A general solution method to the Cauchy Problem (CP) formulated for incremental elastoplasticity is designed. The method extends previous works of the authors on the solution to Cauchy Problems for linear operators and convex nonlinear elasticity in small strain to the case of generalised standard materials defined by two convex potentials. The CP is transformed into the minimisation of an error between the solutions to two well-posed elastoplastic evolution problems. A one-parameter family of errors in the constitutive equation is derived based on Legendre–Fenchel residuals. The method is illustrated by the simple example of a pressurised thick-spherical reservoir made of elastic, linear strain-hardening plastic material. The identification of inner pressure and plasticity evolution has been carried-out using semi-analytical solutions to the elastoplastic behaviours to build the error functional.
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@article{CRMECA_2015__343_5-6_331_0,
author = {Thouraya Nouri Baranger and St\'ephane Andrieux and Thi Bach Tuyet Dang},
title = {The incremental {Cauchy} {Problem} in elastoplasticity: {General} solution method and semi-analytic formulae for the pressurised hollow sphere},
journal = {Comptes Rendus. M\'ecanique},
pages = {331--343},
publisher = {Elsevier},
volume = {343},
number = {5-6},
year = {2015},
doi = {10.1016/j.crme.2015.04.002},
language = {en},
}
TY - JOUR AU - Thouraya Nouri Baranger AU - Stéphane Andrieux AU - Thi Bach Tuyet Dang TI - The incremental Cauchy Problem in elastoplasticity: General solution method and semi-analytic formulae for the pressurised hollow sphere JO - Comptes Rendus. Mécanique PY - 2015 SP - 331 EP - 343 VL - 343 IS - 5-6 PB - Elsevier DO - 10.1016/j.crme.2015.04.002 LA - en ID - CRMECA_2015__343_5-6_331_0 ER -
%0 Journal Article %A Thouraya Nouri Baranger %A Stéphane Andrieux %A Thi Bach Tuyet Dang %T The incremental Cauchy Problem in elastoplasticity: General solution method and semi-analytic formulae for the pressurised hollow sphere %J Comptes Rendus. Mécanique %D 2015 %P 331-343 %V 343 %N 5-6 %I Elsevier %R 10.1016/j.crme.2015.04.002 %G en %F CRMECA_2015__343_5-6_331_0
Thouraya Nouri Baranger; Stéphane Andrieux; Thi Bach Tuyet Dang. The incremental Cauchy Problem in elastoplasticity: General solution method and semi-analytic formulae for the pressurised hollow sphere. Comptes Rendus. Mécanique, Volume 343 (2015) no. 5-6, pp. 331-343. doi : 10.1016/j.crme.2015.04.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.04.002/
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