Basic theorems in linear micromorphic thermoelectroelasticity and their primary application

Cao, Weizhong; Yang, Xinhua; Tian, Xiaobao

doi:10.1016/s0894-9166(13)60016-6

Cited by 5 publications

(4 citation statements)

References 19 publications

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“…Based on MMT, Cordero et al [26] investigated grain size effects in metal polycrystals. The linear micromorphic thermo-electro-elasticity was employed by Cao et al [27] so as to describe the nano- and micro-scale behavior of thermo-electro-elastic materials. Bhattacharyya and Mukhopadhyay [28] performed some modifications to the linear MPT.…”

Section: Introductionmentioning

confidence: 99%

Finite element analysis of micromorphic and micropolar continua based on two-dimensional elasticity

Bazdid-Vahdati

Oskouie

Ansari

et al. 2018

Mathematics and Mechanics of Solids

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In this paper, within the framework of two-dimensional (2D) elasticity, a novel finite element formulation is proposed based on the micropolar theory (MPT) and the micromorphic theory (MMT). First, general formulations are developed for the micromorphic and micropolar continua in the context of 2D elasticity. Then, they are presented in a matrix form which is useful from the computational viewpoint. In the next step, using the matricized MPT and MMT formulations, a linear finite element approach including the effects of micro-deformation and micro-rotation degrees of freedom (DOFs) of material particles is developed, and a quadratic size-dependent element is proposed accordingly. Two test problems are solved to reveal the efficiency of the developed formulation. The influence of the length scale parameter on the bending of micromorphic and micropolar plates is illustrated in the given examples. Furthermore, comparisons are made between the results obtained from classical elasticity theory and those calculated based upon MPT and MMT.

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Section: Introductionmentioning

confidence: 99%

Finite element analysis of micromorphic and micropolar continua based on two-dimensional elasticity

Bazdid-Vahdati

Oskouie

Ansari

et al. 2018

Mathematics and Mechanics of Solids

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“…Based on MMT, Zhang et al (2012) studied the mechanical behavior of a bi-material strip under simple shear. Based on the linear MMT, Cao et al (2013) studied the thermo-electro-elastic materials with remarkable micro-structure. Faraji-Oskouie et al (2019) investigated the free vibration behavior of 3D micromorphic square plates.…”

Section: Introductionmentioning

confidence: 99%

“…(2012) studied the mechanical behavior of a bi-material strip under simple shear. Based on the linear MMT, Cao et al. (2013) studied the thermo-electro-elastic materials with remarkable micro-structure.…”

Section: Introductionmentioning

confidence: 99%

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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“…Several aspects of the micromorphic materials theory have been the subject of a wide number of papers, such as: [11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Influence of Geometric Equations in Mixed Problem of Porous Micromorphic Bodies with Microtemperature

Codarcea-Munteanu

Marín

2020

Mathematics

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The study of the mixed initial-boundary value problem, corresponding to the thermoelasticity of porous micromorphic materials under the influence of microtemperatures, represents the main objective of this article. Achieving qualitative results on the existence, uniqueness and continuous dependence on the initial data and loads, of the solution of the mixed problem, implies a new perspective of approaching these topics, imposed by the large number of unknowns, which increases the complexity of equations and conditions that characterize the thermoelastic porous micromorphic materials with microtemperatures. The use of the semigroup theory of operators represents the optimal solution for deducing these results, the theory being adaptable to the requirements of the demonstrations, the mixed problem turning into a problem of Cauchy type, with regards to an equation of evolution on a Hilbert space, chosen appropriately.

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Basic theorems in linear micromorphic thermoelectroelasticity and their primary application

Cited by 5 publications

References 19 publications

Finite element analysis of micromorphic and micropolar continua based on two-dimensional elasticity

Finite element analysis of micromorphic and micropolar continua based on two-dimensional elasticity

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

Influence of Geometric Equations in Mixed Problem of Porous Micromorphic Bodies with Microtemperature

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