Relation between fourth-order coupling parameters of a lattice and elastic constants

1982 ◽  
Vol 26 (6) ◽  
pp. 3079-3091 ◽  
Author(s):  
James Tasi
Keyword(s):  
Elastic Constants ◽  
Fourth Order ◽  
Coupling Parameters

Elastic anomalies of Hg2X2 compounds

1992 ◽  
Vol 70 (9) ◽  
pp. 745-751
Author(s):  
K. S. Viswanathan ◽  
J. C. Jeeja Ramani
Keyword(s):  
Elastic Constants ◽  
Fourth Order ◽  
Order Parameter ◽  
Zero Point ◽  
Stability Conditions ◽  
Point Energy ◽  
The Third ◽  
Limit Formula ◽  
The Stability ◽  
Elastic Anomalies

The anomalies of the second-, third-, and fourth-order elastic constants are considered for the phase transition of Hg2X2 type of compounds. Expressions are obtained for the equilibrium values of the order parameters in the ferroelastic phase from the stability conditions. The fluctuation in the order parameter is evaluated from the Landau–Khalatnikov equation. An expression is derived for the shift in the zero-point energy in the low-temperature ferroelastic phase and the specific heat anomaly. It is shown that these are proportional to (T − T)2 and (T − Tc), respectively. All the anomalies of the second-order elastic (SOE) constants are obtained from a single general formula, and relations among them are established. The temperature variation of the SOE constants in the limit [Formula: see text] is discussed. Similarly, expressions are derived for the anomalies of the third- and fourth-order elastic constants. In the limit [Formula: see text] it is shown that these constants diverge as [Formula: see text] and [Formula: see text], respectively.

Fourth-order elastic constants and second pressure derivatives of white tin

1991 ◽  
Vol 69 (7) ◽  
pp. 801-807
Author(s):  
R. Ramji Rao ◽  
A. Padmaja
Keyword(s):  
Phase Transformation ◽  
Hydrostatic Pressure ◽  
Elasticity Theory ◽  
Elastic Constants ◽  
Fourth Order ◽  
Finite Strain ◽  
Second Order ◽  
Tetragonal Crystal ◽  
Derivatives Of

The expressions for the 25 fourth-order elastic constants of a body-centered tetragonal crystal are derived with interactions extending to fifth neighbours. The expressions for its effective second-order elastic constants are obtained in terms of its natural second-, third-, and fourth-order elastic constants using the finite strain elasticity theory. The fourth-order elastic constants and the second pressure derivatives of white tin are evaluated using these formulae. All the second pressure derivatives of white tin except that of C11 are positive. The second pressure derivatives C12, C13, and C33 are large suggesting that phase transformation will occur in white tin when subjected to hydrostatic pressure.

On the determination of the fourth‐order elastic constants

1977 ◽  
Vol 48 (9) ◽  
pp. 3752-3755 ◽  
Author(s):  
Xanthippi Markenscoff
Keyword(s):  
Elastic Constants ◽  
Fourth Order

On isotropic tensors and elastic moduli

1974 ◽  
Vol 75 (3) ◽  
pp. 427-436 ◽  
Author(s):  
R. W. Ogden
Keyword(s):  
Elasticity Theory ◽  
Elastic Constants ◽  
Fourth Order ◽  
Elastic Material ◽  
Linear Elasticity ◽  
Elastic Moduli ◽  
Principal Component ◽  
Linear Elasticity Theory ◽  
Non Linear ◽  
Even Order

AbstractThe use of even-order isotropic tensors in non-linear elasticity theory is discussed in this paper. A notation is adopted through which these tensors can be represented conveniently so that their interdependence is clearly shown. Information about the number of independent elastic constants required is then readily available for use in an expansion of the stress to various orders in the strain relative to the undistorted configuration of the elastic material in question.For an incompressible isotropic hyperelastic solid, it is shown that each principal component of the distortional part of the stress is expressible as a function only of the corresponding principal component of strain to the fourth order. Under certain conditions, which are not too restrictive, this result can be extended to higher orders.

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