A thermodynamically consistent plastic-damage framework for localized failure in quasi-brittle solids: Material model and strain localization analysis

Abstract

Aiming for the modeling of localized failure in quasi-brittle solids, this paper addresses a thermodynamically consistent plastic-damage framework and the corresponding strain localization analysis. A unified elastoplastic damage model is first presented based on two alternative kinematic decompositions assuming infinitesimal deformations, with the evolution laws of involved internal variables characterized by a dissipative flow tensor. For the strong (or regularized) discontinuity to form in such inelastic quasi-brittle solids and to evolve eventually into a fully softened one, a novel strain localization analysis is then suggested. A kinematic constraint more demanding than the classical discontinuous bifurcation condition is derived by accounting for the traction continuity and the loading/unloading states consistent with the kinematics of a strong (or regularized) discontinuity. More specifically, the strain jumps characterized by Maxwell's kinematic condition have to be completely inelastic (energy dissipative). Reproduction of this kinematics implies vanishing of the aforesaid dissipative flow tensorial components in the directions orthogonal to the discontinuity orientation. This property allows naturally developing a localized plastic-damage model for the discontinuity (band), with its orientation and the traction-based failure criterion consistently determined a posteriori from the given stress-based counterpart. The general results are then particularized to the 2D conditions of plane stress and plane strain. It is found that in the case of plane stress, strain localization into a strong (or regularized) discontinuity can occur at the onset of strain softening. Contrariwise, owing to an extra kinematic constraint, in the condition of plane strain some continuous inelastic deformations and substantial re-orientation of principal strain directions in general have to take place in the softening regime prior to strain localization. The classical Rankine, Mohr-Coulomb, von Mises (J 2 ) and Drucker-Prager criteria are analyzed as illustrative examples. In particular, both the closed-form solutions for the discontinuity angles validated by numerical simulations and the corresponding traction-based failure criteria are obtained.

Mixed stabilized finite element methods in nonlinear solid mechanics. Part III: Compressible and incompressible plasticity

“…It can be appreciated that the solution obtained with this formulation is not realistic. Figure 13c shows that in this case the obtained plastic strain localizes in a layered pattern which is discontinuous from one Plane stress Analytical [29], [30] Table 2: Results for simply perforated thin-walled cylinder with the mixed "=u formulation. Comparison between the analytical localization angles for uniaxial tension in plane stress conditions and the ones obtained numerically horizontal layer of elements to the ones above or below.…”

“…This procedure, proposed in reference [29] and exploited in reference [30], produces more realistic results than those used beforehand. It makes use of the stress boundedness and decohesion conditions, which, combined, can be shown to be necessary conditions for the shear band to form, and more constrictive than the localization condition.…”

“…Table 2 shows the comparison between the analytical localization angles computed for uniaxial tension in plane stress conditions and the ones obtained numerically. The analytical values are obtained with the procedure presented in references [29] and [30]. Note that the localization angles are di¤erent in plane stress situations than under plane strain conditions.…”

Modelling of internal erosion based on mixture theory: General framework and a case study of soil suffusion

“…Moreover, the skeleton deformation is assumed to be reversible, even when the material is degraded due to erosion. This hypothesis is similar to what has been sometimes adopted in CDM where damage strain is assumed to be recoverable upon unloading . By contrast, the volume content evolution dv F is assumed to contain a reversible part due to mechanical loading dv Fe and explicitly an irreversible part due to erosion dv Fi .…”

On continuum damage mechanics

“…It is therefore somewhat frustrating that so few damage evolution studies have adopted this approach. There are, however, exceptions [23], [24], [25], [26].…”