PHYSICAL REVIEW B 105, 226102 (2022) Reply to “Comment on ‘Nonlinear elasticity of prestressed single crystals at high pressure and various elastic moduli’ ” Valery I. Levitas * Iowa State University, Departments of Aerospace Engineering and Mechanical Engineering, Ames, Iowa 50011, USA and Ames Laboratory, Division of Materials Science and Engineering, Ames, Iowa 50011, USA (Received 19 May 2022; accepted 7 June 2022; published 22 June 2022) DOI: 10.1103/PhysRevB.105.226102 I am glad that critics of my paper [1] on the effective higher-order elastic moduli ∂ nG C̃i jkl... (p) = (1) ∂Ei j ∂Ekl . . . Equation (2) shows that indeed C̃i jkl... (p) allow one to connect σ1 + p and E1 . However, at p = 0 “normal” elastic constants C̄i jkl... (p) for small strains are defined by triggered comment [2], resolving some of the raised issues. Here, G is either the Gibbs energy or enthalpy per unit volume of the material under pressure p, and Ei j are the components of the small but finite Lagrangian strain tensor with respect to the state at pressure p. Definition (1) was introduced in [3] with the statement that the effective elastic constants (1) “take completely into account the presence of the hydrostatic compression and describe the elastic behavior of a hydrostatically compressed cubic crystal just as completely as the normal (second- and higher-order) elastic constants describe the elastic response in the absence of hydrostatic compression. This holds equally true for all different phenomena, such as the stress-deformation relation and elastic wave propagation.” I wrote in [1] that this was not proven in the literature, and comment [2] confirms this by deriving rather than citing the relationship for the Cauchy stress σi j utilizing C̃i jkl... . In particular, in the Voigt notations,   σ1 = −p + C̃11 E1 + C̃11 + 21 C̃111 E12   + − 21 C̃11 + 21 C̃111 + 61 C̃1111 E13 . (2) σ1 = C̄11 E1 + C̄111 E12 + C̄1111 E13 . * A comparison of Eqs. (2) and (3) clearly shows that third- and fourth-order C̃i jkl... (p) differ from the traditional elastic moduli C̄i jkl... , in contrast to the statement in [3]. Consequently, C̃i jkl... do not have the physical meaning of elastic moduli in stress-strain relationships. That is what I meant in [1] when I wrote that “such elastic moduli, starting with the third order do not have any direct physical applications.” However, I agree that that wording could be made much more precise. In addition, the expression for the second-order elastic moduli C̃i jkl , which are the same in the equation for the Gibbs energy and stress-strain relationships, were received in [1,4,5] for an arbitrary crystal symmetry and lattice rotations. In [2], the stress-strain relationships with higher-order moduli are obtained for a cubic lattice and rotation-free deformation only. The last statement should be mentioned in [2] because Eq. (9) in [2] is valid for deformations without rotations only. Support from NSF (CMMI-1943710 and DMR-1904830) and Iowa State University (Vance Coffman Faculty Chair Professorship) is greatly appreciated. vlevitas@iastate.edu [1] V. I. Levitas, Nonlinear elasticity of prestressed single crystals at high pressure and various elastic moduli, Phys. Rev. B 104, 214105 (2021). [2] O. M. Krasilnikov, Yu. Kh. Vekilov, and S. I. Simak, Comment on “Nonlinear elasticity of prestressed single crystals at high pressure and various elastic moduli”, Phys. Rev. B 105, 226101 (2022). 2469-9950/2022/105(22)/226102(1) (3) [3] G. Barsch and Z. Chang, Second-and higher-order effective elastic constants of cubic crystals under hydrostatic pressure, J. Appl. Phys. 39, 3276 (1968). [4] T. H. K. Barron and M. L. Klein, Second-order elastic constants of a solid under stress, Proc. Phys. Soc. London 85, 523 (1965). [5] D. C. Wallace, Thermoelasticity of stressed materials and comparison of various elastic constants, Phys. Rev. 162, 776 (1967). 226102-1 ©2022 American Physical Society