Load capacity of bodies

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For the stress analysis in a plastic body Ω, we prove that there exists a maximal positive number C, the load capacity ratio, such that the body will not collapse under any external traction field t bounded by CY0, where Y0 is the yield stress. The load capacity ratio depends only on the geometry of the body and is given byfrac(1, C) = under(sup, w ∈ LD (Ω)D) frac(∫∂ Ω | w | d A, ∫Ω | ε{lunate} (w) | d V) = ∥ γD ∥ .Here, LD (Ω)D is the space of incompressible vector fields w for which the corresponding linear strains ε{lunate} (w) are assumed to be integrable and γD is the trace mapping assigning the boundary value γD (w) to any w ∈ LD (Ω)D.

Original languageEnglish
Pages (from-to)1016-1023
Number of pages8
JournalInternational Journal of Non-Linear Mechanics
Issue number9
StatePublished - 1 Nov 2006


  • Continuum mechanics
  • Plasticity
  • Stress analysis
  • Trace

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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