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Showing papers on "Isotropy published in 2019"


Journal ArticleDOI
TL;DR: In this paper, a novel family of smooth-shell structures is introduced as mechanical metamaterials of exceptional specific energy absorption capacity, and the exact shape of the shell midplane is determined through the minimization of a bending energy based measure of the overall curvature.
Abstract: A novel family of smooth-shell structures is introduced as mechanical metamaterials of exceptional specific energy absorption capacity. The proposed shell structures respect all symmetries of the face-centered cubic crystal. To obtain a smooth curvature shell structure, the exact shape of the shell mid-plane is determined through the minimization of a bending-energy based measure of the overall curvature. Among the members of this new family, the mechanical properties of a Triply Periodic Minimal Surface (TPMS) -like architecture and an elastically-isotropic derivate are investigated in detail. The TPMS-like structure showed important anisotropy in both its small and large strain responses, with loading-direction dependent differences in stiffness of more than 100%. The mechanical properties of the elastically-isotropic shell-lattice turned out to be close to the mean value for all directions of loading for the TPMS-like structures. For relative densities ranging from 1% to 50%, the shell-lattices always exhibited a higher mechanical performance than truss-lattices of equal density. For relative densities greater than 20%, the mechanical response of the shell-lattices is more stable than that of truss-lattices which makes them particularly suitable as higher order structures in hierarchical metamaterial design. The computational results are partially confirmed through compression experiments on additively-manufactured stainless steel specimens. A direct comparison of the stress–strain curve of additively-manufactured stainless steel 316 L with that of sheets made from the same alloy revealed an increase in yield strength of about 30% related to the selective laser melting process.

172 citations


Journal ArticleDOI
TL;DR: In this paper, three families of shell-lattices are derived from Simple-Cubic (SC), Face-Centered Cubic (FCC) and Body-centered centered cubic (BCC) tube-structures using a parameterized surface-smoothening functional.

144 citations


Journal ArticleDOI
Abstract: The free vibration analysis of laminated nanocomposite plates and shells using first-order shear deformation theory and the generalized differential quadrature method is presented. Each layer of the laminate is modeled as a three-phase composite. An example of such composite material is given by a polymeric matrix reinforced with carbon nanotubes (CNTs). CNTs enhance the mechanical properties of the polymer matrix and the nanocomposite is treated as an isotropic material; a micromechanics model is used to compute the engineering constants of the isotropic hybrid material. This approach based on the Eshelby–Mori–Tanaka scheme takes into account the agglomeration of the nanoparticles in the matrix. The second step consists in combining this enriched matrix with unidirectional and oriented reinforcing fibers to obtain a fibrous composite with improved mechanical features. The overall mechanical properties of each orthotropic ply are evaluated through different micromechanics approaches. Each technique is illustrated in detail and the transversely isotropic properties of the three-phase layers are completely defined. The effects of both CNTs agglomeration and the mass fraction of these particles are investigated comparing with the results obtained by various homogenization techniques. POLYM. COMPOS., 2017. © 2017 Society of Plastics Engineers

139 citations


Journal ArticleDOI
TL;DR: In this article, two classes of nonlinear problems driven by differential operators with unbalanced growth are studied, and the associated energy is a double-phase functional, either isotropic or anisotropic.
Abstract: We are concerned with the study of two classes of nonlinear problems driven by differential operators with unbalanced growth, which generalize the \((p,q)\)- and \((p(x),q(x))\)-Laplace operators. The associated energy is a double-phase functional, either isotropic or anisotropic. The content of this paper is in relationship with pioneering contributions due to P. Marcellini and G. Mingione.

109 citations


Journal ArticleDOI
TL;DR: In this article, the free vibration of porous square plate, circular plate, and rectangle plate with a central circular hole in the framework of isogeometric analysis (IGA) was studied.

102 citations


Journal ArticleDOI
TL;DR: In this article, a fast Fourier transform-based homogenization method was proposed to obtain the elastic tensor of cellular materials with high Young's modulus at the cost of low shear modulus.

101 citations


Journal ArticleDOI
TL;DR: In this paper, the Minimal Geometric Deformation decoupling method was used to obtain general static interior solutions for a BTZ vacuum from the most general isotropic solution.
Abstract: In this work we implement the Minimal Geometric Deformation decoupling method to obtain general static interior solutions for a BTZ vacuum from the most general isotropic solution in $$2+1$$ dimensions including the cosmological constant $$\varLambda $$ . We obtain that the general solution can be generated only by the energy density of the original isotropic sector, so that this quantity plays the role of a generating function. Although as a particular example we study the static star with constant density, the method here developed can be easily applied to more complex situations described by other energy density profiles.

96 citations


Journal ArticleDOI
TL;DR: In this article, a numerical method for calculating the mass transfer coefficient in fibrous media is presented, where pressure driven flow is modelled using the Lattice Boltzmann Method.

81 citations


Journal ArticleDOI
TL;DR: In this paper, the authors obtained analytic anisotropic spherical solutions in f ( R ) scenario through gravitationally decoupled minimal geometric deformation technique and analyzed the physical acceptability and stability of the resulting solutions via graphical observations of effective energy density, effective radial as well as tangential pressure, energy conditions, stability through speed of sound and adiabatic index.

67 citations


Journal ArticleDOI
TL;DR: In this paper, a geometrically nonlinear functionally graded pipe conveying hot fluid subjected to a harmonic lateral excitation is analyzed, where the material properties of the pipe are assumed to vary continuously and smoothly through its radial direction according to a power law function.

64 citations



Journal ArticleDOI
TL;DR: In this paper, the Stoughton and Yoon (2009) criterion was used to model the anisotropic/asymmetry-induced distortion of the yield surface of metal sheets.

Journal ArticleDOI
TL;DR: It is shown how deviations from the multiple Gaussian compartments assumption conflates orientation dispersion with ensemble variance in isotropic diffusivity arising due to intracompartmental kurtosis.

Journal ArticleDOI
TL;DR: In this paper, the global mean Green operator for the entire embedded fiber network is obtained from one of infinite planar alignments of infinite fibers, which the network can be seen as an interpenetrated set of, with the fiber interactions being fully accounted for in the alignments.
Abstract: Composites comprising included phases in a continuous matrix constitute a huge class of meta-materials, whose effective properties, whether they be mechanical, physical or coupled, can be selectively optimized by using appropriate phase arrangements and architectures. An important subclass is represented by “network-reinforced matrices,” say those materials in which one or more of the embedded phases are co-continuous with the matrix in one or more directions. In this article, we present a method to study effective properties of simple such structures from which more complex ones can be accessible. Effective properties are shown, in the framework of linear elasticity, estimable by using the global mean Green operator for the entire embedded fiber network which is by definition through sample spanning. This network operator is obtained from one of infinite planar alignments of infinite fibers, which the network can be seen as an interpenetrated set of, with the fiber interactions being fully accounted for in the alignments. The mean operator of such alignments is given in exact closed form for isotropic elastic-like or dielectric-like matrices. We first exemplify how these operators relevantly provide, from classic homogenization frameworks, effective properties in the case of 1D fiber bundles embedded in an isotropic elastic-like medium. It is also shown that using infinite patterns with fully interacting elements over their whole influence range at any element concentration suppresses the dilute approximation limit of these frameworks. We finally present a construction method for a global operator of fiber networks described as interpenetrated such bundles.

Journal ArticleDOI
TL;DR: In this paper, a generalized micropolar bond-based peridynamic model with shear deformability for linear and non-linear problems is proposed, which is derived from the definition of a specific microelastic energy function for micropolastic nonlocal lattices, giving particular attention to numerical implementation aspects of the model.

Journal ArticleDOI
TL;DR: In this article, a hydromechanical model for materials with two porosity scales that accommodates both transverse isotropy at the larger scale and non-Darcy flow at the smaller scale is presented.

Journal ArticleDOI
TL;DR: The findings not only provide a reference database for the elastic behaviors of versatile MoTe2 phases but also illuminate a general strategy for the mechanical investigation of any isotropic and anisotropic 2D materials.
Abstract: Biaxial deformation of suspended membranes widely exists and is used in nanoindentation to probe elastic properties of structurally isotropic two-dimensional (2D) materials. However, the elastic properties and, in particular, the fracture behaviors of anisotropic 2D materials remain largely unclarified in the case of biaxial deformation. MoTe2 is a polymorphic 2D material with both isotropic (2H) and anisotropic (1T′ and Td) phases and, therefore, an ideal system of single-stoichiometric materials with which to study these critical issues. Here, we report the elastic properties and fracture behaviors of biaxially deformed, polymorphic MoTe2 by combining temperature-variant nanoindentation and first-principles calculations. It is found that due to similar atomic bonding, the effective moduli of the three phases deviate by less than 15%. However, the breaking strengths of distorted 1T′ and Td phases are only half the value of 2H phase due to their uneven distribution of bonding strengths. Fractures of both ...

Journal ArticleDOI
TL;DR: In this article, the authors used Brazilian tests to identify failure conditions for a range of load contact types and anisotropy angles (representing orientations of the transversely isotropic planes with respect to direction normal to the loading).

Journal ArticleDOI
TL;DR: In this article, the face stability of plane strain tunnel heading in anisotropic and non-homogeneous clays is investigated by the LB finite element limit analysis (FELA) with second-order cone programming (SOCP).


Journal ArticleDOI
TL;DR: It is shown that the presence of the perinuclear actin cap (apical stress fibers), such as those encountered in cells subject to physiological forces, causes a strongly non-axisymmetric membrane deformation during indentation reflecting local mechanical anisotropy.
Abstract: The measurement of local mechanical properties of living cells by nano/micro indentation relies on the foundational assumption of locally isotropic cellular deformation As a consequence of assumed isotropy, the cell membrane and underlying cytoskeleton are expected to locally deform axisymmetrically when indented by a spherical tip Here, we directly observe the local geometry of deformation of membrane and cytoskeleton of different living adherent cells during nanoindentation with the integrated Atomic Force (AFM) and spinning disk confocal (SDC) microscope We show that the presence of the perinuclear actin cap (apical stress fibers), such as those encountered in cells subject to physiological forces, causes a strongly non-axisymmetric membrane deformation during indentation reflecting local mechanical anisotropy In contrast, axisymmetric membrane deformation reflecting mechanical isotropy was found in cells without actin cap: cancerous cells MDA-MB-231, which naturally lack the actin cap, and NIH 3T3 cells in which the actin cap is disrupted by latrunculin A Careful studies were undertaken to quantify the effect of the live cell fluorescent stains on the measured mechanical properties Using finite element computations and the numerical analysis, we explored the capability of one of the simplest anisotropic models - transverse isotropy model with three local mechanical parameters (longitudinal and transverse modulus and planar shear modulus) - to capture the observed non-axisymmetric deformation These results help identifying which cell types are likely to exhibit non-isotropic properties, how to measure and quantify cellular deformation during AFM indentation using live cell stains and SDC, and suggest modelling guidelines to recover quantitative estimates of the mechanical properties of living cells

Journal ArticleDOI
TL;DR: In this article, the authors studied the full-time dependence of holographic complexity in anisotropic black branes and showed that the complexity growth rate does not saturate the Lloyd's bound at late times.
Abstract: We use the $\text{complexity}=\text{action}$ (CA) conjecture to study the full-time dependence of holographic complexity in anisotropic black branes. We find that the time behavior of holographic complexity of anisotropic systems shares a lot of similarities with the behavior observed in isotropic systems. In particular, the holographic complexity remains constant for some initial period, and then it starts to change so that the complexity growth rate violates the Lloyd's bound at initial times, and approaches this bound from above at later times. Compared with isotropic systems at the same temperature, the anisotropy reduces the initial period in which the complexity is constant and increases the rate of change of complexity. At late times the difference between the isotropic and anisotropic results is proportional to the pressure difference in the transverse and longitudinal directions. In the case of charged anisotropic black branes, we find that the inclusion of a Maxwell boundary term is necessary to have consistent results. Moreover, the resulting complexity growth rate does not saturate the Lloyd's bound at late times.

Journal ArticleDOI
TL;DR: Stiff isotropic lattices de novo with topology optimization, an approach based on continuum finite element analysis are designed and it is demonstrated that they are as efficient as those designed by rule, despite appearing to violate the Maxwell criterion.
Abstract: Materials with a stochastic microstructure, like foams, typically exhibit low mechanical stiffness, whereas lattices with a designed microarchitecture often show notably improved stiffness. These periodic architected materials have previously been designed by rule, using the Maxwell criterion to ensure that their deformation is dominated by the stretching of their struts. Classical designs following this rule tend to be anisotropic, with stiffness depending on the load orientation, but recently, isotropic designs have been reported by superimposing complementary anisotropic lattices. We have designed stiff isotropic lattices de novo with topology optimization, an approach based on continuum finite element analysis. Here, we present results of experiments on these lattices, fabricated by additive manufacturing, that validate predictions of their performance and demonstrate that they are as efficient as those designed by rule, despite appearing to violate the Maxwell criterion. These findings highlight the enhanced potential of topology optimization to design materials with unprecedented properties.

Journal ArticleDOI
TL;DR: In this article, the free vibration of carbon nanotubes reinforced composite beams is analyzed using the first-order shear deformation theory and the finite element method with various boundary conditions.
Abstract: In the present study, the free vibration of laminated functionally graded carbon nanotube reinforced composite beams is analyzed. The laminated beam is made of perfectly bonded carbon nanotubes reinforced composite (CNTRC) layers. In each layer, single-walled carbon nanotubes are assumed to be uniformly distributed (UD) or functionally graded (FG) distributed along the thickness direction. Effective material properties of the two-phase composites, a mixture of carbon nanotubes (CNTs) and an isotropic polymer, are calculated using the extended rule of mixture. The first-order shear deformation theory is used to formulate a governing equation for predicting free vibration of laminated functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. The governing equation is solved by the finite element method with various boundary conditions. Several numerical tests are performed to investigate the influence of the CNTs volume fractions, CNTs distributions, CNTs orientation angles, boundary conditions, length-to-thickness ratios and the numbers of layers on the frequencies of the laminated FG-CNTRC beams. Moreover, a laminated composite beam combined by various distribution types of CNTs is also studied.

Journal ArticleDOI
TL;DR: In this paper, a unified formulation of full geometrically nonlinear refined plate theory in a total Lagrangian approach was developed to investigate the large-deflection and post-buckling response of isotropic rectangular plates.
Abstract: Accurate predictions of the in-service nonlinear response of highly flexible structures in the geometrically nonlinear regime are of paramount importance for their design and failure evaluation. This paper develops a unified formulation of full geometrically nonlinear refined plate theory in a total Lagrangian approach to investigate the large-deflection and post-buckling response of isotropic rectangular plates. Based on the Carrera Unified Formulation (CUF), various kinematics of two-dimensional plate structures are consistently implemented via an index notation and an arbitrary expansion function of the generalized variables in the thickness direction, resulting in lower- to higher-order plate models with only pure displacement variables via the Lagrange polynomial expansions. Furthermore, the principle of virtual work and a finite element approximation are exploited to straightforwardly and easily formulate the nonlinear governing equations. By taking into account the three-dimensional full Green–Lagrange strain components, the explicit forms of the secant and tangent stiffness matrices of unified plate elements are presented in terms of the fundamental nuclei, which are independent of the theory approximation order. The Newton–Raphson linearization scheme combined with a path-following method based on the arc-length constraint is utilized to solve the geometrically nonlinear problem. Numerical assessments, including the large-deflection response of square plates subjected to transverse uniform pressure and the post-buckling analysis of slender plates under compression loadings, are finally conducted to confirm the capabilities of the proposed CUF plate model to predict the large-deflection and post-buckling equilibrium curves as well as the stress distributions with high accuracy.

Journal ArticleDOI
TL;DR: In this article, the authors consider a triply periodic minimal surface of types Primitive, Diamond, Gyroid, and I-WP and show that core-shell structures respond drastically differently not only in their stiffness but also for each of these observed properties compared to their counterparts with complete filling.

Journal ArticleDOI
TL;DR: In this paper, a five-variable refined plate theory in conjunction with the nonlocal strain gradient theory is developed for hexagonal materials and the results of the displacements are compared with those predicted by other 2D and quasi-3D plate theories available in the literature.

Journal ArticleDOI
TL;DR: In this paper, analytical damped free-vibration and frequency response solutions are obtained for the analysis of composite plates structures embedding viscoelastic layers on the basis of the principle of virtual displacement, layer-wise models related to linear up to fourth order variations of the unknown variables in the thickness direction are treated.

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a data-driven approach to decompose the one-dimensional data into three dimensions for nonlinear elastic material modeling without the construction of analytic mathematical functions for the material law.

Journal ArticleDOI
TL;DR: In this article, a nonconforming finite element formulation for the modelling of nanoplates using second-order positive/negative strain gradient nonlocal theories is presented, which is computationally more efficient than the conforming element with better accuracy and convergence rate.
Abstract: The strain gradient nonlocal theory is important to include the size effects of nanostructures in classical continuum theory with the corresponding development of computationally efficient numerical tool such as finite elements for the analysis of such structures with different boundary conditions. However, there is no literature on the finite element formulation of second-order strain gradient elastic plates. The weak form of the governing equation of motion of the Kirchhoff nanoplate using second-order positive/negative strain gradient nonlocal theories requires C2 continuity of transverse displacement. In this paper, a new computationally efficient nonconforming finite element formulation for the modelling of nanoplates using second-order positive/negative strain gradient nonlocal theories is presented. The performance of the developed finite element is compared with conforming finite element for rectangular isotropic Kirchhoff nanoplates with different boundary conditions. Analytical solution for static bending, free vibration, and buckling under biaxial in-plane compressive loading are also obtained for rectangular all edges simply supported isotropic Kirchhoff nanoplate for the comparison purpose. The nonconforming element is found to be computationally more efficient than the conforming element with better accuracy and convergence rate. The negative strain gradient model predicts results matching with the experimental results available in the literature.