Skip to Main content Skip to Navigation
Journal articles

Fully non-linear wave models in fiber-reinforced anisotropic incompressible hyperelastic solids

Abstract : Many composite materials, including biological tissues, are modeled as non-linear elastic materials reinforced with elastic fibers. In the current paper, the full set of dynamic equations for finite deformations of incompressible hyperelastic solids containing a single fiber family are considered. Finite-amplitude wave propagation ansätze compatible with the incompressibility condition are employed for a generic fiber family orientation. Corresponding non-linear and linear wave equations are derived. It is shown that for a certain class of constitutive relations, the fiber contribution vanishes when the displacement is independent of the fiber direction. Point symmetries of the derived wave models are classified with respect to the material parameters and the angle between the fibers and the wave propagation direction. For planar shear waves in materials with a strong fiber contribution, a special wave propagation direction is found for which the non-linear wave equations admit an additional symmetry group. Examples of exact time-dependent solutions are provided in several physical situations, including the evolution of pre-strained configurations and traveling waves.
Document type :
Journal articles
Complete list of metadata

https://hal.univ-lorraine.fr/hal-01417912
Contributor : Lemta Ul Connect in order to contact the contributor
Submitted on : Friday, December 16, 2016 - 10:53:38 AM
Last modification on : Saturday, October 16, 2021 - 11:22:03 AM

Identifiers

Collections

Citation

A.F. Cheviakov, Jean-François Ganghoffer, S. St. Jean. Fully non-linear wave models in fiber-reinforced anisotropic incompressible hyperelastic solids. International Journal of Non-Linear Mechanics, Elsevier, 2015, 71, pp.8 - 21. ⟨10.1016/j.ijnonlinmec.2015.01.006⟩. ⟨hal-01417912⟩

Share

Metrics

Record views

118