Symmetry properties of two-dimensional Ciarlet-Mooney-Rivlin constitutive models in nonlinear elastodynamics

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:396

Article

Cheviakov, A. F.¹  Ganghoffer, J-F² 

[1] Univ Saskatchewan, Dept Math & Stat, Saskatoon, SK S7N 0W0, Canada

[2] Univ Lorraine, LEMTA ENSEM, Nancy, France

关键词: Nonlinear;    Elasticity;    Equivalence transformations;    Symmetries;    Traveling wave coordinates;   

DOI  :  10.1016/j.jmaa.2012.07.006

来源: Elsevier

【 摘 要 】

Nonlinear dynamic equations for isotropic homogeneous hyperelastic materials are considered in the Lagrangian formulation. An explicit criterion of existence of a natural state for a given constitutive law is presented, and is used to derive natural state conditions for some common constitutive relations. For two-dimensional planar motions of Ciarlet-Mooney-Rivlin solids, equivalence transformations are computed that lead to a reduction of the number parameters in the constitutive law. Point symmetries are classified in a general dynamical setting and in traveling wave coordinates. A special value of traveling wave speed is found for which the nonlinear Ciarlet-Mooney-Rivlin equations admit an additional infinite set of point symmetries. A family of essentially two-dimensional traveling wave solutions is derived for that case. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free