Conditions for strong ellipticity of 4th-order elasticity tensors

The strong ellipticity condition is crucial in nonlinear elasticity and materials. In this paper, we establish sufficient and necessary conditions for the strong ellipticity of a 4th-order 2-dimensional elasticity tensor, and some sufficient conditions for the strong ellipticity of a 4th-order 3-dimensional elasticity tensor. Numerical examples demonstrate the effectiveness of our results in assessing the strong ellipticity condition of elasticity tensors.