crack and found to follow this behavior. The generated radial fractures in transparent media can be modeled with Sneddon’s linear elastic radial fracture model and a Mode I critical stress intensity factor. The LF-DAS characteristic response of a narrowing region of extension surrounded by compression was exhibited as a fracture that approached and intersected the fiber-optic cable. The experimentally derived strain and strain-rate waterfall plots with known fracture geometry, injection rate, and pressure response provide insight in understanding LF-DAS responses in the field. Furthermore, we developed a method to estimate fracture geometry evolution from the fiber-optic strain data and validated the method against the experimental data.
Engineering↗
Identifying crack tip position and stress intensity factors from displacement data
Fracture prognosis and characterization efforts require knowledge of crack tip position and the Stress Intensity Factors (SIFs) acting in the vicinity of the crack. Here, in this work, we present an efficient numerical approach to infer both of these characteristics under a consistent theoretical framework from noisy, unstructured displacement data. The novel approach utilizes the separability of the asymptotic linear elastic fracture mechanics fields to expedite the search for crack tip position and is particularly useful for noisy displacement data. The manuscript begins with an assessment of the importance of accurately locating crack tip position when quantifying the SIFs from displacement data. Next, the proposed separability approach for quickly inferring crack tip position is introduced. Comparing to the widely used displacement correlation approach, the performance of the separability approach is assessed. Cases involving both noisy data and systematic deviation from the asymptotic linear elastic fracture mechanics model are considered, e.g. inelastic material behavior and finite geometries. An open source python implementation of the proposed approach is available for use by those doing field and laboratory work involving digital image correlation and simulations, e.g. finite element, discrete element, molecular dynamics and peridynamics, where the crack tip position is not explicitly defined.
36 MATERIALS SCIENCE↗
Physicochemical and Performance Characterization of Six Commercial Organic Solvent Nanofiltration Membranes
This work introduces a novel, gradient-free metamaterial design method based on Gaussian process regression to represent the density field of a unit cell. The dimension of the design space is determined by the covariance matrix dimension in the Gaussian process regression. We propose compressing this matrix using an autoencoder, enabling the decoder to generate the density field and effectively reduce the originally large design space to a lower-dimensional subspace. In this compressed space, we employ an active learning method, Bayesian Adaptive Direct Search (BADS), for efficient exploration of the design space. We demonstrate that for simple 2D designs aimed at maximizing unit cell stiffness, our method yields results comparable to those of standard topology optimization. Furthermore, we extend our approach to various mechanical problems, from linear elasticity to hyperelastic large deformation and elasto-plasticity under finite deformation, to 3D metamaterial design. This illustrates the method’s versatility and effectiveness across a range of applications.
Wu, Haoran↗
Dynamically morphing microchannels in liquid crystal elastomer coatings containing disclinations
Liquid crystal elastomers (LCEs) hold a major promise as a versatile material platform for smart soft coatings, since their orientational order can be predesigned to program a desired dynamic profile. In this work, we introduce temperature-responsive dynamic coatings based on LCEs with arrays of singular defects-disclinations that run parallel to the surface. The disclinations form in response to antagonistic patterns of the molecular orientation at the top and bottom surfaces, imposed by the plasmonic mask photoalignment. Upon heating, an initially flat LCE coating develops linear microchannels located above each disclination. The stimulus that causes a non-flat profile of LCE coatings upon heating is the activation force induced by the gradients of molecular orientation around disclinations. To describe the formation of microchannels and their thermal response, we adopt a Frank-Oseen model of disclinations in patterned director field and propose a linear elasticity theory to connect the complex spatially-varying molecular orientation to the displacements of the LCE. The thermo-responsive surface profiles predicted by the theory and by the finite element modeling are in good agreement with the experimental data; in particular, higher gradients of molecular orientation produce a stronger modulation of the coating profile. The elastic theory and the finite element simulations allow us to estimate the material parameter that characterizes the elastomer coating’s response to the thermal activation. The disclinations containing LCEs show potential as soft dynamic coatings with a predesigned responsive surface profile.
36 MATERIALS SCIENCE↗
The revised elastic field of an edge dislocation
We modify the traditional linear-elastic field of an edge dislocation. The modifications stem from symmetry and energy requirements imposed in terms of embedded (deformed) coordinates. These requirements are satisfied if a line force is added to the dislocation field. The modification to the stress field is expressed by coefficients that are a function only of Poisson’s ratio. Qualitatively, the field of the dislocation is increased in the glide direction and decreased in the climb direction. There are small changes to the field of a screw dislocation that do not entail the addition of a line force. Effects of nonlinearity, anisotropic elasticity, and image forces are briefly considered.
Hirth, J. P.↗
Multiscale formulation of frictional contact mechanics at the pore scale
Direct numerical simulation (DNS) yields the highest fidelity predictions of mechanical deformation at the pore scale, but is prohibitively expensive for analyzing large or many samples. Discrete element methods (DEM) are an efficient alternative, but are limited to granular media and incapable of estimating or controlling prediction errors. We present a pore-level multiscale method (PLMM) that approximates DNS efficiently and with controllable accuracy. We focus on the linear elastic response of a consolidated geologic porous medium with arbitrary microstructure, heterogeneous mineralogy, containing cracks or defects. PLMM decomposes the solid phase into non-overlapping subdomains, on which local basis functions are constructed. The bases are then coupled with a global interface problem that accounts for slip or stick contact conditions between the subdomains. PLMM produces an initial, but accurate, approximation to DNS that can be iteratively improved. It is amenable to parallelism and allows for different mesh, models, and physics in each subdomain. An algebraic interpretation of PLMM as a preconditioner is also presented to allow non-intrusive implementation into existing solvers. Lastly, this work extends previous developments of PLMM in fluid dynamics to solid mechanics and enables future extensions towards modeling coupled flow and mechanics problems.
42 ENGINEERING↗
Resonant ultrasound spectroscopy for crystalline samples containing initial strain
Resonant ultrasound spectroscopy (RUS) is a mature and robust technique for the nondestructive characterization of the elastic properties of solids capable of providing the elastic constants of anisotropic crystalline solids. The traditional method is based on assuming that the solid is linear elastic and, therefore, obeys a linearized Hookean constitutive relationship (Hooke’s law). In this work, an alternative constitutive law is provided that allows for an initial strain or prestrain to be present stemming from residual stress. Then, the constitutive relationship is integrated into the RUS framework. The model is demonstrated using a realistic prestrain field obtained by simulating shot-peening processing of a polycrystalline Cu sample. The sensitivity of the resonances to the developed prestrain is established and discussed. This work allows researchers to consider the influence of initial strain or residual stress in their samples and the potential influence on accurate elastic constant estimates. The model also supports the potential of RUS for the nondestructive characterization of prestrain in materials.
42 ENGINEERING↗
Predicting Mechanical Properties from Microstructure Images in Fiber-Reinforced Polymers Using Convolutional Neural Networks
Evaluating the mechanical response of fiber-reinforced composites can be extremely time-consuming and expensive. Machine learning (ML) techniques offer a means for faster predictions via models trained on existing input–output pairs and have exhibited success in composite research. This paper explores a fully convolutional neural network modified from StressNet, which was originally used for linear elastic materials, and extended here for a non-linear finite element (FE) simulation to predict the stress field in 2D slices of segmented tomography images of a fiber-reinforced polymer specimen. The network was trained and evaluated on data generated from the FE simulations of the exact microstructure. The testing results show that the trained network accurately captures the characteristics of the stress distribution, especially on fibers, solely from the segmented microstructure images. The trained model can make predictions within seconds in a single forward pass on an ordinary laptop, given the input microstructure, compared to 92.5 h to run the full FE simulation on a high-performance computing cluster. These results show promise in using ML techniques to conduct fast structural analysis for fiber-reinforced composites and suggest a corollary that the trained model can be used to identify the location of potential damage sites in fiber-reinforced polymers.
Sun, Yixuan (ORCID:0000000311093380)↗