Nonlinear elastic response of cubic crystals to biaxial strain

The biaxial Poissons ratio in the nonlinear elastic theory is an important material parameter. We report here an accurate and efficient means of calculating the nonlinear elastic response of thin, homogeneous films to biaxial strain in arbitrary planes using a continuum-elasticity theory model. The general analytic expressions were derived for the elastic energy and the Poissons ratio under biaxial strain for cubic crystals. The biaxial Poisson's ratio did not remain constants, but showed a linear relationship with strain when second- and third-order elastic constants are considered. The expressions were verified with simulated biaxial Poisson's ratio and elastic energy of copper by density-functional theory calculations for three high symmetry planes.