Mathematical framework of nonlinear elastic waves propagating in pre-stressed media

Acoustic nonlinearity holds potential as a method for assessing material stress. Analogous to the acoustoelastic effect, where the velocity of elastic waves is influenced by third-order elastic constants, the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants. Despite this, there has been a notable absence of research exploring this phenomenon. Consequently, this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials. It delves into the impact of pre-stress on higher-order material parameters, and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress. This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.