Nonlocal integral formulations of plasticity and damage : Survey of progress

By Zdenek P. Bazant, Milan Jirásek. 2002

1,392 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6bbd6b3fe110fbd645161b1085de287ccb849198

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

A Method for Gradient Enhancement of Continuum Damage Models (2008, positive): “The integral strategy introduces non-local variables as weighted averages of the local internal variables of the points near the point under consideration, see Bažant and Jirásek (2002). The application of nonlocal integral models together with inelastic materials is not very efficient from the comp”
Numerical solutions of strain localization with nonlocal softening plasticity (2009, positive): “Ill-posed problems can be regularized using various strategies, including visco-plasticity [1,3], Cosserat or micro-polar models [4– 6], higher-order gradient models [7,8] and integral type nonlocal models [9–14].”
A new damage model based on non‐local displacements (2005, background): “However, the concept of non-local displacements can be extended to more complex damage models exhibiting, for instance, anisotropy or plasticity [4, 12].”
Meso-scale modelling of the size effect on the fracture process zone of concrete (2011, positive): “Continuum approaches describe the fracture process by higher-order constitutive models, such as integral-type nonlocal models (Bažant and Jirásek, 2002).”
On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity (2007, positive): “Non-local theories taking into account effects of long-range interactions in elastic materials and their application to problems of solid and fracture mechanics have been studied for a long time, cf. the pioneering work by Kröner [21], Eringen [17] and the references cited therein, the monographs b”
Smeared crack approach: back to the original track (2006, background): “To remedy this, many so-called nonlocal constitutive models have been proposed in the last decade in different versions (micropolar models ([26]), gradient-enhanced models ([26], [27], [28], [29], [30])).”
Prediction of size effects in notched laminates using continuum damage mechanics (2007, background): “the solution is non-objective with respect to the mesh refinement and the computed energy dissipated decreases with a reduction of the element size [42]-[43].”
Mixed stabilized finite element methods in nonlinear solid mechanics: Part II: Strain localization (2010, background): “In the last 25 years, micropolar ([3], [4]), gradient-enhanced ([5], [6], [7], [8], [9]) and non-local , ([5], [10], [11], [12], [13], [14], among others) models have been proposed with the common basic idea of modifying the original continuous problem to introduce an internal length that acts as a ”
A new open-source software developed for numerical simulations using discrete modeling methods (2008, background): “It can be of a different kind such as: a collision, a cohesive link or being governed by a stiffness matrix or a non–local dependency [3, 17].”