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Showing papers on "Isotropy published in 2021"


Journal ArticleDOI
TL;DR: In this article, two isotropic lattice structure design and anisotropy control strategies are proposed in the field of bone implantation, which are applied as acetabular cup implant in this work.

56 citations


Journal ArticleDOI
TL;DR: In this paper, a thermodynamically consistent, microstructurally-guided modeling framework for isotropic, incompressible hard magnetorheological elastomers (h-MREs) is provided.
Abstract: Hard magnetorheological elastomers ( h -MREs) are essentially two phase composites comprising permanently magnetizable metallic inclusions suspended in a soft elastomeric matrix. This work provides a thermodynamically consistent, microstructurally-guided modeling framework for isotropic, incompressible h -MREs. Energy dissipates in such hard-magnetic composites primarily via ferromagnetic hysteresis in the underlying hard-magnetic particles. The proposed constitutive model is thus developed following the generalized standard materials framework, which necessitates suitable definitions of the energy density and the dissipation potential. Moreover, the proposed model is designed to recover several well-known homogenization results (and bounds) in the purely mechanical and purely magnetic limiting cases. The magneto–mechanical coupling response of the model, in turn, is calibrated with the aid of numerical homogenization estimates under symmetric cyclic loading. The performance of the model is then probed against several other numerical homogenization estimates considering various magneto–mechanical loading paths other than the calibration loading path. Very good agreement between the macroscopic model and the numerical homogenization estimates is observed, especially for stiff to moderately-soft matrix materials. An important outcome of the numerical simulations is the independence of the current magnetization to the stretch part of the deformation gradient. This is taken into account in the model by considering an only rotation-dependent remanent magnetic field as an internal variable. We further show that there is no need for an additional mechanical internal variable. Finally, the model is employed to solve macroscopic boundary value problems involving slender h -MRE structures and the results match excellently with experimental data from literature. Crucial differences are found between uniformly and non-uniformly pre-magnetized h -MREs in terms of their pre-magnetization and the associated self-fields.

56 citations


Journal ArticleDOI
TL;DR: In this paper, a high-order shear and normal deformation theory for the bending of FGM plates is presented, and the number of unknown functions involved in displacement field is only four.
Abstract: This paper presents a high-order shear and normal deformation theory for the bending of FGM plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. Based on the novel shear and normal deformation theory, the position of neutral surface is determined and the governing equilibrium equations based on neutral surface are derived. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Navier-type analytical solution is obtained for functionally graded plate subjected to transverse load for simply supported boundary conditions. The accuracy of the present theory is verified by comparing the obtained results with other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending responses of the FGM plates are studied.

55 citations


Journal ArticleDOI
TL;DR: In this paper, the authors make use of up to 570 clusters with measured properties at X-ray, microwave, and infrared wavelengths to construct ten different cluster scaling relations and test the isotropy of the local Universe; to our knowedge, they present five of these scaling relations for the first time.
Abstract: The hypothesis that the late Universe is isotropic and homogeneous is adopted by most cosmological studies, including studies of galaxy clusters. The cosmic expansion rate H 0 is thought to be spatially constant, while bulk flows are often presumed to be negligible compared to the Hubble expansion, even at local scales. The effects of bulk flows on the redshift–distance conversion are hence usually ignored. Any deviation from this consensus can strongly bias the results of such studies, and thus the importance of testing these assumptions cannot be understated. Scaling relations of galaxy clusters can be effectively used for this testing. In previous works, we observed strong anisotropies in cluster scaling relations, whose origins remain ambiguous. By measuring many different cluster properties, several scaling relations with different sensitivities can be built. Nearly independent tests of cosmic isotropy and large bulk flows are then feasible. In this work, we make use of up to 570 clusters with measured properties at X-ray, microwave, and infrared wavelengths to construct ten different cluster scaling relations and test the isotropy of the local Universe; to our knowedge, we present five of these scaling relations for the first time. Through rigorous and robust tests, we ensure that our analysis is not prone to generally known systematic biases and X-ray absorption issues. By combining all available information, we detect an apparent 9% spatial variation in the local H 0 between (l , b )∼(280° , −15° ) and the rest of the sky. The observed anisotropy has a nearly dipole form. Using isotropic Monte Carlo simulations, we assess the statistical significance of the anisotropy to be > 5σ . This result could also be attributed to a ∼900 km s−1 bulk flow, which seems to extend out to at least ∼500 Mpc. These two effects will be indistinguishable until more high-z clusters are observed by future all-sky surveys such as eROSITA.

50 citations


Journal ArticleDOI
TL;DR: In this article, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium, where the medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field.
Abstract: In this investigation, a computational analysis is conducted to study a magneto-thermoelastic problem for an isotropic perfectly conducting half-space medium. The medium is subjected to a periodic heat flow in the presence of a continuous longitude magnetic field. Based on Moore–Gibson–Thompson equation, a new generalized model has been investigated to address the considered problem. The introduced model can be formulated by combining the Green–Naghdi Type III and Lord–Shulman models. Eringen’s non-local theory has also been applied to demonstrate the effect of thermoelastic materials which depends on small scale. Some special cases as well as previous thermoelasticity models are deduced from the presented approach. In the domain of the Laplace transform, the system of equations is expressed and the problem is solved using state space method. The converted physical expressions are numerically reversed by Zakian’s computational algorithm. The analysis indicates the significant influence on field variables of non-local modulus and magnetic field with larger values. Moreover, with the established literature, the numerical results are satisfactorily examined.

45 citations


Journal ArticleDOI
TL;DR: In this article, the first order shear deformation theory of shells is used to investigate the effects of shear strains and rotary inertia on the vibration frequencies of a conical-spherical functionally graded material (FGM) shell.
Abstract: Natural frequencies of a conical–spherical functionally graded material (FGM) shell are obtained in this study. It is assumed that the conical and spherical shell components have identical thickness. The system of joined shell is made from FGMs, where properties of the shell are graded through the thickness direction. The first order shear deformation theory of shells is used to investigate the effects of shear strains and rotary inertia. The Donnel type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations are discretized using the semi-analytical generalized differential quadrature (GDQ) method. Considering various types of boundary conditions for the shell ends and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells with the data of conventional finite element software, parametric studies are carried out for the system of combined moderately thick conical–spherical joined shells made of FGMs and various types of end supports.

45 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used magnetotransport measurements to probe the superconducting anisotropy in Nd0.775Sr0.225NiO2 and found that the upper critical field is surprisingly isotropic at low temperatures despite the layered crystal structure.
Abstract: The recent observation of superconductivity in thin-film infinite-layer nickelates1–3 offers a different angle from which to investigate superconductivity in layered oxides4. A wide range of candidate models have been proposed5–10, which emphasize single- or multi-orbital electronic structure, Kondo or Hund’s coupling and analogies to cuprates. Further experimental characterization of the superconducting state is needed to develop a full understanding of the nickelates. Here we use magnetotransport measurements to probe the superconducting anisotropy in Nd0.775Sr0.225NiO2. We find that the upper critical field is surprisingly isotropic at low temperatures despite the layered crystal structure. In a magnetic field, the superconductivity is strongly Pauli-limited, such that the paramagnetic effect dominates over orbital de-pairing. Underlying this isotropic response is a substantial anisotropy in the superconducting coherence length, which is at least four times longer in-plane than out-of-plane. A prominent low-temperature upturn in the upper critical field indicates the presence of an unconventional ground state. Measurements of a superconducting infinite-layer nickelate show that its upper critical field is largely isotropic despite its quasi-two-dimensional structure. This indicates that, unusually for layered oxides, the superconductivity is Pauli-limited.

44 citations


Journal ArticleDOI
TL;DR: A robust and efficient bottom-up strategy with micro/nanoscale structure design to regenerate an isotropic wood from natural wood particles as a high-performance sustainable structural material that shows superior water resistance and fire retardancy properties to natural pine wood.
Abstract: Construction of sustainable high-performance structural materials is a core part of the key global sustainability goal. Many efforts have been made in this field; however, challenges remain in terms of lowering costs by using all-green basic building blocks and improving mechanical properties to meet the demand of practical applications. Here, we report a robust and efficient bottom-up strategy with micro/nanoscale structure design to regenerate an isotropic wood from natural wood particles as a high-performance sustainable structural material. Regenerated isotropic wood (RGI-wood) exceeds the limitations of the anisotropic and inconsistent mechanical properties of natural wood, having isotropic flexural strength of ∼170 MPa and flexural modulus of ∼10 GPa. RGI-wood also shows superior water resistance and fire retardancy properties to natural pine wood. Mass production of large sized RGI-wood and functional RGI-wood nanocomposites can also be achieved.

42 citations


Journal ArticleDOI
TL;DR: In this article, the authors analyzed the natural frequencies of sigmoid functionally graded (FG) sandwich beams having various configurations employing the high-order shear deformation theory, and derived the governing equations for higher-order HSDT.

41 citations


Journal ArticleDOI
TL;DR: In this paper, two strategies are proposed to design isotropic triply periodic minimal surface (TPMS) structures, where numerical homogenization theory and finite element analysis methods are utilized to study the relationship between TPMS parameters and the elastic modulus or anisotropy properties.

36 citations


Journal ArticleDOI
TL;DR: In this article, the resonance phenomenon in anisotropic and functionally graded nano-size structure is investigated in a doubly curved shell which is modeled exploiting a quasi-three-dimensional model and nonlocal strain gradient theory in order to predict the small-size effects.

Journal ArticleDOI
TL;DR: In this article, a new slippery surface is prepared by infusing lubricant into the shape memory polymer arrays, which enables the surface microstructure to reversibly transit between the random state and 1D ordered state, accordingly, smart switchable isotropic/anisotropic sliding can be displayed.

Journal ArticleDOI
TL;DR: In this article, the structural, elastic, electronic and optical properties of a new layered perovskite-type oxyfluoride: CsSrNb2O6F were investigated.

Journal ArticleDOI
TL;DR: In this article, the elastic contact between isotropic and anisotropic, rigid, randomly rough surfaces and linearly elastic counterfaces as well as the subsequent Reynolds flow through the gap between the two contacting solids was numerically studied.
Abstract: In this work, we numerically study the elastic contact between isotropic and anisotropic, rigid, randomly rough surfaces and linearly elastic counterfaces as well as the subsequent Reynolds flow through the gap between the two contacting solids. We find the percolation threshold to depend on the fluid flow direction when the Peklenik number indicates anisotropy unless the system size clearly exceeds the roll-off wave length parallel to the easy flow direction. A critical contact area near 0.415 is confirmed. Heuristically corrected effective-medium treatments satisfactorily provide Reynolds fluid flow conductances, e.g., for isotropic roughness, we identify accurate closed-form expressions, which only depend on the mean gap and the relative contact area.

Journal ArticleDOI
TL;DR: In this paper, the free vibrations of graphene platelet reinforced composite (GPLRC) cylindrical shells were investigated using the first-order shear deformation theory of shells and the Donnell kinematic relations.


Journal ArticleDOI
TL;DR: In this paper, the authors prove a global uniqueness result for the Calderon inverse problem for a general quasilinear isotropic conductivity equation on a bounded open set with smooth boundary in dimension n ≥ 3.

Journal ArticleDOI
TL;DR: In this paper, a hybrid structure (HS) was designed and fabricated via Fused Deposition Modelling, which combines the geometrical features of a traditional primarily axial-deformation dominated octet cell and a primarily bending-dominated rhombic dodecahedron (RD), and the quasi-static compressive responses of such lattices were examined and compared with those of the constituent structures.
Abstract: Additively manufactured lightweight lattice structures are being widely studied, one aspect being their energy absorption characteristics under large deformation, because their load–deformation responses can be adjusted by specifically tailoring the geometry of constituent cells. In this study, a newly-proposed hybrid structure (HS), which combines the geometrical features of a traditional primarily axial-deformation dominated octet cell and a primarily bending-dominated rhombic dodecahedron (RD), is designed and fabricated via Fused Deposition Modelling. To ascertain whether the geometrical hybrid enhances the energy absorption performance, the quasi-static compressive responses of such lattices are examined and compared with those of the constituent structures, i.e. the octet and RD. It is noted that the layer-wise additive manufacturing process affects the isotropy of the lattices, as it introduces angle-dependent strut material properties. To study this, the mechanical responses of lattice samples compressed along the rise (printing) and transverse directions are compared. Energy absorption efficiency criteria are adopted to identify the onset of the densification phase, and to evaluate how closely they approximate an ideal energy absorber. Finite element models are also established to study the effect of cell topology and loading direction on the resulting deformation modes and failure patterns. Compression tests along the rise direction show that the proposed novel hybrid structure displays a high stiffness and strength comparable to the octet, as well as a relatively stable post-yield stress–strain behaviour similar to that of an RD. The study demonstrates that the octet and HS topologies are significantly affected by the direction of compression, which alters the stress level and changes the deformation mode. The reason for this is analysed by examining deformation at the cell level, and this is substantiated by FE simulation of compression of cell assemblies, and CT scan images of actual lattices.

Journal ArticleDOI
16 Jul 2021
TL;DR: In this article, the authors reviewed 85 isotropic constitutive models based on both the phenomenological theory and the micromechanical network theory proposed from the 1940s to 2019 and developed a fitting algorithm which can realize the automatic fitting optimization and determination of the parameters of all SEFs reviewed.
Abstract: Nonlinear finite element analysis is widely used for structural optimization of the design and the reliability analysis of complex elastomeric components. However, high-precision numerical results cannot be achieved without reliable strain energy functions (SEFs) of the rubber or rubber nanocomposite material. Although hyperelastic constitutive models have been studied for nearly 80 years, selecting one that accurately describes rubber's mechanical response is still a challenge. This work reviews 85 isotropic SEFs based on both the phenomenological theory and the micromechanical network theory proposed from the 1940s to 2019. A fitting algorithm which can realize the automatic fitting optimization and determination of the parameters of all SEFs reviewed is developed. The ability of each SEF to reproduce the experimental data of both the unfilled and highly filled rubber nanocomposite is quantitatively assessed based on a new proposed evaluation index. The top 30 SEFs for the unfilled rubber and the top 14 SEFs for the highly filled rubber nanocomposite are presented in the ranking lists. Finally, some suggestions on how to select an appropriate hyperelastic constitutive model are given, and the perspective on the future progress of constitutive models is summarized.

Journal ArticleDOI
TL;DR: In this paper, a series of uniaxial and triaxial compression tests were performed on slate samples with different diameters at different foliation orientations with respect to the direction of the major principal stress.
Abstract: A series of uniaxial and triaxial compression tests were performed on slate samples with different diameters at different foliation orientations with respect to the direction of the major principal stress. The size effect and anisotropy in slate, as a transversely isotropic rock, were investigated, and the research focused on aspects of elastic properties, uniaxial compressive strength (UCS), triaxial compressive strength (TCS), and triaxial residual strength (TRS). In the five elastic constants for slate, only the Young’s modulus parallel to the isotropic plane is size dependent. The UCS follows a descending size-effect model developed from coal. The size-effect behaviors of the UCS and TCS are similar. Two size-dependent failure criteria are proposed by incorporating the size-effect model for UCS into the modified Hoek–Brown and Saeidi failure criteria and are verified against experimental data. This is the first time that the relationship among the compressive strength, specimen size, foliation orientation and confining pressure has been comprehensively captured for transversely isotropic rock. Without an evident size effect, the anisotropic TRS has also been effectively captured by a modified cohesion loss model, and two bound equations for the brittleness index are finally proposed for transversely isotropic rock. This work promises to provide an upscaling method for determining the mechanical parameters of transversely isotropic rocks in practical engineering.

Journal ArticleDOI
TL;DR: Anssari-Benam and Bucchi as discussed by the authors proposed a two-parameter constitutive model for isotropic incompressible hyperelastic generalized neo-Hookean materials.
Abstract: In a recent paper in this journal by Anssari-Benam and Bucchi (2021), the authors have proposed a new two-parameter constitutive model for isotropic incompressible hyperelastic generalized neo-Hookean materials. The model reflects the limiting chain extensibility characteristic of non-Gaussian molecular models for rubber. A major contribution of Anssari-Benam and Bucchi (2021) is in showing that the model proposed there is superior to the well-known two-parameter Gent model when fitting with a large variety of experimental data for rubber for the homogeneous deformations of uniaxial, equi-biaxial and pure shear. Moreover, for all of these deformations, a fitting with data is achieved with a single set of values for the parameters with a narrow range of variation. In the present note, we establish a simple direct relation between the new model and the classical Gent model. The large body of research results on the mechanical behavior of rubber-like materials based on the latter model are thus readily applicable to the new model. Some other directions for widening the applicability of the new model are also suggested.

Journal ArticleDOI
TL;DR: In this article, a model for the anisotropic and loading-direction dependent stiffness degradation of short-fiber reinforced thermoplastics subjected to high-cycle fatigue loading is investigated.

Journal ArticleDOI
TL;DR: A simple model for the ramp-cliff structures is developed and shown to characterize the scalar derivative statistics very well, which accurately captures how the small-scale isotropy is restored in the large-Sc limit, and additionally suggests a possible correction to the Batchelor length scale as the relevant smallest scale in the Scalar field.
Abstract: Passive scalars advected by three-dimensional Navier-Stokes turbulence exhibit a fundamental anomaly in odd-order moments because of the characteristic ramp-cliff structures, violating small-scale isotropy. We use data from direct numerical simulations with grid resolution of up to 8192^{3} at high Peclet numbers to understand this anomaly as the scalar diffusivity, D, diminishes, or as the Schmidt number, Sc=ν/D, increases; here ν is the kinematic viscosity of the fluid. The microscale Reynolds number varies from 140 to 650 and Sc varies from 1 to 512. A simple model for the ramp-cliff structures is developed and shown to characterize the scalar derivative statistics very well. It accurately captures how the small-scale isotropy is restored in the large-Sc limit, and additionally suggests a possible correction to the Batchelor length scale as the relevant smallest scale in the scalar field.

Journal ArticleDOI
TL;DR: In this paper, numerical models of structural components that deteriorate primarily due to geometric instabilities under multiaxis cyclic loading are sensitive to both the assumed geometric imperfections and the assumed geometry imperfections.
Abstract: Numerical models of structural components that deteriorate primarily due to geometric instabilities under multiaxis cyclic loading are sensitive to both the assumed geometric imperfections

Journal ArticleDOI
TL;DR: Wang et al. as discussed by the authors presented a new computer-aided design compatible body-fitted particle generator, termed as CAD-BPG, for arbitrarily complex 3-D geometry, which can accurately tackle arbitrarily complex geometry representation and describe the corresponding geometry surface by constructing an implicit zero level-set function on Cartesian background mesh.
Abstract: Generating body-fitted particle distribution for arbitrarily complex geometry underpins the applications of particle-based method to engineering and bioengineering and is highly challenging, and thus hinders the potential of particle methods. In this paper, we present a new computer-aided design (CAD) compatible body-fitted particle generator, termed as CAD-BPG, for arbitrarily complex 3-D geometry. By parsing a CAD model, the present method can accurately tackle arbitrarily complex geometry representation and describe the corresponding geometry surface by constructing an implicit zero level-set function on Cartesian background mesh. To achieve a body-fitted and isotropic particle distribution, physics-driven relaxation process with surface bounding governed by the transport-velocity formulation of smoothed particle hydrodynamics (SPH) methodology is conducted to characterize the particle evolution. A set of examples, ranging from propeller, stent structures and anatomical heart models, show simplicity, accuracy and versatility of the present CAD-BPG for generating body-fitted particle distribution of arbitrarily complex 3-D geometry. Last but not least, the present CAD-BPG is applied for modeling wave-structure interaction, where wave interaction with an oscillating wave surge converter is studied, and the results show that the present method not only provides an efficient and easy-to-implement pre-processing tool for particle-based simulation but also improves the numerical accuracy compared with lattice particle distribution. Consequently, the propose CAD-BPG sheds light on simulating real-world applications by particle-based methods for researchers and engineers.

Journal ArticleDOI
TL;DR: In this article, the effect of the bedding plane dip angle and the application of the findings to an anti-dip interbedded rock slope is also studied, and the proposed failure probability model considering rock damage shows good practicality when applied to a slope with discrete failure probabilities in various parts.

Journal ArticleDOI
TL;DR: In this paper, a new generative design method using topology optimization was proposed to find novel micro-lattice architectures, to enable pentamode properties through the overall elastic deformation of the micro lattice.


Journal ArticleDOI
TL;DR: A heterogenous, nearly incompressible, transverse isotropic (NITI) finite element (FE) model with key advantages for use in MR elastography of fibrous soft tissue is described, allowing investigation of MRE inversion performance in a realistic setting where the ground truth and underlying mechanical behavior are known.
Abstract: In this study, we describe numerical implementation of a heterogenous, nearly incompressible, transverse isotropic (NITI) finite element (FE) model with key advantages for use in MR elastography of fibrous soft tissue. MR elastography (MRE) estimates heterogenous property distributions from MR-measured harmonic motion fields based on assumed mechanical models of tissue response. Current MRE property estimation methods usually assume isotropic properties, which cause inconsistencies arising from model-data mismatch when anisotropy is present. In this study, we use a NITI model parameterized by a base shear modulus, shear anisotropy, tensile anisotropy, and an isotropic bulk modulus, which describes the mechanical behavior of tissues with aligned fiber structures well. Property and fiber direction heterogeneity are implemented at the level of FE Gauss points, which allows high-resolution diffusion tensor imaging (DTI) data to be incorporated easily into the model. The resulting code was validated against analytical solutions and a commercial FEM package, and is suitable for incorporation into nonlinear inversion MRE algorithms. Simulations of MRE in brain tissue with heterogeneous properties and anisotropic fiber tracts, which produced wavefields similar to experimental MRE, were generated from anatomical, DTI and MRE image data, allowing investigation of MRE inversion performance in a realistic setting where the ground truth and underlying mechanical behavior are known. Two established isotropic inversion algorithms - nonlinear inversion (NLI) and local direct inversion (LDI) - were applied to simulated MRE data. Both algorithms performed well in simple isotropic homogenous cases; however, heterogeneity cased substantial artifacts in LDI arising from violation of local homogeneity assumptions. NLI was able to recover accurate heterogenous displacement fields in the presence of measurement noise. Isotropic NLI inversion of simulated anisotropic data (generated using the NITI model) produced maps of isotropic mechanical properties with (undesirable) dependence on the wavefield. Local anisotropy also caused wavefield-dependent errors of 7% in nearby isotropic structures, compared to 10% in the anisotropic structures.

Journal ArticleDOI
TL;DR: In this paper, an efficient theoretical mixed mode I/II fracture criterion is proposed for fracture investigation of orthotropic materials considering the effects of non-singular stress term in William's series expansion.