Geometric analysis of hyper-stresses

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Abstract

A geometric analysis of high order stresses in continuum mechanics is presented. Virtual velocity fields take their values in a vector bundle W over the n-dimensional space manifold. A stress field of order k is represented mathematically by an n-form valued in the dual of the vector bundle of k-jets of W. While only limited analysis can be performed on high order stresses as such, they may be represented by non-holonomic hyper-stresses, n-forms valued in the duals of iterated jet bundles. For non-holonomic hyper-stresses, the analysis that applies to first order stresses may be iterated. In order to determine a unique value for the tangent surface stress field on the boundary of a body and the corresponding edge interactions, additional geometric structure should be specified, that of a vector field transversal to the boundary.

Original languageEnglish
Pages (from-to)100-118
Number of pages19
JournalInternational Journal of Engineering Science
Volume120
DOIs
StatePublished - 1 Nov 2017

Keywords

  • Continuum mechanics
  • Differentiable manifolds
  • High order stresses stress
  • Iterated jets
  • Jet bundles
  • Non-holonomic sections
  • Virtual power

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