Détermination de la réponse asymptotique d'une structure anélastique sous chargement thermomécanique cyclique

Abstract

Cet article présente une solution alternative aux méthodes classiques (comme la méthode incrémentale) de résolution de problèmes thermomécaniques cycliques non-linéaires. Il s'agit d'une Méthode Cyclique Directe qui consiste à rechercher directement la solution asymptotique d'une structure anélastique soumise à un chargement thermomécanique périodique, sans suivre l'histoire du chargement. Elle est fondée sur le Grand Incrément de Temps et la périodicité de l'état limite et la transformation de Fourier. solides et structures / cycle limite / thermomécanique / méthode numérique Determination of the asymptotic response of a structure under cyclic thermomechanical loading

Shakedown of elastic-perfectly plastic materials with temperature-dependent elastic moduli

“…A first line of research is concerned with extensions of the original theorem to various nonlinear behaviors, such as hardening plasticity (Pham, 2008;Nguyen, 2003), non standard plasticity (Corigliano et al, 1995;Bodovillé and De Saxcé, 2001), contact with friction (Ahn et al, 2008), phase-transformation (Peigney, 2010). A second (and complementing) line of research is concerned with the development of numerical methods for efficiently determining the shakedown domain in the space of load parameters (Zarka et al, 1988;Maitournam et al, 2002;Carvelli et al, 1999;Peigney andStolz, 2001, 2003;Simon and Weichert, 2012;Spiliopoulos and Panagiotou, 2012). We refer to Weichert and Ponter (2014) for more historical details on the development of shakedown theory.…”

Cyclic steady states in diffusion-induced plasticity with applications to lithium-ion batteries

“…The most intuitive way of estimating the cyclic steady state is to resort to step-by-step incremental analysis over a sufficiently large number of cycles. More computationally efficient methods could possibly be developed by building on various techniques that have been used in standard plasticity (Maitournam et al, 2002;Spiliopoulos and Panagiotou, 2012;Stolz, 2001, 2003). Such 'direct' methods would tentatively reduce the computational effort needed to establish Bree-type diagrams recording the main features of the cyclic steady state as a function of the loading parameters.…”

On shakedown of shape memory alloys structures

“…The property (13) shows that A d à 2 oUð0Þ for t [ s. Since A d 2 oUð _ aÞ and A d à 2 oUð0Þ, Eq. (4) gives…”

“…This implies that the asymptotic regime (shakedown, alternating plasticity, or ratchetting) is path-independent. That property has fostered the development of direct methods aiming at determining the asymptotic regime for a given cyclic loading, without using a step-by-step incremental analysis [1,13,21,22,24,25,27,29].…”