Notes on Global Stress and Hyper-Stress Theories

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The fundamental ideas and tools of the global geometric formulation of stress and hyper-stress theory of continuum mechanics are introduced. The proposed framework is the infinite dimensional counterpart of statics of systems having finite number of degrees of freedom, as viewed in the geometric approach to analytical mechanics. For continuum mechanics, the configuration space is the manifold of embeddings of a body manifold into the space manifold. Generalized velocity fields are viewed as elements of the tangent bundle of the configuration space and forces are continuous linear functionals defined on tangent vectors, elements of the cotangent bundle. It is shown, in particular, that a natural choice of topology on the configuration space, implies that force functionals may be represented by objects that generalize the stresses of traditional continuum mechanics.
Original languageEnglish
Title of host publicationGeometric Continuum Mechanics
EditorsReuven Segev, Marcelo Epstein
Place of PublicationCham
PublisherBirkhauser/Springer International Publishing
StatePublished - 14 May 2020

Publication series

NameAdvances in Mechanics and Mathematics
ISSN (Print)1571-8689
ISSN (Electronic)1876-9896


  • Continuum mechanics
  • Differentiable manifold
  • Stress
  • Hyper-stress
  • Global analysis
  • Manifold of mappings
  • de Rham currents


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