scholarly journals Elasticity Approach to Predict Shape Transformation of Functionally Graded Mechanical Metamaterial under Tension

Materials ◽  
2021 ◽  
Vol 14 (13) ◽  
pp. 3452
Author(s):  
Mohammad Javad Khoshgoftar ◽  
Ali Barkhordari ◽  
Sajjad Seifoori ◽  
Mohammad Javad Mirzaali
Keyword(s):  
Elastic Stiffness ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Unit Cell ◽  
Uniaxial Tensile ◽  
Geometrical Parameters ◽  
Design Strategies ◽  
Shape Transformation ◽  
Complex Deformation ◽  
Mechanical Metamaterials

The re-entrant structures are among the simple unit cell designs that have been widely used in the design of mechanical metamaterials. Changing the geometrical parameters of these unit cell structures, their overall elastic properties (i.e., elastic stiffness and Poisson’s ratio), can be simultaneously tuned. Therefore, different design strategies (e.g., functional gradient) can be implemented to design advanced engineering materials with unusual properties. Here, using the theory of elasticity and finite element modeling, we propose a fast and direct approach to effectively design the microarchitectures of mechanical metamaterials with re-entrant structures that allow predicting complex deformation shapes under uniaxial tensile loading. We also analyze the efficiency of this method by back calculating the microarchitectural designs of mechanical metamaterials to predict the complex 1-D external contour of objects (e.g., vase and foot). The proposed approach has several applications in creating programmable mechanical metamaterials with shape matching properties for exoskeletal and soft robotic devices.

The Influence of Multiple Inclusions on the Cauchy Stress of a Spherical Particle-Reinforced Composite Under Uniaxial Loading

2014 ◽  
Author(s):  
Ke Niu ◽  
Armin Abedini ◽  
Zengtao Chen
Keyword(s):  
Spherical Particle ◽  
Single Particle ◽  
Volume Fraction ◽  
Unit Cell ◽  
Spherical Particles ◽  
Uniaxial Tensile ◽  
Cauchy Stress ◽  
Particle Volume ◽  
Volume Fractions ◽  
Unit Cells

This paper investigates the influence of multiple inclusions on the Cauchy stress of a spherical particle-reinforced metal matrix composite (MMC) under uniaxial tensile loading condition. The approach of three-dimensional cubic multi-particle unit cell is used to investigate the 15 non-overlapping identical spherical particles which are randomly distributed in the unit cell. The coordinates of the center of each particle are calculated by using the Random Sequential Adsorption algorithm (RSA) to ensure its periodicity. The models with reinforcement volume fractions of 10%, 15%, 20% and 25% are evaluated by using the finite element method. The behaviour of Cauchy stress for each model is analyzed at a far-field strain of 5%. For each reinforcement volume fraction, four models with different particle spatial distributions are evaluated and averaged to achieve a more accurate result. At the same time, single-particle unit cell and analytical model were developed. The stress-strain curves of multi-particle unit cells are compared with single-particle unit cells and the tangent homogenization model coupled with the Mori-Tanaka method. Only little scatters were found between unit cells with the same particle volume fractions. Multi-particle unit cells predict higher response than single particle unit cells. As the volume fraction of reinforcements increases, the Cauchy stress of MMCs increases.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

scholarly journals Structural Transformations in Crystals Induced by Radiation and Pressure. Part 7. Molecular and Crystal Geometries as Factors Deciding about Photochemical Reactivity under Ambient and High Pressures

Crystals ◽  
2018 ◽  
Vol 8 (7) ◽  
pp. 299 ◽  
Author(s):  
Krzysztof Konieczny ◽  
Arkadiusz Ciesielski ◽  
Julia Bąkowicz ◽  
Tomasz Galica ◽  
Ilona Turowska-Tyrk
Keyword(s):  
High Pressures ◽  
Unit Cell ◽  
Geometrical Parameters ◽  
Isopropyl Group ◽  
Unit Cell Parameters ◽  
Photochemical Reactivity ◽  
Space Group ◽  
Cell Parameters ◽  
Pressure Part ◽  
Asymmetric Unit Cell

We studied the photochemical reactivity of salts of 4-(2,4,6-triisopropylbenzoyl)benzoic acid with propane-1,2-diamine (1), methanamine (2), cyclohexanamine (3), and morpholine (4), for compounds (1), (3), and (4) at 0.1 MPa and for compounds (1) and (2) at 1.3 GPa and 1.0 GPa, respectively. The changes in the values of the unit cell parameters after UV irradiation and the values of the intramolecular geometrical parameters indicated the possibility of the occurrence of the Norrish–Yang reaction in the case of all the compounds. The analysis of the intramolecular geometry and free spaces revealed which o-isopropyl group takes part in the reaction. For (1), the same o-isopropyl group should be reactive at ambient and high pressures. In the case of (2), high pressure caused the phase transition from the space group I2/a with one molecule in the asymmetric unit cell to the space group P1¯ with two asymmetric molecules. The analysis of voids indicated that the Norrish–Yang reaction is less probable for one of the two molecules. For the other molecule, the intramolecular geometrical parameters showed that except for the Norrish–Yang reaction, the concurrent reaction leading to the formation of a five-membered ring can also proceed. In (3), both o-isopropyl groups are able to react; however, the bigger volume of a void near 2-isopropyl may be the factor determining the reactivity. For (4), only one o-isopropyl should be reactive.

Thermo-mechanical analysis and optimization of functionally graded rotating disks

2020 ◽  
Vol 55 (5-6) ◽  
pp. 159-171
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande ◽  
Luciano Moro
Keyword(s):  
Finite Element ◽  
Equivalent Stress ◽  
Rotating Disk ◽  
Mechanical Analysis ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Rotating Disks ◽  
Maximum Equivalent Stress ◽  
Quadratic Programming Method ◽  
Stress Uniformity

The behavior of thermo-mechanical stresses in functionally graded axisymmetric rotating hollow disks with variable thickness is analyzed. The material is assumed to be functionally graded in the radial direction. First, a two-dimensional axisymmetric model of the functionally graded rotating disk is developed using the finite element method. Exact solutions for stresses are then obtained assuming that the plane theory of elasticity holds. These solutions are in accordance with finite element ones, thus showing the validity of the assumption. Finally, in order to reduce the maximum equivalent stress along the radius, the optimization of the material distribution is addressed. To avoid subsequent finite element simulations in the optimization process, which can be computationally demanding, a nonlinear constrained optimization problem is proposed, for which the solution is obtained numerically by the sequential quadratic programming method, showing prominent results in terms of equivalent stress uniformity.

scholarly journals INFLUENCE OF CREEP CONCRETE ON SPACE STABILITY THIN-WALLED DOME COVERINGS

2021 ◽  
Vol 1 (24) ◽  
Author(s):  
Ekaterina Prokshits ◽  
Sergey Gridnev ◽  
Olga Sotnikova ◽  
Iana Zolotukhina
Keyword(s):  
Theory Of Elasticity ◽  
Deformation Condition ◽  
Software Systems ◽  
Geometrical Parameters ◽  
Loss Of Stability ◽  
Construction Mechanics ◽  
Body Construction ◽  
Calculation Results ◽  
Load Action ◽  
Thin Walled

The task was set, due to the capabilities of modern software systems, to assess the effect of the increase in inelastic deformations under prolonged load action on the loss of stability of thin-walled dome coverings. The study of the dependences of the forms of the loss of stability of dome covering from creep concrete that will help further with optimization calculations when determining of the most influencing parameters of designs. Calculation results of thin-walled concrete dome roof of circular outline under the influence of operational loadings with use of two modern program complexes are given in article. It is investigated intense and deformation condition of dome coverings as a part of construction from position of forecasting of possible forms of loss of stability, with use of opportunities of the final and element «MidasCivil» computer system. In work provisions of the theory of elasticity, mechanics of deformation of solid body, construction mechanics and also methods of mathematical modeling based on application of finite element method are used. The received results give the chance to rationally select geometrical parameters and material of design and also to set structural strength safety factors at the solution of problems of stability of different covers taking into account possible creep of material.

Influence of coupled fields on free vibration and static behavior of functionally graded magneto-electro-thermo-elastic plate

2017 ◽  
Vol 29 (7) ◽  
pp. 1430-1455 ◽  
Author(s):  
Vinyas Mahesh ◽  
Piyush J Sagar ◽  
Subhaschandra Kattimani
Keyword(s):  
Finite Element ◽  
Electric Fields ◽  
Elastic Plate ◽  
Coupling Effect ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Geometrical Parameters ◽  
Element Formulation ◽  
Elastic Plates

In this article, the influence of full coupling between thermal, elastic, magnetic, and electric fields on the natural frequency of functionally graded magneto-electro-thermo-elastic plates has been investigated using finite element methods. The contribution of overall coupling effect as well as individual elastic, piezoelectric, piezomagnetic, and thermal phases toward the stiffness of magneto-electro-thermo-elastic plates is evaluated. A finite element formulation is derived using Hamilton’s principle and coupled constitutive equations of magneto-electro-thermo-elastic material. Based on the first-order shear deformation theory, kinematics relations are established and the corresponding finite element model is developed. Furthermore, the static studies of magneto-electro-elastic plate have been carried out by reducing the fully coupled finite element formulation to partially coupled state. Particular attention has been paid to investigate the influence of thermal fields, electric fields, and magnetic fields on the behavior of magneto-electro-elastic plate. In addition, the effect of pyrocoupling on the magneto-electro-elastic plate has also been studied. Furthermore, the effect of geometrical parameters such as aspect ratio, length-to-thickness ratio, stacking sequence, and boundary conditions is studied in detail. The investigation may contribute significantly in enhancing the performance and applicability of functionally graded magneto-electro-thermo-elastic structures in the field of sensors and actuators.

Size-Dependent Geometrically Nonlinear Forced Vibration Analysis of Functionally Graded First-Order Shear Deformable Microplates

2016 ◽  
Vol 32 (5) ◽  
pp. 539-554 ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
A. Shahabodini
Keyword(s):  
Size Effect ◽  
Nonlinear Equations ◽  
Forced Vibration ◽  
Plate Theory ◽  
Couple Stress Theory ◽  
Continuation Method ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Governing Equations ◽  
First Order

AbstractIn this paper, a non-classical plate model capturing the size effect is developed to study the forced vibration of functionally graded (FG) microplates subjected to a harmonic excitation transverse force. To this, the modified couple stress theory (MCST) is incorporated into the first-order shear deformation plate theory (FSDPT) to account for the size effect through one length scale parameter, only. Strong form of nonlinear governing equations and associated boundary conditions are obtained using Hamilton's principle. The solution process is implemented on two domains. The generalized differential quadrature (GDQ) method is first employed to discretize the governing equations on the space domain. A Galerkin-based scheme is then applied to extract a reduced set of the nonlinear equations of Duffing-type. On the second domain, through a time differentiation matrix operator, the set of ordinary differential equations are transformed into the discrete form on time domain. Eventually, a system of the parameterized nonlinear equations is acquired and solved via the pseudo-arc length continuation method. The frequency response curve of the microplate is sketched and the effects of various material and geometrical parameters on it are evaluated.

scholarly journals Divergent Design of Mechanical Metamaterials Clan Deducted from Arc-serpentine Curve

2021 ◽  
Author(s):  
Shengli Mi ◽  
Hongyi Yao ◽  
Xiaoyu Zhao ◽  
Wei Sun
Keyword(s):  
Thick Plate ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Design Strategies ◽  
Shape Morphing ◽  
Mechanical Metamaterials ◽  
Unit Cells ◽  
Combinatorial Principles ◽  
Composite Curve ◽  
Typical Design

Abstract The exotic properties of mechanical metamaterials are determined by their unit-cells' structure and spatial arrangement, in analogy with the atoms of conventional materials. Companioned with the mechanism of structural or cellular materials1–5, the ancient wisdom of origami6–11 and kirigami12–16 and the involvement of multiphysics interaction2,17,18 enrich the programable mechanical behaviors of metamaterials, including shape-morphing8,12,14,16,19, compliance4,5,8,17,20, texture2,18,21, and topology11,18,22−25. However, typical design strategies are mainly convergent, which transfers various structures into one family of metamaterials that are relatively incompatible with the others and do not fully bring combinatorial principles3,10,26 into play. Here, we report a divergent strategy that designs a clan of mechanical metamaterials with diverse properties derived from a symmetric curve consisting of serpentines and arcs. We derived this composite curve into planar and cubic unit-cells and modularized them by attaching magnetics. Moreover, stacking each of them yields two- and three-dimensional auxetic metamaterials, respectively. Assembling with both modules, we achieved three thick plate-like metamaterials separately with flexibility, in-plane buckling, and foldability. Furthermore, we demonstrated that the hybrid of paradox properties is possible by combining two of the above assembles. We anticipate that this divergent strategy paves the path of building a hierarchical library of diverse combinable mechanical metamaterials and making conventional convergent strategies more efficient to various requests. Main

scholarly journals Mechanical metamaterials at the theoretical limit of isotropic elastic stiffness

Nature ◽  
2017 ◽  
Vol 543 (7646) ◽  
pp. 533-537 ◽  
Author(s):  
J. B. Berger ◽  
H. N. G. Wadley ◽  
R. M. McMeeking
Keyword(s):  
Elastic Stiffness ◽  
Theoretical Limit ◽  
Mechanical Metamaterials

Stress-Constrained Design of Functionally Graded Lattice Structures With Spline-Based Dimensionality Reduction

2019 ◽  
Author(s):  
Jenmy Zimi Zhang ◽  
Conner Sharpe ◽  
Carolyn Conner Seepersad
Keyword(s):  
Three Dimensional ◽  
Surrogate Models ◽  
Functionally Graded ◽  
Unit Cell ◽  
Cell Stiffness ◽  
Stress Constraint ◽  
Compact Representation ◽  
Lattice Structures ◽  
Worst Case ◽  
Graded Lattice

Abstract This paper presents a computationally tractable approach for designing lattice structures for stiffness and strength. Yielding in the mesostructure is determined by a worst-case stress analysis of the homogenization simulation data. This provides a physically meaningful, generalizable, and conservative way to estimate structural failure in three-dimensional functionally graded lattice structures composed of any unit cell architectures. Computational efficiency of the design framework is ensured by developing surrogate models for the unit cell stiffness and strength as a function of density. The surrogate models are then used in the coarse-scale analysis and synthesis. The proposed methodology further uses a compact representation of the material distribution via B-splines, which reduces the size of the design parameter space while ensuring a smooth density variation that is desirable for manufacturing. The proposed method is demonstrated in compliance minimization studies using two types of unit cells with distinct mechanical properties. The effects of B-spline mesh refinement and the presence of a stress constraint on the optimization results are also investigated.

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