Some Novel Developments in Finite Element Procedures for Gradient‐dependent Plasticity

Abstract

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Localization of deformation and failure around elliptical perforations based on a polar continuum

“…One of the unresolved issue with this approach is related to the integration of damage near the boundary of a structure. Another nonlocal regularization approach is based on incorporation of higher order deformation gradients (Vardoulakis and Aifantis, 1991;de Borst and Pamin, 1996;Ramaswamy and Arava 1998a, b;Zervos et al, 1999). The extra boundary conditions for the higher order gradient theories have not yet fully understood and in addition, higher order elements are generally required for the numerical implementation.…”

“…Exploiting the progress in numerical techniques and the evolution in computer power the last decade many dedicated studies appeared on bifurcation for more complicated boundary-value problems and, more importantly, for post-bifurcation analyzes implementing higher order continuum theories (de Borst and Sluys 1991;Papanastasiou and Vardoulakis, 1992;Tejchman and Wu, 1993;de Borst and Pamin, 1996;Aravas, 1997a, 1997b;Ehlers and Volk 1998). The majority of these studies had a main objective to demonstrate the superiority of the new theories over the limitations of the classical elastoplasticity.…”

Necking of anisotropic micro-films with strain-gradient effects

“…However, here only tension without kinematic hardening will be considered and oscillatory stress behaviors are not a problem. The finite element procedure adopted here follows the method used by de Borst and Pamin [48] for timeindependent plasticity and Borg et al [42] for viscoplasticity, where both the conventional displacement increments, D, as well as the increments of the effective plastic strain rates, ε p , appear as unknowns. However, they solved for D and ε p simultaneously, even though the system of equations decouples.…”

A mixed finite volume formulation for the solution of gradient elasticity problems

“…Special focus is also given in the numerical solution of strain gradient equations via finite and boundary element methods. Tsamasphyros [21,22], Markolefas [15], Amanatidou [1], Borst [3,4] are some of the many researchers working towards this direction.…”