Comptes Rendus
no. 2
Second-order work and dissipation on indirect paths
[Travail du deuxième ordre et dissipation sur des chemins indirects]
Henryk Petryk1
1 Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland
Comptes Rendus. Mécanique, Volume 330 (2002) no. 2, pp. 121-126.

Nous développons le concept de dissipation du deuxième ordre sur des chemins complexes arbitraires dans l'espace des variables d'état internes. On adopte un cadre général pour les solides dissipatifs indépendants du temps qui contient la plasticité, la micro-fissuration et les changements de phase mortensitiques. On établit les circonstances dans lesquelles la dissipation évaluée au deuxième ordre est minimisée sur un chemin radical. En tant qu'application on utilise cette propriété de minimum pour simplifier une condition suffisante pour le stabilité de l'équilibre.

The concept of the second-order dissipation on arbitrary complex paths in the space of internal state variables is developed. A general framework for time-independent dissipative solids is adopted which encompasses plasticity, micro-cracking or martensitic phase transformation. Circumstances are established in which the dissipation evaluated to the second order is minimized on a radial path. As an application, this minimum property is used to simplify a sufficiency condition for stability of equilibrium.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-0721(02)01437-7
Keywords: solids and structures, dissipative materials, energy, path-dependence, stability
Mot clés : solides et structures, matériaux dissipatifs, énergie, stabilité

Henryk Petryk 1

1 Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, 00-049 Warsaw, Poland 
@article{CRMECA_2002__330_2_121_0,
     author = {Henryk Petryk},
     title = {Second-order work and dissipation on indirect paths},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {121--126},
     publisher = {Elsevier},
     volume = {330},
     number = {2},
     year = {2002},
     doi = {10.1016/S1631-0721(02)01437-7},
     language = {en},
}
TY  - JOUR
AU  - Henryk Petryk
TI  - Second-order work and dissipation on indirect paths
JO  - Comptes Rendus. Mécanique
PY  - 2002
SP  - 121
EP  - 126
VL  - 330
IS  - 2
PB  - Elsevier
DO  - 10.1016/S1631-0721(02)01437-7
LA  - en
ID  - CRMECA_2002__330_2_121_0
ER  - 
%0 Journal Article
%A Henryk Petryk
%T Second-order work and dissipation on indirect paths
%J Comptes Rendus. Mécanique
%D 2002
%P 121-126
%V 330
%N 2
%I Elsevier
%R 10.1016/S1631-0721(02)01437-7
%G en
%F CRMECA_2002__330_2_121_0
Henryk Petryk. Second-order work and dissipation on indirect paths. Comptes Rendus. Mécanique, Volume 330 (2002) no. 2, pp. 121-126. doi : 10.1016/S1631-0721(02)01437-7. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01437-7/

[1] D.C. Drucker Some implications of work hardening and ideal plasticity, Quart. Appl. Math., Volume 7 (1950), pp. 411-418

[2] R. Hill A general theory of uniqueness and stability in elastic-plastic solids, J. Mech. Phys. Solids, Volume 6 (1958), pp. 236-249

[3] R. Hill On consitutive inequalities for simple materials, J. Mech. Phys. Solids, Volume 16 (1968), pp. 229-242 (315–322)

[4] H. Petryk On the second-order work in plasticity, Arch. Mech., Volume 43 (1991), pp. 377-397

[5] Q.S. Nguyen Stability and Nonlinear Solid Mechanics, Wiley, Chichester, 1999

[6] Q.S. Nguyen Bifurcation and stability of time-independent standard dissipative systems (Q.S. Nguyen, ed.), CISM Courses and Lectures, 327, Springer, Wien–New York, 1993, pp. 45-94

[7] J.J. Moreau Sur les lois de frottement, de plasticité et de viscosité, C. R. Acad. Sci. Paris, Série A, Volume 271 (1970), pp. 608-611

[8] H. Petryk Stability and constitutive inequalities in plasticity (W. Muschik, ed.), CISM Courses and Lectures, 336, Springer, Wien–New York, 1993, pp. 259-329

Cité par Sources :

Commentaires - Politique