Coupling Effects of Initial Stresses and Nonlinear Elasticity on the Propagation Characteristics of Elastic Waves

MI Hongrui; LI Wenqiang; HU Hengshan

doi:10.21656/1000-0887.470002

Volume 47 Issue 6

Jun. 2026

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MI Hongrui, LI Wenqiang, HU Hengshan. Coupling Effects of Initial Stresses and Nonlinear Elasticity on the Propagation Characteristics of Elastic Waves[J]. Applied Mathematics and Mechanics, 2026, 47(6): 750-772. doi: 10.21656/1000-0887.470002

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Coupling Effects of Initial Stresses and Nonlinear Elasticity on the Propagation Characteristics of Elastic Waves

doi: 10.21656/1000-0887.470002

MI Hongrui^1
,,
LI Wenqiang^{1
,
,},
HU Hengshan^2
,

1.
Faculty of Civil Engineering and Mechanics, Kunming University of Science and Technology, Kunming 650500, P. R. China
2.
Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001, P. R. China

Received Date: 2026-01-04
Rev Recd Date: 2026-02-12
Publish Date: 2026-06-01

Abstract

Abstract

The propagation of elastic waves in solids is influenced by initial stresses and material nonlinearity. Accurately characterizing the propagation of elastic waves in initially stressed media is crucial for stress nondestructive testing, structural health monitoring, and geophysical exploration. However, the distinct roles of stress-related geometric nonlinearity and material nonlinearity remain unclear. A theoretical framework based on acoustoelasticity and coupling finite initial deformation with material nonlinearity was developed. Approximate analytical solutions for the phase velocities of body waves were derived with the perturbation theory, to give an efficient approach for the rapid calculation of elastic wave propagation in initial stress media. Furthermore, the characteristic equation was solved for plane waves, the coupled effects of initial stress and nonlinear elasticity were systematically analyzed. The results show that, the effects of initial stresses stem from the competition between geometric and physical nonlinearity. Under tensile initial stresses, geometric nonlinearity will increase wave speeds, while physical nonlinearity will decrease them. Physical nonlinearity induces more pronounced changes in phase velocity and velocity anisotropy of shear waves. For the 7075-T651 aluminum alloy, the shear wave anisotropy reaches 2%~3%.
- initial stress,
- acoustoelastic theory,
- elastic wave propagation,
- geometrically and physically nonlinearity,
- perturbation theory

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References(33)

References

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