Constitutive equations for micropolar hyper-elastic materials

Ramezani, Shojaa; Naghdabadi, R.; Sohrabpour, Saeed

doi:10.1016/j.ijsolstr.2008.10.009

Cited by 31 publications

(34 citation statements)

References 24 publications

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“…, and Ramezani et al . . An elastic‐predictor/plastic‐corrector algorithm has been developed and described in detail.…”

Section: Discussionmentioning

confidence: 99%

“…Motivated by Ramezani et al . , the elastic part of the specific free energy potential is chosen as where Note that because of plastic incompressibility; that is, . Furthermore, given that , where b e is the elastic part of the standard left Cauchy–Green tensor, the term

\overset{ρ}{true} ψ_{NH} ({\overset{bold-italicV}{true}}^{e})

is identified as a standard Neo‐Hook free energy potential.…”

Section: The Constitutive Modelmentioning

confidence: 99%

“…Following Gauthier and Jashman , we introduced an internal length scale L as

L MathClass-punc: MathClass-rel= \sqrt{\frac{β MathClass-bin+ γ}{2 μ}} MathClass-punc.

We note that the expression in Equation deviates from the corresponding terms in only in the choice of g ( J ).…”

Section: The Constitutive Modelmentioning

confidence: 99%

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Micropolar hyper‐elastoplasticity: constitutive model, consistent linearization, and simulation of 3D scale effects

Bauer

Dettmer

Perić

et al. 2012

Numerical Meth Engineering

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SUMMARY A computational model for micropolar hyperelastic‐based finite elastoplasticity that incorporates isotropic hardening is developed. The basic concepts of the non‐linear micropolar kinematic framework are reviewed, and a thermodynamically consistent constitutive model that features Neo‐Hooke‐type elasticity and generalized von Mises plasticity is described. The integration of the constitutive initial value problem is carried out by means of an elastic‐predictor/plastic‐corrector algorithm, which retains plastic incompressibility. The solution procedure is developed carefully and described in detail. The consistent material tangent is derived. The micropolar constitutive model is implemented in an implicit finite element framework. The numerical example of a notched cylindrical bar subjected to large axial displacements and large twist angles is presented. The results of the finite element simulations demonstrate (i) that the methodology is capable of capturing the size effect in three‐dimensional elastoplastic solids in the finite strain regime, (ii) that the formulation possesses a regularizing effect in the presence of strain localization, and (iii) that asymptotically quadratic convergence rates of the Newton–Raphson procedure are achieved. Throughout this paper, effort is made to present the developments as a direct extension of standard finite deformation computational plasticity. Copyright © 2012 John Wiley & Sons, Ltd.

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“…, and Ramezani et al . . An elastic‐predictor/plastic‐corrector algorithm has been developed and described in detail.…”

Section: Discussionmentioning

confidence: 99%

\overset{ρ}{true} ψ_{NH} ({\overset{bold-italicV}{true}}^{e})

is identified as a standard Neo‐Hook free energy potential.…”

Section: The Constitutive Modelmentioning

confidence: 99%

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Micropolar hyper‐elastoplasticity: constitutive model, consistent linearization, and simulation of 3D scale effects

Bauer

Dettmer

Perić

et al. 2012

Numerical Meth Engineering

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“…It should not be confused with 'penalty multiplier' as in [17] or [18]. From (37) it follows that for typical values v ∈ [0; 0.5] one obtains α t ∈ [2,3]. The values of α t so estimated are greater than those usually used in numerical simulations presented, among others, in [5][6][7][8].…”

Section: Numerical Examplesmentioning

confidence: 98%

“…Some of the recent advances concerning micropolar hyperelasticity in planar case may be found e.g. in [3] and references given therein.…”

Section: Introductionmentioning

confidence: 99%

On some constitutive equations for micropolar plates

ChrÃ3sÌcielewski

Witkowski²

2009

Z Angew Math Mech

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In this paper we discuss the constitutive relations for micropolar plates recently obtained by Altenbach and Eremeyev. We pay particular attention to their relation for the resultant drilling stress couple and compare it with that used so far in the statically and kinematically exact nonlinear six‐parameter shell theory. Using the results of Altenbach and Eremeyev, we present bounds on values of the constitutive parameter αt from the six‐parameter shell theory model. Some representative numerical simulations show how the drilling stiffness αt affects the FEM results.

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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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Constitutive equations for micropolar hyper-elastic materials

Cited by 31 publications

References 24 publications

Micropolar hyper‐elastoplasticity: constitutive model, consistent linearization, and simulation of 3D scale effects

Micropolar hyper‐elastoplasticity: constitutive model, consistent linearization, and simulation of 3D scale effects

On some constitutive equations for micropolar plates

A micropolar shell model for hard‐magnetic soft materials

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