On modelling of wave propagation in microstructured solids

Engelbrecht, Jüri; Berezovski, Arkadi

doi:10.3176/eng.2013.3.01

Cited by 2 publications

(1 citation statement)

References 34 publications

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“…This way the rightful criticism of Truesdell [45] does not hold for our treatment. This generality has already proved to be crucial for the idea of dual internal variables [27], which turned out to be a powerful unification method for waves in solids [46,47,48,49,50], and also for deriving generalized mechanics [51,28].…”

Section: Introductionmentioning

confidence: 99%

Distinguished rheological models for solids in the framework of a thermodynamical internal variable theory

Asszonyi

Fülöp

Ván

2014

Continuum Mech. Thermodyn.

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We present and analyze a thermodynamical theory of rheology with single internal variable. The universality of the model is ensured as long as the mesoscopic and/or microscopic background processes satisfy the applied thermodynamical principles, which are the second law, the basic balances and the existence of an additional-tensorial-state variable. The resulting model, which we suggest to call the Kluitenberg-Verhás body, is the Poynting-Thomson-Zener body with an additional inertial element, or, in other words, is the extension of Jeffreys model to solids. We argue that this Kluitenberg-Verhás body is the natural thermodynamical building block of rheology. An important feature of the presented methodology is that nontrivial inequality-type restrictions arise for the four parameters of the model. We compare these conditions and other aspects to those of other known thermodynamical approaches, like Extended Irreversible Thermodynamics or the original theory of Kluitenberg.

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Section: Introductionmentioning

confidence: 99%

Distinguished rheological models for solids in the framework of a thermodynamical internal variable theory

Asszonyi

Fülöp

Ván

2014

Continuum Mech. Thermodyn.

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Soliton-like solutions based on geometrically nonlinear Cosserat micropolar elasticity

2016

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The Cosserat model generalises an elastic material taking into account the possible microstructure of the elements of the material continuum. In particular, within the Cosserat model the structured material point is rigid and can only experience microrotation, which is also known as micropolar elasticity. We present the geometrically nonlinear theory taking into account all possible interaction terms between the elastic and microelastic structure. This is achieved by considering the irreducible pieces of the deformation gradient and of the dislocation curvature tensor. In addition we also consider the so-called Cosserat coupling term. In this setting we seek soliton type solutions assuming small elastic displacements, however, we allow the material points to experience full rotations which are not assumed to be small. By choosing a particular ansatz we are able to reduce the system of equations to a Sine-Gordon type equation which is known to have soliton solutions.

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On modelling of wave propagation in microstructured solids

Cited by 2 publications

References 34 publications

Distinguished rheological models for solids in the framework of a thermodynamical internal variable theory

Distinguished rheological models for solids in the framework of a thermodynamical internal variable theory

Soliton-like solutions based on geometrically nonlinear Cosserat micropolar elasticity

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