The role of material and geometric nonlinearities in acoustoelasticity

• Published in: Wave motion Vol. 86; pp. 79 - 90
• Main Authors: Pau, Annamaria, Vestroni, Fabrizio
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2019; Elsevier BV
• Subjects: Acoustoelasticity; Bulk waves; Longitudinal waves; Prestressed solid; Prestressing; Propagation; Strain energy density; Surface acoustic waves; Three dimensional models; Wave propagation; Wave speed in solids; Strain energy density; Acoustoelasticity; Bulk waves; Wave speed in solids; Prestressed solid
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2018.12.005

Wave propagation in prestressed and prestrained continua can be modelled by the theory of acoustoelasticity, which typically includes different assumptions. These are third or fourth order expressions of hyperelastic strain energy, as well as finite initial strains and a formulation of balance equations in the current configuration. In this paper, we use a model describing wave propagation in a three dimensional elastically prestrained continuum to clarify the role of different mechanical aspects taken into account in the classical hypotheses of the theory. We consider different states of prestress: hydrostatic, biaxial and uniaxial. Changes in shear and longitudinal wave speeds and their polarization as a function of the initial prestress are described for all directions of propagation. The role of the strain energy power order in changes of speed is elucidated. Moreover, material and geometric nonlinearities are shown to affect changes with the opposite sign, depending also on the direction of propagation. •The sources of nonlinearity classically accounted for in acoustoelasticity, i.e. material and geometric nonlinearities, are investigated individually to understand how they affect the change in bulk wave speed and polarization.•A hydrostatic, a plane and a uniaxial state of prestress are investigated by studying the changes in the acoustic tensor.•Material and geometric nonlinearities affect changes in wave speed with different intensity and opposite sign, depending also on the kind of wave, on the direction of propagation and on the symmetry of prestress.•The amount of speed change due to material nonlinearity is greater than that due to geometric nonlinearity.•The prestress is capable of turning an isotropic material into one that is orthotropic and to produce coupling between shear and normal waves.