<p>We investigate universal deformations in compressible isotropic Cauchy elastic solids with residual stress, without assuming any specific source for the residual stress. We show that universal deformations must be homogeneous, and the associated residual stresses must also be homogeneous. Since a non-trivial residual stress cannot be homogeneous, it follows that residual stress must vanish. Thus, a compressible Cauchy elastic solid with a non-trivial distribution of residual stress cannot admit universal deformations. These findings are consistent with the results of Yavari and Goriely (Proc. R. Soc. A 472(2196):20160690, <CitationRef CitationID="CR80">2016</CitationRef>), who showed that in the presence of eigenstrains, universal deformations are covariantly homogeneous and in the case of simply-connected bodies the universal eigenstrains are zero-stress (impotent).</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

Universal Deformations in Compressible Isotropic Cauchy Elastic Solids with Residual Stress

  • Arash Yavari,
  • José Merodio,
  • Mohd H. B. M. Shariff

摘要

We investigate universal deformations in compressible isotropic Cauchy elastic solids with residual stress, without assuming any specific source for the residual stress. We show that universal deformations must be homogeneous, and the associated residual stresses must also be homogeneous. Since a non-trivial residual stress cannot be homogeneous, it follows that residual stress must vanish. Thus, a compressible Cauchy elastic solid with a non-trivial distribution of residual stress cannot admit universal deformations. These findings are consistent with the results of Yavari and Goriely (Proc. R. Soc. A 472(2196):20160690, 2016), who showed that in the presence of eigenstrains, universal deformations are covariantly homogeneous and in the case of simply-connected bodies the universal eigenstrains are zero-stress (impotent).