Energy pairs in the micropolar continuum

Ramezani, Shojaa; Naghdabadi, R.

doi:10.1016/j.ijsolstr.2006.12.006

Cited by 29 publications

(20 citation statements)

References 20 publications

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“…Additionally, such an approach allows one to analyse other possible work-conjugate pairs of the stress and strain measures within the non-linear micropolar continuum. Some of such pairs have recently been discussed by Ramezani and Naghdabadi (2007).…”

Section: Principle Of Virtual Work and Work-conjugate Strain Measuresmentioning

confidence: 99%

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On natural strain measures of the non-linear micropolar continuum

Pietraszkiewicz

Eremeyev²

2009

International Journal of Solids and Structures

222

125

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a b s t r a c tWe discuss three different ways of defining the strain measures in the non-linear micropolar continuum: (a) by a direct geometric approach, (b) considering the strain measures as the fields required by the structure of local equilibrium conditions, and (c) requiring the strain energy density of the polar-elastic body to satisfy the principle of invariance under superposed rigid-body deformations. The geometric approach (a) generates several twopoint deformation measures as well as some Lagrangian and Eulerian strain measures. The ways (b) and (c) allow one to choose those Lagrangian strain measures which satisfy the additional mechanical requirements. These uniquely selected relative strain measures are called the natural ones. All the strain measures discussed here are formulated in the general coordinate-free form. They are valid for unrestricted translations, stretches and changes of orientations of the micropolar body, and are required to identically vanish in the absence of deformation. The relation of the Lagrangian stretch and wryness tensors derived here to the ones proposed in the literature is thoroughly discussed.

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Section: Principle Of Virtual Work and Work-conjugate Strain Measuresmentioning

confidence: 99%

“…Ramezani and Naghdabadi (2007) referring to Kafadar and Eringen (1971) introduced the coordinate-free form of two Lagrangian strain measures…”

Section: Badur and Pietraszkiewicz (1986)mentioning

confidence: 99%

On natural strain measures of the non-linear micropolar continuum

Pietraszkiewicz

Eremeyev²

2009

International Journal of Solids and Structures

222

125

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“…as a strain measure; tensor Φ * T F * is usually referred to as the Cosserat deformation tensor in micropolar elasticity [Ramezani and Naghdabadi 2007]. For a nonpolar medium, the strain energy is restricted to be a function of a symmetric strain parameter ε * S , which is connected to the symmetric part of the above strain measure by the strain-displacement relation…”

Section: 1mentioning

confidence: 99%

Computational shell mechanics by helicoidal modeling, I: Theory

Merlini

Morandini

2011

J. Mech. Mater. Struct.

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Starting from recently formulated helicoidal modeling in three-dimensional continua, a low-order kinematical model of a solid shell is established. It relies on both the six degrees of freedom (DOFs) on the reference surface, including the drilling DOF, and a dual director -six additional DOFs -that controls the relative rototranslation of the material particles within the thickness. Since the formulation pertains to the framework of the micropolar mechanics, the solid shell mechanical model includes a workless stress variable -the axial vector of the Biot stress tensor, referred to as the Biot-axial -that allows us to handle nonpolar materials. The local Biot-axial is approximated with a linear field across the thickness and relies on two vector parameters. On the reference surface, the dual director is condensed locally together with one Biot-axial parameter, leaving the surface strains and the other Biot-axial parameter as the basic variables governing the two-dimensional internal work functional.The continuum-based shell mechanics are cast in weak incremental form from the beginning. They yield the two-dimensional nonlinear constitutive law of the shell in incremental form, built dynamically along the solution process. Poisson thickness locking, related to the low-order kinematical model, is prevented by a dynamical adaptation of the local constitutive law. No hypotheses are introduced that restrict the amplitudes of displacements, rotations, and strains, so the formulation is suitable for computations with strong geometrical and material nonlinearities, as shown in Part II.

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“…Angle of rotation of the micro-structure constitutes a rotation (pseudo) vector ϕ with magnitude θ and contravariant components ϕ k . The proper orthogonal micro-rotation tensor R corresponding to ϕ is in the following form [1,23] …”

Section: Kinematicsmentioning

confidence: 99%

“…Also, P = det(F) F −1 σ and M = det(F) F −1 m are the micropolar first Piola-Kirchhoff stress and couple stress tensors, respectively. For the case of a purely mechanical process, the power of deformation P per unit reference volume can be written as [1,23] …”

Section: Kinematicsmentioning

confidence: 99%

Micropolar hypo-elasticity

Ramezani

Naghdabadi

2010

Arch Appl Mech

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In this paper, the concept of hypo-elasticity is generalized to the micropolar continuum theory, and the general forms of the constitutive equations of the micropolar hypo-elastic materials are presented. A new co-rotational objective rate whose spin is the micropolar gyration tensor is introduced which describes the deformation of the material in view of an observer attached to the micro-structure. As special case, simplified versions of the proposed constitutive equations are given in which the same fourth-order elasticity tensors are used as in the micropolar linear elasticity. A 2-D finite element formulation for large elastic deformation of micropolar hypo-elastic media based on the simplified constitutive equations in conjunction with Jaumann and gyration rates is presented. As an example, buckling of a shallow arc is examined, and it is shown that an increase in the micropolar material parameters results in an increase in the buckling load of the arc. Also, it is shown that micropolar effects become important for deformations taking place at small scales.

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Energy pairs in the micropolar continuum

Cited by 29 publications

References 20 publications

On natural strain measures of the non-linear micropolar continuum

On natural strain measures of the non-linear micropolar continuum

Computational shell mechanics by helicoidal modeling, I: Theory

Micropolar hypo-elasticity

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