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<p>This study provides an example demonstrating that a universal deformation does not constrain the shape of a body. We show that bending, inflation, azimuthal shearing, and expansion or contraction of the major radius of a toroidal sector belong to the class of Family 5 deformations. Therefore, this family of universal deformations for incompressible isotropic solids is not restricted to an annular wedge. The proposed example is shown to be a family of inhomogeneous deformations in which the Cauchy deformation tensor has constant principal invariants&#xa0;— a property which is found only in the Family 5 class of deformations.</p>

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A Note on the Universal Deformations of Incompressible Isotropic Bodies

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Seyedemad Motaghian

摘要

This study provides an example demonstrating that a universal deformation does not constrain the shape of a body. We show that bending, inflation, azimuthal shearing, and expansion or contraction of the major radius of a toroidal sector belong to the class of Family 5 deformations. Therefore, this family of universal deformations for incompressible isotropic solids is not restricted to an annular wedge. The proposed example is shown to be a family of inhomogeneous deformations in which the Cauchy deformation tensor has constant principal invariants — a property which is found only in the Family 5 class of deformations.