Bifurcation and size effect in a viscoelastic non-local damageable continuum

Theocaris Baxevanis (1) , Gilles Pijaudier-Cabot (2) , Frédéric Dufour (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique
2 LFCR - Laboratoire des Fluides Complexes et leurs Réservoirs

The growth of microcracks in progressively fracturing rate-independent materials is a fairly distributed process which is associated with stable material response. However, for certain stress trajectories such as tertiary creep, a different deformation mode may prevail, consisting of formation of discrete failure planes (macrocracks). In the latter case, the mechanical response as observed on the macroscale becomes, in general, unstable. The inception of such a localized mode may be considered as a bifurcation problem related to the loss of positive definiteness of the tangent material stiffness operator governing the homogeneous deformation (Rudnicki and Rice [11]). In mathematical terms, the elliptic character of the set of governing differential equations, in quasi-static problems, is lost (ill-posedness of the related boundary value problem). This result was derived for the linearized rate equation problem, considering what is commonly denoted as a linear comparison solid (Hill [5]).

Domaines: Mécanique [physics.med-ph]; Matériaux

Theocaris Baxevanis, Gilles Pijaudier-Cabot, Frédéric Dufour. Bifurcation and size effect in a viscoelastic non-local damageable continuum. 16th European Conference of Fracture, 2006, Alexandropoulis, Greece. pp.1379-1380, ⟨10.1007/1-4020-4972-2_685⟩. ⟨hal-01007944⟩