A Biot–Cosserat two-dimensional elastic nonlinear model for a micromorphic medium

Giorgio, Ivan; Angelo, Michele De; Turco, Emilio; Misra, Anil

doi:10.1007/s00161-019-00848-1

Cited by 52 publications

(20 citation statements)

References 87 publications

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“…Moreover, the phase velocity is found to be greater in case of an interfacial wave (Figure 3(b)) than for a surface wave (Figure 3(a)). Figure 4(a) represents the frequency curve for equation (28) satisfying the cut-off frequency c s k < ω < c 2 k and Figure 4(b) represents the frequency curve for equation (40) satisfying c s k < ω < min(c − 2 k, c + 2 k). In both figures, dispersion curves can be observed for larger values of wave number (k ≥ 1) and for ω ≤ ω 0 and ω ≤ min(ω − 0 , ω + 0 ), respectively, it is found that the angular frequency increases with increasing wave number.…”

Section: Numerical Analysismentioning

confidence: 99%

“…As a result, the micropolar model found various applications in the modelling of media with complex inner microstructures and rotational interactions of material particles, such as granular media [9–12], masonry [13–16], foams and other porous media [17–19], bones [20–22], beam lattices [23, 24], composites and inhomogeneous materials [25–27] and non-linear models [28]. It is also worth noting the straightforward measurements of micropolar moduli provided by Lakes [17], Roger and Lakes [18, 19, 29, 30] and Rueger et al [31].…”

Section: Introductionmentioning

confidence: 99%

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Surface and interfacial anti-plane waves in micropolar solids with surface energy

Chaki

Eremeyev

Singh

2020

Mathematics and Mechanics of Solids

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In this work, the propagation behaviour of a surface wave in a micropolar elastic half-space with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial anti-plane wave between two micropolar elastic half-spaces with interfacial strain and kinetic energies localized at the interface have been studied. The Gurtin–Murdoch model has been adopted for surface and interfacial elasticity. Dispersion equations for both models have been obtained in algebraic form for two types of anti-plane wave, i.e. a Love-type wave and a new type of surface wave (due to micropolarity). The angular frequency and phase velocity of anti-plane waves have been analysed through a numerical study within cut-off frequencies. The obtained results may find suitable applications in thin film technology, non-destructive analysis or biomechanics, where the models discussed here may serve as theoretical frameworks for similar types of phenomena.

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Section: Numerical Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Surface and interfacial anti-plane waves in micropolar solids with surface energy

Chaki

Eremeyev

Singh

2020

Mathematics and Mechanics of Solids

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“…It has also to be remarked that the proposed model has also a strong relation to the so-called generalized models of continuum with scalar (one-dimensional) microstructure by Capriz [17] or Eringen [52,53], see also [23,64,94,104,106]. So it can be used for various applications to material modelling of pressure sensitive materials as those studied in [95,131] or to study some phenomena of phase transitions occurring in solid materials [69,110].…”

Section: Introductionmentioning

confidence: 91%

On nonlinear dilatational strain gradient elasticity

Eremeyev

Cazzani

Dell’Isola

2021

Continuum Mech. Thermodyn.

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We call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the only second gradient effects are due to the inhomogeneous dilatation state of the considered deformable body. The dilatational second gradient continua are strictly related to other generalized models with scalar (one-dimensional) microstructure as those considered in poroelasticity. They could be also regarded to be the result of a kind of “solidification” of the strain gradient fluids known as Korteweg or Cahn–Hilliard fluids. Using the variational approach we derive, for dilatational second gradient continua the Euler–Lagrange equilibrium conditions in both Lagrangian and Eulerian descriptions. In particular, we show that the considered continua can support contact forces concentrated on edges but also on surface curves in the faces of piecewise orientable contact surfaces. The conditions characterizing the possible externally applicable double forces and curve forces are found and examined in detail. As a result of linearization the case of small deformations is also presented. The peculiarities of the model is illustrated through axial deformations of a thick-walled elastic tube and the propagation of dilatational waves.

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“…It is worth noting that this simplification may lose its applicability for materials that possess strong variations and discontinuities of stiffnesses or have highly disordered micro-geometries, which could be deliberately designed as in pantographic metamaterials [17,[43][44][45][46][47][48][49][50][51][52][53][54][55][56][57] or in granular (meta)materials [58]. In these cases, Taylor's series expansion is not representative and additional kinematic descriptors may be introduced to accurately describe the response as in Cosserat or micromorphic media [59,60]. The Green-Saint-Venant tensor G, as well as its gradient…”

Section: Relative Inter-granular Displacement and Related Continuum Deformation Measuresmentioning

confidence: 99%

Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution

Timofeev¹,

Barchiesi

Misra

et al. 2020

Mathematics and Mechanics of Solids

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Mechanical behavior of materials with granular microstructures is confounded by unique features of their grain-scale mechano-morphology, such as the tension–compression asymmetry of grain interactions and irregular grain structure. Continuum models, necessary for the macro-scale description of these materials, must link to the grain-scale behavior to describe the consequences of this mechano-morphology. Here, we consider the damage behavior of these materials based upon purely mechanical concepts utilizing energy and variational approach. Granular micromechanics is accounted for through Piola’s ansatz and objective kinematic descriptors obtained for grain-pair relative displacement in granular materials undergoing finite deformations. Karush–Kuhn–Tucker (KKT)-type conditions that provide the evolution equations for grain-pair damage and Euler–Lagrange equations for evolution of grain-pair relative displacement are derived based upon a non-standard (hemivariational) variational approach. The model applicability is illustrated for particular form of grain-pair elastic energy and dissipation functionals through numerical examples. Results show interesting damage-induced anisotropy evolution including the emergence of a type of chiral behavior and formation of finite localization zones.

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A Biot–Cosserat two-dimensional elastic nonlinear model for a micromorphic medium

Cited by 52 publications

References 87 publications

Surface and interfacial anti-plane waves in micropolar solids with surface energy

Surface and interfacial anti-plane waves in micropolar solids with surface energy

On nonlinear dilatational strain gradient elasticity

Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution

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