Simple Shear Deformation Research Articles

Electrothermally actuated lattice metamaterials with remarkable shear deformation

Active metamaterials with specific deformation responses present great promise in fields such as multifunctional antennas, stretchable electronic devices and reconfigurable soft robots, due to their ability to switch between different operational states within a single system. However, the previous researches on active metamaterials with shear deformation responses exhibit two issues: inability to further enhance the shear deformation magnitude of the active metamaterials and inability to achieve precise customized design of the metamaterials, such as realizing simple shear deformation. Moreover, the inverse design of active metamaterials is challenging because theoretical models describing the finite deformation of active metamaterials under external-field actuation are lacking. To address the aforementioned issues, this study reports a design strategy for the electrothermally actuated lattice metamaterials to realize remarkable shear deformation with the maximum shear angle exceeding 26° and the capability to precisely achieve desired mechanical responses of the active metamaterials. The shear angle of the electrothermally actuated lattice metamaterials reported in this paper has increased by approximately 82% compared to that achieved in previous studies. Theoretical models for the electrothermally actuated metamaterials are established to describe the shear deformation behaviors. The theoretical models are demonstrated through both qualitative and quantitative comparisons with finite element analyses (FEAs) and experimental results. Theoretical models provide detailed predictions of the configuration after electric heating and offer analytical solutions for crucial mechanical quantities, such as the effective strains and shear angle for the electrothermally actuated lattice metamaterials exhibiting shear deformations. Moreover, experimental results and FEA calculations show that the simple shear deformation mode can be realized in the active metamaterials through the design strategies proposed in this paper, while it cannot be achieved in previous researches. This demonstrates the capability of the design strategies proposed in this paper to precisely realize required mechanical responses of the active metamaterials.

Vorticity Estimation of the Terrane Boundary Shear Zone of the Eastern Ghats Mobile Belt, and its Tectonic Significance

ABSTRACT The Terrane Boundary Shear Zone (TBSZ) of the Eastern Ghats Mobile Belt on the NW front against Bastar Craton shows northwesterly vergent thrust kinematics; and on the northern front with Singhbhum Craton shows dextral strike-slip tectonics. The kinematic vorticity numbers are as follows: the NW front, Wm(RGN) is 0.70–0.83 and Wm (Rs/ θ ) is 0.82–1.0; and the northern front, Wm(RGN) is 0.60–0.81 and Wm(Rs/θ) is 0.61–1.0. The estimates suggest that the Wm (Rs/ θ ) values are larger which indicates that the last incremental strain is dominated by simple shear. Further, both fronts are deformed by transpressional to simple shear deformation. However, the northern boundary shear zone has a transtensional component suggesting the TBSZ has undergone shear zone perpendicular extension. The development of the Mahanadi rift valley on the northern front may be related to such extension.

Multiple episodes of late Neoproterozoic rifting in the Tarim Craton during its separation from the supercontinent Rodinia

In this paper, we review and evaluate the magmatic history, regional stratigraphy, structural patterns and sedimentary provenance features of the Late Neoproterozoic Tarim Craton to elucidate the nature and different modes of extensional tectonics during the Latest Neoproterozoic, a critical time coinciding with the disintegration of the supercontinent Rodinia. New detrital zircon U–Pb ages and geochemical data acquired from quartz schists and spatially associated granites in the Tugerming anticline along the northern margin of the Tarim Craton have revealed Cryogenian ages, as opposed to Early Neoproterozoic and older ages as reported in previous studies. Granitic intrusions are dated at 656–637 Ma, which involved remelting of the ancient crust following the decline of the initial (Cryogenian) rift stage. They are unconformably overlain by terrestrial clastic deposits. Based on the available detrital zircons from the Late Neoproterozoic sedimentary rock assemblages, we identify a major change in the provenance of the basinal strata at the end of the Cryogenian period. This inferred provenance change, associated with basement exhumation, overlaps in time with resumed magmatic activities, basin inversion and uplift along the northern margin of the craton. The initial, Cryogenian rifting stage was facilitated by pure shear deformation that produced rift basins in and across the Tarim Craton. The subsequent rifting stage was facilitated by simple shear deformation, confined to the northern edge of the craton as the break-up of the supercontinent Rodinia further progressed. Episodic rifting of the Tarim Craton and its separation from Rodinia were aided by thermal weakening of its lithosphere owing to the periodic impingement of mantle upwelling beneath it throughout the Cryogenian and Ediacaran periods.

Multi-phase-field lattice Boltzmann modeling and simulations of semi-solid simple shear deformation

Semi-solid deformation is a versatile phenomenon that occurs during the solidification of alloys. Semi-solid simple shear deformation is simulated using the multi-phase-field lattice Boltzmann (MPF-LB) method, which has been originally devised to capture polycrystalline solidification accompanied with melt flow and solid motion. MPF-LB simulations of semi-solid simple shear deformation, with variations in solid fractions, reveal the transition from a liquid-like behavior to a solid-like one. Especially, the shear band formed via dilatancy effects is thoroughly examined in the high solid fraction region. The relationship between grain rearrangement and mechanical behaviors during the formation process of the shear band is investigated in detail. In addition, the effect of domain size and initial grain arrangement on shear band formation is evaluated. Finally, the mechanism of shear band formation is clarified. The developed MPF-LB simulation method is promising for comprehensive evaluations of semi-solid deformation.

Crystallographic Preferred Orientation of Phase D at High Pressure and Temperature: Implications for Seismic Anisotropy in the Mid‐Mantle

AbstractSeismic anisotropy has been widely observed in the lower mantle transition zone and the uppermost lower mantle near several subducting slabs, which is typically attributed to the crystallographic preferred orientation (CPO) of constituent minerals. In this study, well‐controlled uniaxial and simple shear deformation experiments were conducted on Mg‐endmember phase D and Al‐bearing phase D aggregates at 20 GPa and 500–1,000°C. Strong (0001) fabrics were observed in the uniaxially compressed samples. The CPO from all experiments, including extension and simple shear, indicated that the most active slip systems in phase D were <110>(0001) and <100>(0001), with a dominance of <110>(0001). The calculated seismic velocity suggests that the deformed phase D generates positive radial seismic anisotropy (VSH > VSV) in both subhorizontal shearing and subvertical compression, causing significant shear‐wave splitting time. Our results suggest that the observed seismic anisotropy in the mid‐mantle in several cold subduction zones can be well explained by the presence of deformed phase D.

Geometry of plastic deformation in metals as piecewise isometric transformations

Deformation mechanisms of crystalline solids has been the subject of research for more than two centuries. The theory of dislocations dominates modern views but still has significant gaps demanding the introduction of additional concepts for the coherent quantitative description of physical phenomena. In this work, we propose a coherent geometric description of motion and deformation in crystalline solids as piecewise isometric transformations (PWIT). The latter only includes operations that, similar to interatomic spacing in crystalline lattice, do not alter distances between reference points, i.e. translations, rotations and mirror reflections. The difference between solid-body translations and plastic deformations is that the isometric transformations have discontinuities that in real-life materials realise through dislocations (termination of shifts), disclinations (termination of rotations), and twins (mirror reflections). The conceptual description of plastic deformations as PWIT can be useful for the better description of physical phenomena, proposing new hypothesis, and for developing predictive analytical models. In this paper, the use of this conceptual description enables proposing new hypothesis about the nature of such interesting phenomena in severe plastic deformation as (i) stationary ‘solid state turbulence’ stage in high pressure torsion, and (ii) rate of mass transfer (mechanically assisted diffusion) in simple-shear deformation.

Modeling Simple Shear Deformation in Hyperelastoplasticity: A Numerical Integration Algorithm in the Intermediate Configuration

Modeling Simple Shear Deformation in Hyperelastoplasticity: A Numerical Integration Algorithm in the Intermediate Configuration

Effect of the deformation temperature and strain on the strain rate sensitivity of fcc medium-entropy alloys

The primary objective of the present investigation is to elucidate the operative micromechanisms influencing the strain rate sensitivity and activation volume in (FeCrNi)99Si1 and FeMnNi medium-entropy alloys. Room-temperature nanoindentation experiments at different loading rates were performed to study the evolution of the strain rate sensitivity and activation volume in (FeCrNi)99Si1 and FeMnNi medium-entropy alloys. The (FeCrNi)99Si1 samples were subjected to plane strain deformation by rolling at 77 and 300 K to study the effect of temperature on the strain rate sensitivity, while the FeMnNi and (FeCrNi)99Si1 samples were subjected to simple shear deformation by high-pressure torsion at 300 K to examine the effect of strains. Contrary to the well-documented trend observed in fcc metals and alloys, where the strain rate sensitivity typically increases with decreasing grain size, the present study reveals a distinct behavior for the current alloys. Similarly, these alloys are characterized by extremely low activation volumes of a few tens of b3 compared to 100–1000 b3 for conventional fcc metals and alloys in the microcrystalline grain size regime. Unlike conventional fcc metals and alloys, there is an insignificant change in the activation volume of the current high-/medium-entropy alloy (H/MEA) with decreasing grain size from the microcrystalline to nanocrystalline regime. The unique evolution of strain rate sensitivity and activation volume in H/MEAs is explained in terms of the evolution of distinct dislocation structures as well as synergistic operation of additional mechanisms such as twinning, phase transformation from fcc to hcp phases, cluster strengthening, and short-range ordering due to the aperiodic energy landscape existing in MEAs.

Non-stationary response analysis for sandwich panels with corrugated cores under moving random loads

In this work, a recursion reverberation-ray matrix method (RRRM) is presented to formulate an exact and unified solution for the non-stationary responses analysis of the sandwich panels with corrugated cores (SPCC) subjected to the moving random loads. The governing equations for the basic units are obtained by employing the simple first-order shear deformation theory (S-FSDT) and Hamilton's principle. Then, based on the traditional reverberation ray matrix method (MRRM), the RRRM is established by incorporating a bidirectional recursion technique to effectively calculate the exact solutions of the whole model. Thereinto, the kinematic relation matrix between the cell units can be constructed to facilitate the coupling of various desired numbers of elements by employing the virtual coupling spring. In addition, a unified loading mechanism for multi-scenario loads is proposed by integrating the pseudo-excitation method (PEM) with the load stage division technique. The applicability and accuracy of the current method to non-stationary response behaviors of the SPCC are clarified by carrying out sufficient comparative studies between the calculated results with reference solutions from FEM and Monte Carlo simulation method. Furthermore, several meaningful conclusions are drawn regarding the effects of structural and load parameters on the vibration characteristic, non-stationary displacement response, power spectrum density (PSD), and time-varying root mean square (RMS).

Atomistic Insights into Nucleation of Ferroelastic Domains in PbTiO3.

Understanding the nucleation mechanism of domains is essential for domain engineering of perovskite ferroelectric materials. We proposed and examined atomistic details for nucleating ferroelastic (FS) domains by integrating topological analysis and first-principles calculations. FS domains are crystallographically treated as deformation twins. The conventional shear-shuffle nucleation mechanism under simple shear deformation is ruled out because the 1-layer elementary twinning disconnection (TD) cannot nucleate and glide in a perfect matrix. Thus, the pure-shuffle nucleation mechanism under pure shear deformation is proposed due to kinetically favored atomic shuffling. The coherency stress associated with the coherent nucleus is relaxed via forming misfit dislocations, accompanied by formation and sharpening of diffused (110)m∥(110)d domain walls (DWs). The sharp DWs enable growth of the FS nucleus through successive nucleation and gliding of TDs. These findings enrich the knowledge of domain behavior in perovskite ferroelectric materials.

Time-frequency analysis of plate-shell coupled structures under moving stochastic load

Random vibration is of critical importance in understanding the dynamic behavior of engineering structures, especially the nonstationary responses for their coupled enclosers consisting of plates and shells subjected to moving stochastic loads. In this study, the pseudo excitation method (PEM) is integrated into the method of reverberation ray matrix (MRRM) to establish a full-domain stochastic dynamic system. With the help of rearrangement matrices and coupling spring connection technologies, the two plate-shell models of sequential and reinforced coupling are considered by employing the simple first-order shear deformation shell theory (S-FSDST) and Hamilton's principle. Then, the continuous movement of the excitation between each substructure is achieved through load coordinate normalization in nonhomogeneous equations, which are separated from the generalized solutions in the frequency domain. Therefore, it can be easily converted into a global pseudo-excitation and obtain the time-history responses relying on the inverse Laplace transform. After matching the present results with the finite element software and Monte Carlo simulation (MCS), the accuracy and efficiency of the proposed RRM-PEM are well-confirmed. Finally, by performing a series of numerical cases of power spectral density (PSD) and time-varying root mean square (RMS) under different loading velocities, frequency bands and system modal dampings, the time-frequency rules for different substructures of closed plate-shell coupled system under moving random loads are revealed for the first time.

Modelling the rate-dependent mechanical behaviour of the brain tissue

A new modelling approach is employed in this work for application to the rate-dependent mechanical behaviour of the brain tissue, as an incompressible isotropic material. Extant datasets encompassing single- and multi-mode compression, tension and simple shear deformation(s) are considered, across a wide range of deformation rates from quasi-static to rates akin to blast loading conditions, in the order of 1000 s−1 . With a simple functional form and a reduced number of parameters, the model is shown to capture the considered rate-dependent behaviours favourably, including in both single- and multi-mode deformation fits, and over all range of deformation rates. The provided modelling results here are obtained from either first fitting the model to the quasi-static data, or/and predicting the behaviour at a different rate than those used for calibrating the model parameters. Given its simplicity, versatility, predictive capability and accuracy, the application of the utilised modelling framework in this work to the rate-dependent mechanical behaviour of the brain tissue is proposed.

Multi-phase-field lattice Boltzmann simulations of semi-solid simple shear deformation in thin film

Semi-solid deformation during casting often results in significant solidification defects, such as segregation bands. Consequently, the development of a numerical simulation tool is crucial for accurately replicating semi-solid deformation. In our previous study, we applied a multi-phase-field lattice Boltzmann (MPF-LB) model to semi-solid deformation, facilitating seamless simulation from polycrystalline solidification to semi-solid deformation in a two-dimensional (2D) problem. This study extends the 2D MPF-LB model to a three-dimensional (3D) problem and develops a simulation method for semi-solid simple shear deformation in thin films. To enhance the efficiency of the 3D semi-solid simulation, we implemented parallel computations using multiple graphics processing units. Through a discussion of the relationships among the stress–strain curve, grain rearrangement behavior, and fluid flow, we confirmed that the developed 3D MPF-LB model successfully reproduced the characteristic phenomena of semi-solid deformation, and has high potential to investigate the nuanced mechanisms of semi-solid deformation.

Continuous Softening as a State of Hyperelasticity: Examples of Application to the Softening Behavior of the Brain Tissue.

The continuous softening behavior of the brain tissue, i.e., the softening in the primary loading path with an increase in deformation, is modeled in this work as a state of hyperelasticity up to the onset of failure. That is, the softening behavior is captured via a core hyperelastic model without the addition of damage variables and/or functions. Examples of the application of the model will be provided to extant datasets of uniaxial tension and simple shear deformations, demonstrating the capability of the model to capture the whole-range deformation of the brain tissue specimens, including their softening behavior. Quantitative and qualitative comparisons with other models within the brain biomechanics literature will also be presented, showing the clear advantages of the current approach. The application of the model is then extended to capturing the rate-dependent softening behavior of the tissue by allowing the parameters of the core hyperelastic model to evolve, i.e., vary, with the deformation rate. It is shown that the model captures the rate-dependent and softening behaviors of the specimens favorably and also predicts the behavior at other rates. These results offer a clear set of advantages in favor of the considered modeling approach here for capturing the quasi-static and rate-dependent mechanical properties of the brain tissue, including its softening behavior, over the existing models in the literature, which at best may purport to capture only a reduced set of the foregoing behaviors, and with ill-posed effects.

Multimaxima crystallographic fabrics (CPO) in warm, coarse-grained ice: New insights

Multimaxima crystallographic c-axis fabrics (CPOs) commonly observed in coarse-grained ice have been interpreted in several different ways but remain enigmatic. We review previous interpretations of these fabrics and present new data from Storglaciären, northern Sweden, for comparative purposes using both U-stage methods (c-axes only) and electron backscatter diffraction (EBSD) (both c-axis and a-axis orientations). Consistent with most previous studies, microstructures in our study indicate that all grains have been dynamically recrystallized with grain boundary migration as the dominant process. The CPO is characterized by grains oriented favorably for easy glide on the basal plane, given the local kinematics. When a representative sample is obtained, areas on the glacier margin undergoing non-coaxial deformation have a CPO generally consistent with simple shear. Multimaxima CPOs developed in the center of the glacier, which is associated with more coaxial deformation, likely represent a small circle girdle or partial girdle fabric associated with flow-parallel compression. In both locations, sampling bias, resulting from repeat measurements of single parent grains appearing several times as “island grains” in a 2D thin section, is likely responsible for the observed multiple maxima that, with bias removed, simplify to patterns expected for simple shear or coaxial deformation. An earlier study suggesting that multimaxima CPOs may result from twinning is not borne out from our data combining c-axes and a-axes that do not show the symmetry required of twinning.

The subloading surface model in hyperelastic-based plasticity with time integration algorithms in intermediate and current configurations

This paper introduces a novel application of subloading surface concept to effectively model the elastoplastic behavior of materials in the finite strain regime. The subloading surface approach allows for a smoother and more seamless transition from the elastic to the plastic region. Two time integration schemes are presented in this study, one in the intermediate configuration and the other in the current configuration. In the first time integration scheme, co-rotational objective time rates are not required, and the formulation utilizes the Mandel stress. In the second time integration scheme, implemented in Eulerian description, the Kirchhoff stress defined in the current configuration is utilized.The results obtained for the simple shear deformation case demonstrate the absence of oscillations. Additionally, these results show excellent agreement with experimental data and existing findings from the literature. Furthermore, a computational comparison between the time integration schemes using the subloading surface model and a model discussed in the literature reveals that the proposed algorithms in this paper require significantly fewer increments in the given time integrations. This indicates a higher computational efficiency and reduced computational time for the proposed methods. Overall, the predicted responses of all the analyzed cases from the provided time integrations exhibit excellent agreement with each other, confirming the accuracy and effectiveness of the presented model.

On the wave propagation characteristics of functionally graded porous shells

This paper concentrates on the wave propagation characteristics of functionally graded (FG) porous shells. The transversal shear deformation of the shell is taken into consideration by employing a simple higher-ordered shear deformation shell theory. The equations of motion are derived for the proposed model based on Hamilton’s principle. An eigenvalue problem that relates the wave propagation elements is formulated and solved to present the various dispersion relations of FG cylindrical and spherical shells. The effects of porosities, shells’ geometrical parameters, FG material exponent, and wavenumbers on the principal wave propagation frequency and the associated phase velocity are investigated in detail.

An approximate analytical solution for a dynamical simple shear deformation problem of an infinite strip including flexoelectric and micro‐inertial effects by Laplace transform

AbstractWe study the flexoelectric effect induced in an infinite strip of a dielectric material, due to an applied shear deformation at the upper surface, while the lower surface is fixed. The model incorporates dynamic spontaneous polarization, flexocoupling deformation, and microinertia effects to evaluate these effects combined. The variation of the Hamiltonian functional in the medium, and of the external forces yields the governing equations and the boundary conditions. There are many types of applied boundary conditions besides the initial conditions, where the initial conditions are imposed due to the dynamics of many effects in the mathematical modelling formulation. In addition to that, the boundary conditions are divided into two groups, where the first group contains mechanical boundary conditions such as traction boundary conditions and displacement boundary conditions for the classical treatment as in the theory of elasticity while for the strain gradient theory of elasticity, conditions for higher‐order traction vector should be imposed and cannot be neglected. The proposed technique depends on applying Laplace's transform to the field equations to obtain the characteristic equation, the roots of which are expressed in terms of the ‐transform parameter and other parameters related to the elastic and electric properties of the material. Those roots which produce a bounded solution are then approximated using Taylor's expansion, then the boundary conditions are applied to complete the solution. This technique enables to obtain the solution in terms of simple analytical functions that are easily inverted from the ‐domain to the time domain. This technique is applied to a simple shear deformation problem to study the dynamical flexoelectric effect in dielectric materials due to shear displacement and external electric potential. A suitable material, such as Strontium Titanate material, , is used for numerical simulation, and the results are analyzed, discussed, and represented graphically.

Examination of the high-frequency behavior of functionally graded porous nanobeams using nonlocal simple higher-order shear deformation theory

Examination of the high-frequency behavior of functionally graded porous nanobeams using nonlocal simple higher-order shear deformation theory

DIC technique for experimental validation of higher order numerical models

This paper presents an adaptation to the Digital Image Correlation (DIC) technique to aid and improve standard measurement methods in experimental mechanics. The practical application is demonstrated by the validation of the Cosserat Continuum model, using small-scale masonry specimens. Numerical models, such as the Cosserat continuum, play an important role in the identification and description of the mechanical behaviour of structures. Especially when it comes to anisotropic and quasi-brittle materials like masonry, these models are needed to evaluate significant aspects like performance, safety, or the effects of various strengthening interventions. The experimental investigation to validate a numerical model is not always straightforward and several of them remain theoretical. Addressing this, the experimentation presented in this paper evaluates the Cosserat identification in shear, where along with simple shear deformation, rigid rotations, micro rotations and micro couples are also exhibited. With such complex deformations, conventional techniques, such as strain gauges, or extensometers can no longer be adopted. The adapted DIC allows the quantification of these deformation data and validates the numerical model.