Mechanics of Quasi-Periodic Alloys

Mariano, Paolo Maria

doi:10.1007/s00332-005-0654-5

Cited by 46 publications

(64 citation statements)

References 33 publications

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“…The external boundary of the body can be also considered as a structured surface endowed with a surface energy depending on the normal (if the boundary is anisotropic), the surface gradient of deformation, the curvature tensor, the morphological descriptor and its surface gradient. In this case, the derivative of the surface energy with respect to the gradient of the morphological descriptor, applied to the normal, is the boundary datum in term of substructural action [40]. Of course, the choice of an explicit expression of the surface energy is strictly of constitutive nature.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…Experiments show that the elastic energy of quasicrystals does not depend on ν while it depends only on its spatial gradient N besides the gradient of macroscopic deformation. Moreover, quasicrystals are characterized by a self-action of dissipative nature, that is by dissipation inside each material element, a dissipation strictly associated with substructural events (see [40]). Although this type of tendence to material metastability, it has been shown experimentally that quasicrystals may admit in some cases ground states (see [54] and references therein).…”

Section: Ground States Of Thermodynamically Stable Quasicrystalsmentioning

confidence: 99%

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Ground states in complex bodies

Mariano

Modica

2008

ESAIM: COCV

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Abstract.A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and Cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and Cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role of the balance of configurational actions follows. After describing a list of possible applications of the general results collected here, a concrete discussion of the existence of ground states in thermodynamically stable quasicrystals is presented at the end.

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Section: Boundary Conditionsmentioning

confidence: 99%

Section: Ground States Of Thermodynamically Stable Quasicrystalsmentioning

confidence: 99%

Ground states in complex bodies

Mariano

Modica

2008

ESAIM: COCV

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“…There are no bulk external fields acting on phason degrees of freedom, except we presume phason inertia [18][19][20]. However, it is proven that bulk phason self-action which has both the dissipative (frictional force) and conservative components with the latter being dependent on the phason field [20].…”

Section: Mathematical Formulationsmentioning

confidence: 99%

Elastodynamic Analysis of a Hollow Cylinder with Decagonal Quasicrystal Properties: Meshless Implementation of Local Integral Equations

Hosseini

Sládek

2016

Crystals

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Abstract:A meshless approximation and local integral equation (LIE) formulation are proposed for elastodynamic analysis of a hollow cylinder made of quasicrystal materials with decagonal quasicrystal properties. The cylinder is assumed to be under shock loading. Therefore, the general transient elastodynamic problem is considered for coupled phonon and phason displacements and stresses. The equations of motion in the theory of compatible elastodynamics of wave type for phonons and wave-telegraph type for phasons are employed and can be easily modified to the elasto-hydro dynamic equations for quasicrystals (QCs). The angular dependence of the tensor of phonon-phason coupling coefficients handicaps utilization of polar coordinates, when the governing equations would be given by partial differential equations with variable coefficients. Despite the symmetry of the geometrical shape, the local weak formulation and meshless approximation are developed in the Cartesian coordinate system. The response of the cylinder in terms of both phonon and phason stress fields is obtained and studied in detail.

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“…Within the multi-field description of the mechanics of quasi-crystals (see Lubensky et al 1985;De & Pelcovits 1987;Mariano 2006), we adopt generalized elastic constitutive prescriptions (Hu et al 2000;Ricker et al 2001). We provide closed form expressions for phonon and phason fields for a gliding and climbing dislocation, within the infinitesimal deformation setting.…”

Section: Introductionmentioning

confidence: 99%

Steady-state propagation of dislocations in quasi-crystals

Radi

Mariano

2011

Proc. R. Soc. A.

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We analyse the steady propagation at constant speed, lower than the shear wave-speed, of a straight dislocation in an unbounded elastic quasi-crystal with five-fold symmetry. We discuss only the ideal elastic behaviour, neglecting the dissipation associated with the atomic rearrangements. Under these conditions, we provide the expressions of phonon and phason fields in closed form. Both phonon and phason stresses appear to be singular near to the dislocation core. We also find the explicit expression of the energy per unit length around a moving dislocation.

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Mechanics of Quasi-Periodic Alloys

Cited by 46 publications

References 33 publications

Ground states in complex bodies

Ground states in complex bodies

Elastodynamic Analysis of a Hollow Cylinder with Decagonal Quasicrystal Properties: Meshless Implementation of Local Integral Equations

Steady-state propagation of dislocations in quasi-crystals

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