Geometrically nonlinear models of static deformation of micropolar elastic thin plates and shallow shells

Sargsyan, A. A.; Sargsyan, S. H.

doi:10.1002/zamm.202000148

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…Formulations of the micropolar theory to model localized elastic‐plastic deformations (e.g., References 45‐51) and size‐dependent elastic deformations (e.g., References 52‐57) have been developed. Some formulations to model micropolar shells have been also proposed (e.g., References 58‐60). Moreover, the theory has been used in the modeling of lattice structures, crystal plasticity, phononic crystals, chiral auxetic lattices, phase‐field fracture mechanics, and vertebral trabecular bone 61‐66 …”

Section: Introductionmentioning

confidence: 99%

A micropolar shell model for hard‐magnetic soft materials

Dadgar‐Rad

Hossain

2022

Numerical Meth Engineering

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Hard-magnetic soft materials (HMSMs) are particulate composites that particles with high coercivity are dispersed in a soft matrix. Since applying the magnetic loading induces a body couple in HMSMs, the resulting Cauchy stress is predicted to be asymmetric. Therefore, the micropolar continuum theory can be employed to capture the deformation of these materials. On the other hand, the geometries and structures made of HMSMs often possess small thickness compared to the overall dimensions of the body. Accordingly, in the present contribution, a 10-parameter micropolar shell formulation to model the finite elastic deformation of thin hard-magnetic soft structures under magnetic stimuli is developed. The proposed shell formulation allows for using three-dimensional constitutive laws without any need for modification to apply the plane stress assumption in thin structures. A nonlinear finite element formulation is also presented for the numerical solution of the governing equations. To alleviate the locking phenomenon, the enhanced assumed strain method is employed. Several examples are presented that demonstrate the performance and effectiveness of the proposed formulation.

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Section: Introductionmentioning

confidence: 99%

A micropolar shell model for hard‐magnetic soft materials

Dadgar‐Rad

Hossain

2022

Numerical Meth Engineering

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“…Formulations of the micropolar theory to model localized elastic-plastic deformations (e.g., [44][45][46][47][48][49][50]) and size-dependent elastic deformations (e.g., [51][52][53][54][55][56]) have been developed. Some formulations to model micropolar shells have been also proposed (e.g., [57][58][59]). Moreover, the theory has been used in the modeling of lattice structures, crystal plasticity, phononic crystals, chiral auxetic lattices, phase-field fracture mechanics, and vertebral trabecular bone (e.g., [60][61][62][63][64][65]).…”

Section: Introductionmentioning

confidence: 99%

A micropolar shell model for hard-magnetic soft materials

Dadgar‐Rad¹,

Hossain²

2022

Preprint

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Hard-magnetic soft materials (HMSMs) are particulate composites that consist of a soft matrix embedded with particles of high remnant magnetic induction. Since the application of an external magnetic flux induces a body couple in HMSMs, the Cauchy stress tensor in these materials is asymmetric, in general. Therefore, the micropolar continuum theory can be employed to capture the deformation of these materials. On the other hand, the geometries and structures made of HMSMs often possess small thickness compared to the overall dimensions of the body.Accordingly, in the present contribution, a 10-parameter micropolar shell formulation to model the finite elastic deformation of thin structures made of HMSMs and subject to magnetic stimuli is developed. The present shell formulation allows for using three-dimensional constitutive laws without any need for modification to apply the plane stress assumption in thin structures. Due to the highly nonlinear nature of the governing equations, a nonlinear finite element formulation for numerical simulations is also developed. To circumvent locking at large distortions, an enhanced assumed strain formulation is adopted. The performance of the developed formulation is examined in several numerical examples. It is shown that the proposed formulation is an effective tool for simulating the deformation of thin bodies made of HMSMs.

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Large deformation problem of hyperbolic shallow shells with bimodular effect: A perturbation‐variation method

He,

Wang,

Chang

et al. 2024

Z Angew Math Mech

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As an important analytical method, the perturbation‐variation method combines the advantages of perturbation method and variational method, and is widely used for the solution of nonlinear plate and shell problems. In this study, the perturbation‐variation method is used to solve the large deformation problem of a flexible hyperbolic thin shallow shells with different moduli in tension and compression (bimodular effect). First, we establish the governing equations expressed in terms of three displacement components, in which the bimodular effect of materials is considered in physical equations and the large deformation of shell is considered in geometrical equations. Next, we use the perturbation‐variation method to solve the governing equations established, obtaining the perturbation‐variation solution up to third‐order. During the application of the method, the displacements are expressed into perturbation formulas of all levels first, and the unknown constants and functions in the perturbation formulas are determined by the extreme value conditions of the functional established (variational principle), hence the perturbation‐variation method gets its name from this practice. The numerical results from FEM basically agree with the perturbation‐variation solution obtained. The method proposed may be extended into the solution of similar partial differential equations established in applied fields.

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Geometrically nonlinear models of static deformation of micropolar elastic thin plates and shallow shells

Cited by 5 publications

References 12 publications

A micropolar shell model for hard‐magnetic soft materials

A micropolar shell model for hard‐magnetic soft materials

A micropolar shell model for hard-magnetic soft materials

Large deformation problem of hyperbolic shallow shells with bimodular effect: A perturbation‐variation method

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