A note on the derivation of rigid-plastic models

Babadjian, Jean‐François; Francfort, Gilles A.

doi:10.1007/s00030-016-0389-7

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2022

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“…Remark 1.1. The previous assumption is also related to the so-called slip line theory, widely used in mechanics to get exact solutions to plane-stress rigid-plasticity problems; see [7] for a description of the mathematical framework of rigid plasticity. There, the spatial hyperbolic structure of the stress equations is used in combination with the method of characteristics to construct non trivial solutions to the stress problem and to determine the associated velocities [32,Section 5.1].…”

Section: The Specific Contextmentioning

confidence: 99%

Continuity Equation and Characteristic Flow for Scalar Hencky Plasticity

Babadjian

Francfort

2022

Comm Pure Appl Math

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We investigate uniqueness issues for a continuity equation arising out of the simplest model for plasticity, Hencky plasticity. The associated system is of the form curl (µσ ) = 0 where µ is a nonnegative measure and σ a two-dimensional divergence free unit vector field. After establishing the Sobolev regularity of that field, we provide a precise description of all possible geometries of the characteristic flow, as well as of the associated solutions.1. Introduction 2. Notation and preliminaries 3. Hencky plasticity 4. Sobolev regularity of the stress 5. Rigidity properties of the solutions 6. Geometry of the solutions Appendix. Bibliography

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Section: The Specific Contextmentioning

confidence: 99%