eprintid: 59635 rev_number: 9 eprint_status: archive userid: 11441 dir: disk0/00/05/96/35 datestamp: 2012-02-02 09:19:09 lastmod: 2021-09-22 19:28:01 status_changed: 2012-02-02 09:19:09 type: article metadata_visibility: show item_issues_count: 0 creators_name: Domanski, W. creators_name: Ogden, R.W. creators_orcid: 0000-0002-7002-7028 title: On the null condition for nonlinearly elastic solids ispublished: pub divisions: 30501000 abstract: Smooth solutions to the Cauchy problem for the equations of nonlinear elastodynamics exist typically only locally in time. However, under the assumption of small initial data and an additional restriction, the so-called null condition, global existence and uniqueness of a classical solution can be proved. In this paper, we examine this condition for the elastodynamic equations and study its connection with the property of genuine nonlinearity as well as its relation with the phenomenon of self-resonance of nonlinear elastic waves. Using a special structure of plane waves elastodynamics [13], we provide an alternative and simple formulation of the null condition. This condition is then evaluated for some examples of elastic constitutive laws in order to determine the nature of the restrictions that it imposes. date: 2006 date_type: published official_url: http://am.ippt.gov.pl/index.php/am/index uniqueid: glaseprints:2006-59635 scopus_impact: 5 scopus_cluster: 2-s2.0-33750459082 scopus_datestamp: 2013-05-23 05:04:59 wos_impact: 5 wos_cluster: WOS:000241635800004 wos_datestamp: 2013-10-25 08:27:19 full_text_status: none publication: Archives of Mechanics volume: 58 number: 4-5 pagerange: 339-361 refereed: TRUE issn: 0373-2029 hoa_compliant: 305 hoa_date_pub: 2006 hoa_exclude: FALSE hoa_gold: FALSE citation: Domanski, W. and Ogden, R.W. (2006) On the null condition for nonlinearly elastic solids. Archives of Mechanics , 58(4-5), pp. 339-361.