This paper investigates the interaction of weakly nonlinear waves in a hyperelastic, fiber-reinforced orthotropic material. The study focuses on quadratically nonlinear effects. Using a multiple scale asymptotic expansion, the coupled evolution equations for the amplitudes of different pairs of waves are derived. It turns out that unlike as it is in the isotropic case, the quadratically nonlinear coupling is possible between shear elastic waves. The derived coupled evolution equations for the amplitudes of interacting wave pairs offer new insights into the behavior of elastic waves in such complex material systems, contributing to the understanding of wave phenomena in fiber-reinforced materials.
WinemanAPenceTJ. Fiber-reinforced composites: nonlinear elasticity and beyond. J Eng Math2021; 127(1): 30.
2.
EngelbrechtJBerezovskiA. Reflections on mathematical models of deformation waves in elastic microstructured solids. Math Mech Complex Syst2015; 3(1): 43–82.
3.
GalichPISlesarenkoVRudykhS. Shear wave propagation in finitely deformed 3D fiber-reinforced composites. Int J Solids Struct2017; 110: 294–304.
4.
AroraNXiangYRudykhS. Multiscale analysis of elastic waves in soft materials: from molecular chain networks to fiber composites. Int J Mech Sci2021; 200: 106433.
5.
DomańskiWNorrisAN. Degenerate weakly non-linear elastic plane waves. Int J Non Linear Mech2009; 44(5): 486–493.
6.
KubeCMRoyAJensenDS, et al. A unifying model of weakly nonlinear elastic waves; large on large theory. J Acoust Soc Am2022; 151(2): 1294–1310.
7.
DomańskiWJemiołoSFranusA. Propagation and interaction of weakly nonlinear plane waves in transversely isotropic elastic materials. J Eng Math2021; 127(1): 8.
8.
AmendolaASaccomandiGSperanziniE. On shear motions in nonlinear transverse isotropic elastodynamics. Math Mech Solids2023; 28(4): 931–942.
FranusAJemiołoSDomańskiW. Elastic waves of a polyconvex hyperelastic model. In: MałyszkoLBilkoP (eds) Lightweight structures contemporary problems. theoretical and experimental studies in mechanics of lightweight structures. Olsztyn: UWM, 2020, pp. 83–92.
16.
BallJM. Convexity conditions and existence theorems in nonlinear elasticity. Arch Ration Mech An1976; 63(4): 337–403.
17.
SchröderJNeffP. Invariant formulaiton of hyperelastic transverse isotropy based on polyconvex free energy functions. Int J Solids Struct2003; 40(2): 401–445.
18.
SpencerAJM. Modelling of finite deformations of anisotropic materials. In: GittusJZarkaJNemat-NasserS (eds) Large deformations of solids: Physical basis and mathematical modelling. Dordrecht: Springer, 1986.
19.
DomańskiW. Propagation and interaction of hyperbolic plane waves in nonlinear elastic solids. IFTR Rep2006; 4: 3–169.
20.
HouZBaylyPVOkamotoRJ. Shear wave speeds in nearly-incompressible fibrous materials with two fiber families. J Acoust Soc Am2021; 149(2): 1097–1106.
21.
DomańskiW. On nonlinearity parameters describing elastic wave interactions. In: Proceedings of meetings on acoustics, vol. 34, Santa Fe, NM, 9–13 July, 2018. Melville, NY: Acoustical Society of America.
