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Description
This paper investigates the interaction of weakly nonlinear waves in fiber-reinforced materials [1]. The constitutive relations consist of hyperelastic, polyconvex models incorporating a description that facilitates the modeling of mechanical dissipation. Models of this type can be used, for example, to describe membrane-shell structures made of textile materials or elastomeric bearings [2]
We analyze equations characterizing plane wave motion. The study focuses on quadratically nonlinear effects for shear plane waves. Using the method of weakly nonlinear asymptotics, the coupled evolution equations for the amplitudes of different pairs of waves are derived. It turns out that, in contrast to the isotropic case, quadratic nonlinear coupling is possible between shear waves in anisotropic solids [3,4]. We illustrate some properties by presenting numerical solutions for the evolution equations.
References
[1]Domański W., Franus A. (2025). Quadratically nonlinear interactions of shear elastic waves in fiber-reinforced orthotropic materials. Mathematics and Mechanics of Solids, 10812865251319246.
[2]Franus A., Jemioło S., Domański W. (2025). Enrichment of fiber-reinforced material models with dissipative effects. Mathematics and Mechanics of Solids, 10812865241307663.
[3]Domański W., Jemioło S., Franus A. (2021). Propagation and interaction of weakly nonlinear plane waves in transversely isotropic elastic materials. Journal of Engineering Mathematics, 127(1), 8.
[4]Cormack J. M. (2021). Plane nonlinear shear wave propagation in transversely isotropic soft solids. The Journal of the Acoustical Society of America, 150(4), 2566-2576.
