Numerical Evaluation of Size Effect in Piezoelectric Micro-Beam with Linear Micromorphic Electroelastic Theory

Cao, Weizhong; Yang, Xinhua; Tian, Xiaobao

doi:10.1017/jmech.2014.25

Cited by 12 publications

(4 citation statements)

References 34 publications

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“…(2012) introduced a novel formulation to model the mechanical behavior of steel fiber-reinforced concrete. Cao et al. (2014) proposed a linear micromorphic electro-elastic theory to solve the bending problems of piezoelectric micro-beams.…”

Section: Introductionmentioning

confidence: 99%

“…Based on MMT, Oliver et al (2012) introduced a novel formulation to model the mechanical behavior of steel fiber-reinforced concrete. Cao et al (2014) proposed a linear micromorphic electro-elastic theory to solve the bending problems of piezoelectric micro-beams. Based on the generalized MMT, Lee and Wang (2011) presented the constitutive equations for solids and fluids.…”

Section: Introductionmentioning

confidence: 99%

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Vibration analysis of two-dimensional micromorphic structures using quadrilateral and triangular elements

Vajargah

Ansari²

2022

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PurposeThe paper aims to presents a numerical analysis of free vibration of micromorphic structures subjected to various boundary conditions.Design/methodology/approachTo accomplish this objective, first, a two-dimensional (2D) micromorphic formulation is presented and the matrix representation of this formulation is given. Then, two size-dependent quadrilateral and triangular elements are developed within the commercial finite element software ABAQUS. User element subroutine (UEL) is used to implement the micromorphic elements. These non-classical elements are capable of capturing the micro-structure effects by considering the micro-motion of materials. The effects of the side length-to-length scale parameter ratio and boundary conditions on the vibration behavior of 2D micro-structures are discussed in detail. The reliability of the present finite element method (FEM) is confirmed by the convergence studies and the obtained results are validated with the results available in the literature. Also, the results of micromorphic theory (MMT) are compared with those of micropolar and classical elasticity theories.FindingsThe study found that the size effect becomes very significant when the side length of micro-structures is close to the length scale parameter.Originality/value The study is to analyze the free vibrations of 2D micro-structures based on MMT; to develop a 2D formulation for micromorphic continua within ABAQUS; to propose quadrilateral and triangular micromorphic elements using UEL and to investigate size effects on the vibrational behavior of micro-structures with various geometries.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibration analysis of two-dimensional micromorphic structures using quadrilateral and triangular elements

Vajargah

Ansari²

2022

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“…Madeo et al [53] used the relaxed micromorphic model proposed in [54,55] so as to investigate wave propagation in unbounded continua with microstructure. The linear micromorphic electroelastic theory was utilized by Cao et al [56] to solve the bending problems of piezoelectric microbeams. Rcently, Misra and Poorsolhjouy [57] employed the granular micromechanics approach to develop a micromorphic continuum model for elasticity of granular media.…”

Section: Introductionmentioning

confidence: 99%

Micromorphic prism element

Ansari

Bazdid-Vahdati

Shakouri

et al. 2016

Mathematics and Mechanics of Solids

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Within the framework of micromorphic elasticity theory, a finite element approach capable of capturing the microstructure effect is developed to describe the bending behavior of microplates. To this end, the micromorphic theory is generally formulated first. The matrix representation of this formulation is then given from which a prism micromorphic element, including the effects of micro-deformation degrees of freedom of material particles, is proposed. The element is applied to the bending problem of micromorphic rectangular and circular plates subject to different boundary conditions. Selected numerical results are presented to show the microstructure influence on the bending of plates with various geometrical parameters. It is revealed that the element is capable of predicting the mechanical behavior of micromorphic continua in an efficient way.

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“…However, their implementations to the mechanics of advanced structures, e.g., beams, are scarce. A few studies used the micromorphic theory for the electroelastic bending of piezoelectric beams 36 , the finite element modeling of micromorphic continua [37][38][39] , the static deformation of geometrically nonlinear micromorphic shells 40,41 , and the static bending of micropolar beams 42,43 .…”

mentioning

confidence: 99%

A Micromorphic Beam Theory for Beams with Elongated Microstructures

Shaat

Ghavanloo

Emam

2020

Sci Rep

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A novel micromorphic beam theory that considers the exact shape and size of the beam's microstructure is developed. the new theory complements the beam theories that are based on the classical mechanics by modeling the shape and size of the beam's microstructure. this theory models the beam with a microstructure that has shape and size and exhibits microstrains that are independent of the beam's macroscopic strains. this theory postulates six independent degrees of freedom to describe the axial and transverse displacements and the axial and shear microstrains of the beam. the detailed variational formulation of the beam theory is provided based on the reduced micromorphic model. For the first time, the displacement and microstrain fields of beams with elongated microstructures are developed. In addition, six material constants are defined to fully describe the beam's microscopic and macroscopic stiffnesses, and two length scale parameters are used to capture the beam size effect. A case study of clamped-clamped beams is analytically solved to show the influence of the beam's microstructural stiffness and size on its mechanical deformation. The developed micromorphic beam theory would find many important applications including the mechanics of advanced beams such as meta-, phononic, and photonic beams. Various beam theories have been developed based on the classical theory of mechanics. In these theories, the beam is a colony of an infinite number of particles each of which is a mass point. The beam exhibits a displacement field that describes the motion of a particle in a two-dimensional domain. In Euler-Bernoulli beam theory, the displacement field is expressed in terms of the axial and transverse displacements of the beam's mid-plane, and it assumes that the normal to the mid-plane remains undeformed and normal to the mid-plane after deformation 1-4. The Euler-Bernoulli beam theory is limited to slender beams with high length-to-thickness ratio where the transverse shear effect is neglected. It was revealed that the Euler-Bernoulli beam theory is applicable for beams with length-to-thickness ratio of 20 and above depending on the material 1-4. For thick beams, the Euler-Bernoulli beam theory underestimates the deflection (i.e., the transverse displacement of the mid-plane) and overestimates the natural frequencies 1-5. Timoshenko beam theory outweighs the Euler-Bernoulli beam theory by accounting for the transverse shear strain and the rotary inertia effects 1,2,6. The displacement field of the Timoshenko beam theory is expressed assuming that the normal to the mid-plane can rotate independently, but it remains straight after deformation 1,2,6. More advanced beam theories that account for the distortion of the normal to the mid-plane have been developed 4,5,7. With the development of advanced materials, beams with independent microstructure are developed. The microstructure of these advanced beams would rotate and/or deform. These beams gave exceptional dynamical characteristics 8-12. For instance, metamaterial...

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Numerical Evaluation of Size Effect in Piezoelectric Micro-Beam with Linear Micromorphic Electroelastic Theory

Cited by 12 publications

References 34 publications

Vibration analysis of two-dimensional micromorphic structures using quadrilateral and triangular elements

Vibration analysis of two-dimensional micromorphic structures using quadrilateral and triangular elements

Micromorphic prism element

A Micromorphic Beam Theory for Beams with Elongated Microstructures

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