Arbitrary Strain Research Articles

Evidence of Dislocation Mixed Climb in Quartz From the Main Central and Moine Thrusts: An Electron Tomography Study

AbstractIn this study we apply electron tomography to characterize 3D dislocation microstructures in two quartz mylonite specimens from the Moine and Main Central Thrusts, both of which accommodated displacements by dislocation creep in the presence of water. Both specimens show dislocation activity with dislocation densities of the order of 3–4 × 1012 m−2 and evidence of recovery from the presence of subgrain boundaries. 〈a〉 slip occurs predominantly on pyramidal and prismatic planes (〈a〉 basal glide is not active). [c] Glide is not significant. On the other hand, we observe a very high level of activation of 〈c + a〉 glide on the , , (n = 1,2) and even planes. Approximately 60% of all dislocations show evidence of climb with a predominance of mixed climb, a deformation mechanism characterized by dislocations moving in a plane intermediate between the glide and the climb planes. This atypical mode of deformation demonstrates comparable glide and climb efficiency under natural deformation conditions. It promotes dislocation glide in planes not expected for the quartz structure, probably by inhibiting lattice friction. Our quantitative characterization of the microstructure enables us to assess the strain that dislocations can generate. We show that glide systems indicated by the observed dislocations are sufficient to accommodate any arbitrary 3D strain by themselves. Although historically dislocation glide has been regarded as being primarily responsible for producing strain, activation of climb can also directly contribute to the finite strain. On the basis of this characterization, we propose a numerical modeling approach for attempting to characterize the local stress state that gave rise to the observed microstructure.

Time-varying compressive properties and constitutive model of EPDM rubber materials for tunnel gasketed joint

The stress relaxation of ethylene propylene diene monomer (EPDM) rubber material in a compressed state significantly increases the risk of water leakage at tunnel precast segmental joints. Additionally, EPDM rubber gaskets typically experience a complex precompression strain state, further complicating the prediction of long-term stress relaxation. Therefore, it is imperative to propose a novel constitutive model that realistically reflects the stress relaxation of rubber with arbitrary precompression strain, providing a reference for the long-term waterproof design of shield tunnels. In this study, the time-varying properties of EPDM rubber at material level were studied in detail. At first, a comprehensive set of accelerated aging tests were conducted on EPDM rubber samples with varying precompression strains. The hardening effect of rubber without precompression and the stress relaxation effect of rubber with precompression were explored. The time-varying law and mechanism governing rubber properties under these two effects were analyzed. Subsequently, a conversion relationship between the EPDM rubber test conditions and the actual service time was established. The predicted hardening coefficient for uncompressed EPDM after 100 years is 1.468, whereas the relaxation coefficient for compressed EPDM is 0.359. Comparative analysis revealed that the compression set index do not consider the beneficial effects of hardening, resulting in a 54.1% overestimation of the design water pressure. Finally, the analytical study on the constitutive model of EPDM rubber material was carried out. The error in compression curve for unaged sample obtained from empirical formulas exceeded three times that of the analytical model, underscoring the need to study time-varying constitutive models. An interpolation method was employed to extend the test curve, leading to the development of a new constitutive model that represents the stress relaxation characteristics of EPDM materials under arbitrary precompression strain states. By combining the proposed constitutive model with the timetemperature conversion relationship, the time-varying expressions of the constitutive parameters for relaxation and hardening effects during the service life were derived. In comparison with existing models, the proposed model demonstrates wider applicability, effectively captures the time-varying characteristics of EPDM materials under arbitrary precompression strains, offering an efficient approach for studying the long-term stress relaxation prediction of rubber gaskets in shield tunnels under complex precompression strain states.

Integrated accelerated testing methodology for CFRP durability

Integrated ATM, an integrated accelerated testing methodology for CFRP durability, is described herein. It is expressed as a single formula including several parameters representing the life of CFRP under an arbitrary environmental temperature and an arbitrary strain ratio R from R = 0 to 1. Integrated ATM is based on Christensen's viscoelastic crack kinetics and conventional ATM. First, Integrated ATM is introduced based on the matrix resin viscoelasticity. Second, important parameters which affect CFRP life are found for the longitudinal tensile strength of a unidirectional CFRP as an Integrated ATM application. Finally, the parameter influences on CFRP life are assessed.

A terahertz meta-sensor array for 2D strain mapping

Large-scale stretchable strain sensor arrays capable of mapping two-dimensional strain distributions have gained interest for applications as wearable devices and relating to the Internet of Things. However, existing strain sensor arrays are usually unable to achieve accurate directional recognition and experience a trade-off between high sensing resolution and large area detection. Here, based on classical Mie resonance, we report a flexible meta-sensor array that can detect the in-plane direction and magnitude of preloaded strains by referencing a dynamically transmitted terahertz (THz) signal. By building a one-to-one correspondence between the intrinsic electrical/magnetic dipole resonance frequency and the horizontal/perpendicular tension level, arbitrary strain information across the meta-sensor array is accurately detected and quantified using a THz scanning setup. Particularly, with a simple preparation process of micro template-assisted assembly, this meta-sensor array offers ultrahigh sensor density (~11.1 cm−2) and has been seamlessly extended to a record-breaking size (110 × 130 mm2), demonstrating its promise in real-life applications.

A data-driven rate and temperature dependent constitutive model of the compression response of a syntactic foam

Polymeric syntactic foams are used in aerospace and marine applications requiring low density and low moisture absorption together with high specific strength and stiffness. Their mechanical response is highly sensitive to temperature and strain rate and such sensitivity must be modelled accurately. In this study, the uniaxial compressive response of a polymeric syntactic foam is measured at strain rates in the range [10−3, 2.5·103] /s and temperatures varying between −25°C and 100°C. The resulting dataset is used to train a neural network to predict the compressive response of the foam at arbitrary strain rates and temperatures. It is found that the surrogate model is highly effective in predicting the material response at temperature and rates not included in its training set. Finally, a stochastic version of the data-driven model to allow predictions of the variability in the stress versus strain response is proposed.

A 3D viscoelastic–viscoplastic behavior of carbon nanotube‐reinforced polymers: Constitutive model and experimental characterization

AbstractDue to the widespread use of carbon nanotube (CNT)‐reinforced polymers in various industries, investigating the dynamic mechanical response of these materials under impact loading is of significant importance. A three‐dimensional viscoelastic (VE)–viscoplastic (VP) constitutive model for CNT/epoxy nanocomposites is developed. A proper rheological model is established using the generalized Maxwell model to represent the VE behavior and propose an exponential function to express the elasto‐VP response. Employing an empirical logarithmic relationship to estimate material properties at different strain rates, the VP behavior is modeled based on the overstress concept. The 3D numerical discretization of the proposed rate‐dependent material model is also carried out to develop a user‐defined material model (UMAT) for the commercial finite element (FE) software of Abaqus. The performed FE simulations based on the proposed rate‐dependent constitutive material can properly capture stress relaxation and hysteresis behaviors of the nanocomposites. Comparing the estimated tensile and shear stress–strain curves through developed material models with experimental measurements, an excellent agreement is observed.Highlights Tensile/shear properties of CNT/epoxy are measured at three strain rates. An empirical constitutive model is proposed for any arbitrary strain rates Viscoplastic behavior is captured based on over‐stress concept A 3D incremental form of a viscoelastic–viscoplastic material model is developed.

Aerosol Jet Printing of Strain Sensors for Soft Robotics

The field of soft robotics is rapidly progressing toward applications including; wearable electronics, prosthetics, and biomedical devices. This is leading to demand for flexible, embedded high‐performance strain sensors to deliver real‐time feedback on the static configurations and dynamic motions of these robotic devices, to ultimately enable the levels of autonomous control and structural monitoring required for intelligent manipulation. Herein, aerosol jet printing (AJP) technology is utilized to generate arbitrary piezoresistive strain sensor layouts on fibrous paper suitable for direct integration into elastomeric soft robots. A custom graphene nanoplatelet ink with a viscosity of around 2.70 cP has been formulated for optimized atomization and patterning of conductive traces via AJP. Single and multilayer printing onto different paper substrates are explored; with the nominal resistance of the printed tracks varying from 272 to 4900 kΩ depending on paper type and number of layers. Maximum gauge factors of 24.2 ± 1.8 and 56.5 ± 4.5 are determined for sensor surfaces under tensile and compression modes, respectively. To demonstrate the possibility for direct integration of this approach for soft robotics, strain sensors are directly printed onto the strain‐limiting layer of a pneumatic soft robotic gripper, to provide continuous feedback of the gripper over curvatures up to 80 m−1.

A perturbation analysis of pure torsion of incompressible hyperelastic cylinders

The stretch-based formulation of basic problems for incompressible isotropic hyperelastic materials has been the subject of renewed recent attention largely motivated by application to modelling the mechanical response of soft tissues. Here we are concerned with the classical problem of simple torsion of a circular cylinder which has in the past been primarily investigated by employing the classical approach of Rivlin in terms of invariants of the Cauchy–Green deformation tensors. Here we propose a perturbation approach to the pure torsion problem for thin (but not necessarily infinitesimally thin) cylindrical specimens motivated by potential applications to rubber-like or biological filaments and for the infinitesimal twisting of thick cylinders. The advantage of this approach is that the results are valid for all strain–energy functions whether based in terms of the principal stretches or in terms of the classical deformation invariants. The asymptotic results obtained for the resultant force and moment are applied to the special case of the one-term stretch-based Ogden model. In particular, a prediction of a transition in the Poynting effect for values of the Ogden parameter α>6 is obtained. Other illustrative examples for both invariant and stretch-based strain energies are described. In view of the complexity of a general analysis of torsion for arbitrary strain energies, the perturbation approach provides a viable alternative for assessing the resultant force and moment.

Second-Order Work Criterion in the Stability Analysis of an Earth Dam Subjected to Seepage

Abstract Failure may take different forms: reaching the Mohr–Coulomb limit stress condition is accompanied by yielding, strain localisation may occur in shear, compaction or dilatant bands, arbitrary large strain and loss of strength may be accompanied by a field of chaotic displacements of soil particles. Failure is also related to material instability. It takes place when there is a loss of uniqueness of constitutive relationships. It has been found that instability domains exist strictly inside the Mohr–Coulomb failure surface. Material instability can be detected by local Hill's criterion, that is the second-order work at a point. Results of a coupled hydro-mechanical finite element analysis of an ‘earth dam – subgrade’ system at changing hydraulic boundary conditions have been presented in the article. Normalised values of the second-order work and factor of safety values by the shear strength reduction procedure for corresponding stages of the analysis were calculated. It has been shown that the value of the safety factor corresponds to the values of the second-order work. The analysis results show that a decrease in the value of the safety factor is accompanied by a decrease in the value of the second-order work until negative values occur at some points.

Surrogate modeling for the homogenization of elastoplastic composites based on RBF interpolation

We propose a new framework for creating a surrogate model of computational homogenization for elastoplastic composite materials that serves as a homogenized constitutive law for decoupled two-scale analysis. Two key ingredients of the proposed surrogate modeling are the introduction of a variable representing the macroscopic strain history along with the macroscopic strain and the application of radial basis function (RBF) interpolation. Not only the coefficients of the RBF but also the type of its function form are considered hyperparameters and are determined by applying an optimization algorithm. In the offline process, numerical material tests (NMTs) are performed on a unit cell consisting of multiple elastoplastic materials subjected to various patterns of macroscopic strain to create a database that stores the discrete relationships between variables representing macroscopic deformation states with the macroscopic stresses. Then, RBF interpolation is applied to represent the macroscopic stress in a continuous function with these input data as independent variables. In the online process, this function is used as a macroscopic constitutive law in the macroscopic analysis, which can be followed by localization analysis using an arbitrary macroscopic strain history if necessary.

Finite element implementation of a certain class of elasto-viscoplastic constitutive models

In this paper a selected type of elasto-viscoplastic constitutive equations is considered. The viscoplastic model which was proposed by Marquis is generalized by allowing multiple terms describing the isotropic and the kinematic hardening. Furthermore, the presented model formulation enables one to use an arbitrary equivalent plastic strain function to describe the isotropic hardening behavior. What is more, the backstress evolution equation which was proposed by Marquis was modified so that any equivalent plastic strain function can be used in the recovery term now. The general form of the generalized constitutive model obtained this way was subsequently implemented into the finite element method (FEM). For that purpose, the radial-return mapping algorithm was utilized. The consistent tangent operator was derived for the considered class of models and is presented in the paper. A developed user material subroutine (UMAT) which allows one to use the viscoplastic models under consideration in the FEM program CalculiX is attached in the appendix section. A number of numerical simulations were conducted in order to verify the performance of the developed UMAT code.

Heterogeneous Structure Omnidirectional Strain Sensor Arrays With CognitivelyLearned Neural Networks.

Mechanically stretchable strain sensors gain tremendous attention for bioinspired skin sensation systems and artificially intelligent tactile sensors. However, high-accuracy detection of both strain intensity and direction with simple device/array structures is still insufficient. To overcome this limitation, an omnidirectional strain perception platform utilizing a stretchable strain sensor array with triangular-sensor-assembly (three sensors tilted by 45°) coupled with machine learning (ML) -based neural network classification algorithm, is proposed. The strain sensor, which is constructed with strain-insensitive electrode regions and strain-sensitive channel region, can minimize the undesirable electrical intrusion from the electrodes by strain, leading to a heterogeneous surface structure for more reliable strain sensing characteristics. The strain sensor exhibits decent sensitivity with gauge factor (GF) of ≈8, a moderate sensing range (≈0-35%), and relatively good reliability (3000 stretching cycles). More importantly, by employing a multiclass-multioutput behavior-learned cognition algorithm, the stretchable sensor array with triangular-sensor-assembly exhibits highly accurate recognition of both direction and intensity of an arbitrary strain by interpretating the correlated signals from the three-unit sensors. The omnidirectional strain perception platform with itsneural network algorithm exhibits overall strain intensity and direction accuracy around 98% ± 2% over a strain range of ≈0-30% in various surface stimuli environments.

Impact of uniaxial strain on oxygen monovacancy diffusion in uranium dioxide: A molecular dynamics study

Understanding defect diffusion kinetics in a strain field is essential for multiscale modeling of UO2 microstructure evolution, particularly in the case of creep, swelling, crack, etc. Although the diffusion kinetics of point defects in UO2 is well explored both experimentally and theoretically, the kinetics under strain conditions is not well understood. In the present study, the diffusion of oxygen monovacancy in UO2 subjected to uniaxial tensile strain as much as 3% in the directions of <100>, <110>, and <111> is investigated by means of molecular dynamics (MD) simulations in the temperature range of 600–1000 K. The results show that in the case of strain in <100> direction, diffusivity decreases with tensile strain, especially at high temperatures above 700 K. In contrast, diffusion is promoted with stretching in <110> and <111> directions. It is assumed that this may be the combined result of independent variation of migration energy (Em) and pre-factor (D0), according to the Arrhenius equation. Further investigations are made with nudged elastic bands (NEB) calculations for a better interpretation of the effect of directional strain on migration energy. It is found that the effect is anisotropic, and the variation of Em is in good agreement with that of MD calculations. Stretching along the <100> direction results in the decrease of Em in all three directions, with <100> the most profound. Stretching in <110> and <111> directions exert negligible effect. The present study provides insights into the effect of strain on the diffusion of oxygen vacancy in UO2, however, further research is needed for the effect of arbitrary strain on poly-crystalline UO2.

Interpretation of constant suction direct shear test

Constant suction direct shear test enables the understanding of the failure mechanism in rainfallinduced landslides. It can be conducted using a conventional direct shear apparatus with some modifications. The constant suction direct shear test is carried out in two stages. In the first stage, the unsaturated soil specimen is consolidated to the target net normal stress and matric suction then sheared in the second stage. Matric suction is usually controlled using the axis-translation principle. It is commonly observed that the shear stress of an unsaturated soil sheared in the direct shear shows a strain-hardening behaviour at large displacements making the determination of the failure stress difficult. Hence, the objective of this study is to critically examine the constant suction direct shear tests and the analysis of the test results to obtain the shear strength parameters for unsaturated soils. Constant suction direct shear test data were collated from the literature. It was found that the interpretation of the direct shear test has two inconsistencies: (1) taking failure shear stress at arbitrary displacement strain or limit, dependent on the size of the direct shear apparatus, and (2) correcting only shear stress for contact area. The effect of these two consequences on the interpretation of the direct shear test range from negligible to significant. The study shows that arbitrary determination of failure shear stress can be resolved by plotting the direct shear test results using a stresspath plot. The effects of area correction are shown to be almost negligible for small horizontal displacements of less than 2 mm for both square and circular shear boxes. A more consistent interpretation of the constant suction direct shear test is demonstrated where both these inconsistencies are considered.

On the yield criterion of two-scale porous materials by using Eshelby-type velocity field and Steigmann–Ogden surface model

In this work, we investigate the yield strength of porous metallic materials in the presence of both microvoids and nanovoids. A two-level hierarchical model composed of both microscopic and macroscopic representative volume elements (RVEs) are proposed for this purpose. The lower level RVE is made up of an incompressible, perfectly elastoplastic, von Mises matrix and multiple dilute nanovoids. By using a micromechanics-based homogenization method, a microscopic yield criterion is first established in terms of the overall equivalent stress, uniaxial yield strength of the microscopic matrix, Gurtin–Murdoch and Steigmann–Ogden nanovoids surface constants, as well as the microscopic porosity. The lower level RVE is then treated as a material point in the upper level RVE matrix. The macroscopic dissipation rate is evaluated from the conventional deviatoric strain rate used in Gurson’s classical criterion, an Eshelby-type exterior velocity field and the compressibility rate of the macroscopic matrix. Closed-form solutions are eventually determined for such a velocity field and the macroscopic yield function, by simultaneously satisfying the arbitrary macroscopic strain rate boundary conditions and enforcing the principle of minimum dissipation rate. Compared to similar criteria available in the literature, two distinct features can be identified. First, the full version Steigmann–Ogden surface model is considered on nanovoids surface. Second, both the hydrostatic and deviatoric deformation of the microvoid are considered in the velocity field. Extensive parametric studies are conducted to investigate the effects of nanovoids surface bulk modulus, surface shear modulus, surface flexural rigidity, nanovoids radius, and both levels of porosities on the macroscopic yield loci. The results obtained in this article are helpful to the better design and manufacturing of nanoporous metallic materials.

Hot Workability and Dynamic Recrystallization Behaviors of Medium-Carbon Cr-Mo Alloys for High Strength Cold Heading Quality Wire Rod

The hot deformation behavior of medium-carbon Cr-Mo alloy, which has been developed for high strength cold-heading quality wire rod, was investigated to evaluate its hot workability. A flow curve was derived using the hot torsion test, under conditions with temperatures of 1173-1273 K and strain rates of 0.1-1.0 s-1. At lower deformation temperature and higher strain rate, the overall stress of the flow curve increased, and the flow curve showed a three-stage variation related to the offset of dynamic recrystallization and dynamic recovery. First, as the strain increased, the stress also increased due to work hardening, and reached peak stress. After that, the stress decreased due to softening of the dynamic recrystallization. And when the effect of the dynamic recrystallization and the dynamic recovery reached equilibrium, the stress became steady state. In this paper, the constitutive equation of the peak stress was established using a form of a hyperbolic sine function, and here the thermal activation energy for deformation of the specimen was 244.90 kJ/mol. The peak stresses calculated from the constitutive equation were in good agreement with the experimental results. The dynamic-recrystallized grains were observed using electron backscatter diffraction (EBSD). It showed that the volume fraction of dynamic recrystallization increased as the strain increased under hot deformation. Based on the Avrami kinetic equation, a dynamic recrystallization kinetic model was established. The volume fraction of dynamic recrystallization was predicted from the kinetic model, and can be applied at arbitrary deformation temperatures and strain rates.

A new concept for continuum distortional plasticity

This paper presents hexah, a framework based on the homogeneous anisotropic hardening (HAH) model. It aims at recreating the effects of arbitrary strain path changes over the plastic behavior of metals. Its core relies on the concept of microstructure deviator, a tensor representing one set of active slip systems. The present theory makes use of an arbitrary number of microstructure deviators spawned by abrupt changes of loading paths. A formalism is detailed to describe a smooth evolution from one set of activated slip systems to another. This new approach carries significant advantages: evolution equations are simplified, the number of parameters decreased, and the behavior near cross-loading stabilized.

Unconditional stability in large deformation dynamic analysis of elastic structures with arbitrary nonlinear strain measure and multi-body coupling

Stability is a fundamental feature of a time integration method in long simulations of elastic bodies in large deformations. It is well known that energy conservation is the key to achieve it. The implicit one-step conserving method of Simo and Tarnow is simple and effective for quadratic strain measures. However, the issue of unconditional stability does not yet have a definitive solution for general nonlinear strain measures and multi-body couplings. This article shows how to reach this goal by a simple modification of the Simo and Tarnow method. In practice, the mean internal force vector of the time step is evaluated using the average value of the stress at the end-points and an integral mean of the strain–displacement tangent operator over the step computed by time integration points. Compared to other proposals, the approach conserves energy for any structural model regardless of its spatial finite element discretization and does not require Lagrange multipliers, discrete derivatives, approximations of the strain–displacement law or special iterative solutions. Long term stability is proved using dynamic analyses of Reissner beams and Kirchhoff–Love shells, discretized spatially with Lagrangian and isogeometric elements respectively. Moreover, the proposed energy-conserving scheme is extended to multi-body analyses with nonlinear couplings by means of a penalty formulation, with focus on the rotational continuity for generic multi-patch Kirchhoff–Love shells.

Confined vortex surface and irreversibility. 2. Hyperbolic sheets and turbulent statistics

We continue the study of Confined Vortex Surfaces (CVS) that we introduced in the previous paper. We classify the solutions of the CVS equation and find the analytical formula for the velocity field for arbitrary background strain eigenvalues in the stable region. The vortex surface cross-section has the form of four symmetric hyperbolic sheets with a simple equation [Formula: see text] in each quadrant of the tube cross-section ([Formula: see text] plane). We use the dilute gas approximation for the vorticity structures in a turbulent flow, assuming their size is much smaller than the mean distance between them. We vindicate this assumption by the scaling laws for the surface shrinking to zero in the extreme turbulent limit. We introduce the Gaussian random background strain for each vortex surface as an accumulation of a large number of small random contributions coming from other surfaces far away. We compute this self-consistent background strain, relating the variance of the strain to the energy dissipation rate. We find a universal asymmetric distribution for energy dissipation. A new phenomenon is a probability distribution of the shape of the profile of the vortex tube in the [Formula: see text] plane. This phenomenon naturally leads to the “multifractal” scaling of the moments of velocity difference [Formula: see text]. More precisely, these moments have a nontrivial dependence of [Formula: see text], [Formula: see text], approximating power laws with effective index [Formula: see text]. We derive some general formulas for the moments containing multidimensional integrals. The rough estimate of resulting moments shows the log–log derivative [Formula: see text] which is approximately linear in [Formula: see text] and slowly depends on [Formula: see text]. However, the value of effective index is wrong, which leads us to conclude that some other solution of the CVS equations must be found. We argue that the approximate phenomenological relations for these moments suggested in a recent paper by Sreenivasan and Yakhot are consistent with the CVS theory. We reinterpret their renormalization parameter [Formula: see text] in the Bernoulli law [Formula: see text] as a probability to find no vortex surface at a random point in space.

Material behaviour of austenitic stainless steel subjected to cyclic and arbitrary loading

In this paper, an experimental program on cyclic loading of austenitic stainless steel specimens is presented. The program encompasses a series of forty specimens subjected both cyclic (low and extremely low) and arbitrary loading (following certain rules). These protocols include companion, multiple-step and a set of arbitrary earthquake-like strain history, which represents a novelty in the material understanding. Stainless steel exhibits strain hardening as a key feature for structural applications. This feature is fundamental in the definition of cross-sectional resistance, cross-section classification, ductility and energy dissipation. In recent years, the strategic use of stainless steel as a potential structural material in dissipative zones of earthquake-resistant elements is under consideration. When it comes to seismic design, strain-hardening must be known precisely for further characterization of the seismic structural behaviour of the actual system in which stainless steel is used strategically. The use of stainless steel in dissipative zones of earthquake-resistant structures requires research related to cyclic loading at many levels. Thus, its potential use in seismic areas, as well as the performance of existing structures, can be considered. A systematic analysis of the results, which include cyclic hardening, stabilisation and material degradation, is presented. In addition, these results are used for the further numerical implementation of cyclic hardening in non-linear models.