Publication

Plane-polarised finite-amplitude shear waves in deformed incompressible materials

Destrade, Michel
Saccomandi, Giuseppe
Citation
Destrade, Michel, & Saccomandi, Giuseppe. (2022). Plane-polarised finite-amplitude shear waves in deformed incompressible materials. Mathematics and Mechanics of Solids, 27(8), 1494-1503. doi:10.1177/10812865221089588
Abstract
We investigate how two finite-amplitude, transverse, plane body waves may be superposed to propagate in a deformed hyperelastic incompressible solid. We find that the equations of motion reduce to a well-determined system of partial differential equations, making the motion controllable for all solids. We find that in deformed Mooney¿Rivlin materials, they may travel along any direction and be polarised along any transverse direction, an extension of a result by Boulanger and Hayes (Quart. J. Mech. Appl. Math. 45 (1992) 575). Furthermore, their motion is governed by a linear system of partial differential equations, making the Mooney¿Rivlin special in that respect. We select another model to show that for other materials, the equations are nonlinear. We use asymptotic equations to reveal the onset of nonlinearity for the waves, paying particular attention to how close the propagation direction is to the principal axes of pre-deformation.
Funder
Publisher
SAGE Publications
Publisher DOI
10.1177/1081286522108958
Rights
CC BY-NC-ND 3.0 IE