Skip to Main content Skip to Navigation
Journal articles

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes

Abstract : The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures.
Document type :
Journal articles
Complete list of metadata

https://hal.univ-lorraine.fr/hal-01432022
Contributor : Lemta Ul <>
Submitted on : Wednesday, January 11, 2017 - 2:23:50 PM
Last modification on : Monday, March 29, 2021 - 4:03:06 PM

Identifiers

Collections

Citation

A.F. Cheviakov, Jean-François Ganghoffer. One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes. Journal of the mechanical behavior of biomedical materials, Elsevier, 2015, 58, pp.105 - 121. ⟨10.1016/j.jmbbm.2015.08.027⟩. ⟨hal-01432022⟩

Share

Metrics

Record views

148