PSI - Issue 32

O.B. Naimark et al. / Procedia Structural Integrity 32 (2021) 144–151 Author name / Structural Integrity Procedia 00 (2019) 000–000

146

3

shear elasticity was established. The explanation of this long relaxation time anomaly is linked by Derjaguin (1992) with a coordinated displacement and reorientation of groups of molecules, which longer times. GMS as a coordinated displacement of groups of molecules (similarly to coordinated relative slipping of blocks or grains in solids) can be realized during nucleation of mesoscopic defects (microshears) arising between these groups of molecules. The structural image of the k -gap, reflecting the rigidity of the transition at low packing fractions, can be introduced as a localized shear collective mode corresponding to the coordinated movement of groups of molecules in the elastic field of shear stresses. These localized shears are of a mesoscopic (dislocation) nature and reflect a local breaking of the symmetry of the distortion tensor. 1.2. Gapped Momentum States as Defects Induced Criticality in Condensed Matter Thermodynamics and kinetics of a condensed matter with localized shears (microshears) was developed by Naimark (2004) and is based on a statistical-thermodynamic description of the collective properties of an ensemble of microshears and the concepts of the gauge field theory to substantiate the form of the thermodynamic potential of a continuum with microshears and conditions for thermalization of a nonequilibrium system. The out-of-equilibrium free energy was represented by Naimark (2010) in the generalized Ginzburg-Landau form for microshear induced strain p

   −

6  −   p

   −

2  −   p

(

) 2

1

1

1

δ

δ

(4)

Bp + C 4

χ D p+ σ

p

F = A

2 1

4

6 1

δ

δ

l

*

с

It was shown by Naimark (2004) that the bifurcation points c δ , δ * play the role that is similar to characteristic temperatures in the Ginzburg-Landau phase transition theory. The gradient term in (4) describes non-local interaction in the mesodefect ensemble; A, B,C, D and χ are the phenomenological parameters. The kinetic equation for parameter p reads

  

  

dt dp

δ δ

δ

,

(5)

− − − D σ )p 5 1

)p Bp +C( 3

1

− A( Γ =

∂ x ( p χ

)

− −

p

δ

x

c

l

l

where p Γ is the kinetic coefficient. The kinetics of spinodal decomposition for qualitative different free energy metastability is given by Naimark (2004) as the self-similar solutions: in the range *, c δ < δ < δ

1 2

2 1

1

4 2

2 1

C χ

  

  

[

( ) = ζ , ζ ]

(

)

(

)

( ) Δp Γ χC ,V = 1 2

(6)

1 tanh −

Δp p x Vt = −

Vt , L = x −

S

p

L

Δp

S

1 ≈ c δ < δ

in the range

m

−   

  

t

.

(7)

− 1

L = x ζ φ(t)f(ζ), p(x,t)=

Φ = φ(t) ,

0

t

c

c

The free energy metastability at 1.3 ≈ δ < δ is related by Naimark (2003) to the orientation transition in mesodefect ensembles and the generation of collective modes which provides the mechanism of momentum transfer in solid with defects well known as plasticity. Solution (6) describes solitary wave dynamics due to the free energy

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