Micromorphic prism element

Ansari, R.; Bazdid-Vahdati, M.; Shakouri, Amir; Norouzzadeh, A.; Rouhi, H.

doi:10.1177/1081286516637115

Cited by 23 publications

(14 citation statements)

References 60 publications

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“…This is also consistent with the constitutive relations proposed in high-order gradient continuum theories consists of the term ml 2 or ll 2 . Such an approach was also used in later research works [20][21][22][23]. So, for determined values of c 1 and c 2 , considering the constitutive equations and strain energy function leads to write the micro-scale parameters in the following form…”

Section: Constraints On Elastic Parametersmentioning

confidence: 99%

“…Isbuga and Regueiro [21] provided a three-dimensional FEA of a linear isotropic micromorphic cube structure. Recently, three-dimensional (3D) and two-dimensional (2D) micromorphic elements were developed by Ansari et al [22,23] to address the bending behavior of small-scale materials. Also, examples of non-classical finite element models of micropolar materials can be found in the literature [24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

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Large elastic deformation of micromorphic shells. Part II. Isogeometric analysis

Norouzzadeh

Ansari

Darvizeh

2019

Mathematics and Mechanics of Solids

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In Part I of this study, a variational formulation was presented for the large elastic deformation problem of micromorphic shells. Using the novel matrix-vector format presented for the kinematic model, constitutive relations, and energy functions, an isogeometric analysis (IGA)-based solution strategy is developed, which appropriately estimates the macro- and micro-deformation field components. Due to the capability of constructing exact geometries and the powerful mesh refinement tools, IGA can be successfully applied to solve the equilibrium equations with dominant nonlinear terms. It is known that different types of locking phenomena take place in the conventional finite element analysis of thin shells based on low-order elements. Non-standard finite element models with mixed interpolation schemes and additional degrees of freedom (DOFs) or the ones used the high-order Lagrangian shell elements which require high computational costs, are the available solutions to tackle locking issues. The present 16-DOFs IGA is found to be efficient because of possessing a good rate of convergence and providing locking-free stable responses for micromorphic shells. Such a conclusion is found from several comparative studies with available data in the well-known macro-scale benchmark problems based on the classical elasticity as well as the corresponding numerical examples studied in nano-scale beam-, plate-, cylindrical shell- and spherical shell-type structures on the basis of the micromorphic continuum theory.

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Section: Constraints On Elastic Parametersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Large elastic deformation of micromorphic shells. Part II. Isogeometric analysis

Norouzzadeh

Ansari

Darvizeh

2019

Mathematics and Mechanics of Solids

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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 .…”

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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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“…In 3M theories, each particle can rotate and deform independently regardless of the motion of the centroid of the particle. More details about the 3M theories as well as their applications can be found in [19][20][21][22][23][24][25]. The nonlocal elasticity theory was originally proposed by Kroner [26] and improved by Eringen [27][28] and Eringen and Edelen [29].…”

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confidence: 99%

A review of continuum mechanics models for size-dependent analysis of beams and plates

Thai

Nguyen

et al. 2017

Composite Structures

326

112

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This paper presents a comprehensive review on the development of higher-order continuum models for capturing size effects in small-scale structures. The review mainly focus on the size-dependent beam, plate and shell models developed based on the nonlocal elasticity theory, modified couple stress theory and strain gradient theory due to their common use in predicting the global behaviour of small-scale structures. In each higher-order continuum theory, various size-dependent models based on the classical theory, first-order shear deformation theory and higher-order shear deformation theory were reviewed and discussed. In addition, the development of finite element solutions for size-dependent analysis of beams and plates was also highlighted. Finally a summary and recommendations for future research are presented. It is hoped that this review paper will provide current knowledge on the development of higher-order continuum models and inspire further applications of these models in predicting the behaviour of micro-and nano-structures.

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Micromorphic prism element

Cited by 23 publications

References 60 publications

Large elastic deformation of micromorphic shells. Part II. Isogeometric analysis

Large elastic deformation of micromorphic shells. Part II. Isogeometric analysis

A Micromorphic Beam Theory for Beams with Elongated Microstructures

A review of continuum mechanics models for size-dependent analysis of beams and plates

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