Localization Analysis of Nonlocal Model Based on Crack Interactions

Abstract

The conventional non local model, often used as a localization limiter for continuum-based constitutive laws with strain·softening, has been based on an isotropic averaging function. It has recently been shown that this type of nonlocal averaging leads to a model that cannot satisfactorily reproduce experimental results for very different test geometries without modifying the value of the characteristic length depending on geometry. A micromechanically based enrichment of the nonlocal operator by a term taking into account the directional dependence of crack interactions can be expected to improve the performance of the nonlocal model. The aim of this paper is to examine this new model in the context of a simple localization problem reducible to a one·dimensional description. Strain localization in an infinite layer under plane stress is studied using both the old and the new non local formulations. The importance of a renormalization of the averaging function in the proximity of a boundary is demonstrated and the differences between the localization sensitivity of the old and new model are pointed out. In addition to the detection of bifurcations from an initially uniform state, the stable branch of the load·displacement diagram is followed using an incremental procedure.

Multiscale Modeling of Concrete

“…According to [76][77][78], nonlocality is caused by the heterogeneity of the material microstructure, by the fact that the growth of a microcrack depends on the overall energy release in the vicinity of that microcrack, and by interactions between microcracks. As shown in [79], the consideration of long-range interactions between microcracks requires a different type of nonlocal formulation, which is not used in this work. Short-range effects are taken into account by standard nonlocal models, (33), with isotropic averaging function.…”

Lagrangian formulations with nonlocal residual-based arguments

“…Contributions to this subject have been made by many authors, e.g. Altan [9] and Eringen [10] for nonlocal thermoelasticity; Polizzotto [11], Marotti de Sciarra [12] and Di Paola et al [13] for elasticity; Stromberg et al [14], Borino et al [15] and Marotti de Sciarra [16] for plasticity; and Bazant [17] and Jirasek et al [18] Recently, Di Paola et al [13,19] advanced a physicallybased model of nonlocal elasticity (PPZ model), and gave the relevant variational principle. In the PPZ model, a noteworth feature is that nonlocal terms appearing in the Euler-Lagrangian equation (see Eq.…”

High‐performance parallel simulation of structure degradation using non‐local damage models

“…Elementary external forces can be obtained from the right-hand side of Equation (14). The global internal forces (q int ) are obtained by assembling the elementary contributions q e u and q e f .…”