A kinematic elastic nonshakedown theorem for implicit standard materials |
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Authors: | G Bodovillé |
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Institution: | (1) 3, rue du Mesnil, 51130 Villeneuve Renneville Chevigny, France, FR |
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Abstract: | Summary Criteria for a priori recognition of the type of steady-state response induced by cyclic loads and prediction whether a structure
will shakedown elastically or not, without the necessity of performing a step-by-step full analysis, have considerable importance.
Melan and Koiter theorems provide criteria that guarantee whether elastic shakedown occurs or not under cyclic loads in case
of perfect plasticity. However, there remain some aspects of the shakedown theory which deserve further study. One of these,
concerned with more realistic nonassociative elastic–plastic constitutive material models, allowing for nonlinear kinematic
and isotropic hardening suitable to describe the cyclic plastic behaviour of metallic materials, has strong motivation. Koiter's
elastic nonshakedown theorem is reconsidered here, with the objective of extending it to the de Saxcé's implicit standard
material class, which contains a wide class of nonassociative elastic–plastic material behaviours. Shakedown analysis is formulated
by a kinematic approach based on the plastic accumulation mechanism concept due to Polizzotto. A sufficient condition for
elastic nonshakedown and a distinct necessary condition are established. Then, an upper bound to the shakedown multiplier
is evaluated.
Received 15 February 2001; accepted for publication 18 October 2001 |
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Keywords: | Nonassociative plasticity Implicit standard material Shakedown |
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