Functions of bounded deformation
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We study the space BD(Ω), composed of vector functions u for which all components eij=1/2(ui, j+uj, i) of the deformation tensor are bounded measures. This seems to be the correct space for the displacement field in the problems of perfect plasticity. We prove that the boundary values of every such u are integrable; indeed their trace is in L1 (Γ)N. We show also that if a distribution u yields ɛij which are measures, then u must lie in Lp(Ω) for p≦N/(N−1).
- Massachusetts Institute of Technology United States
- University of Paris-Saclay France
- University of Paris France
all components of deformation tensor are bounded measures, Spaces of vector- and operator-valued functions, trace theorem, space for displacement field, perfect plasticity, Minimal surfaces and optimization, Plastic materials, materials of stress-rate and internal-variable type, functions of bounded deformation, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
all components of deformation tensor are bounded measures, Spaces of vector- and operator-valued functions, trace theorem, space for displacement field, perfect plasticity, Minimal surfaces and optimization, Plastic materials, materials of stress-rate and internal-variable type, functions of bounded deformation, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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