Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour

By R. Engelen, Mgd Marc Geers, F. Baaijens. 2003

344 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/a09c41fa7eb1515abac88a057320d24fd4206748

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Gradient plasticity theory with a variable length scale parameter (2005, background): “…many others in solving the localization problem (see for example de Borst and Mühlhaus, 1992; de Borst et al., 1993; de Borst and Pamin, 1996; Claudia and Perego, 1996; Chen et al., 2000; Zervos et al., 2001; Voyiadjis et al., 2001, 2003, 2004; Engelen et al., 2003; and references quoted therein).”
Filters in topology optimization based on Helmholtz‐type differential equations (2011, methodology): “The Helmholtz PDE has also been applied for imposing length scale in damage mechanics [15] and in non-local plasticity [16].”
A discontinuous Galerkin formulation for classical and gradient plasticity. Part 2: Algorithms and numerical analysis (2007, methodology): “The example problem initially analysed by Pamin [5], and subsequently in [42–44], is slightly modified here and analysed using the classical and gradient plasticity formulations.”
Micromorphic Approach for Gradient Elasticity, Viscoplasticity, and Damage (2009, methodology): “In the reference Engelen et al. 2003 , after introducing the partial differential Eq.”
Dwell fatigue crack nucleation model based on crystal plasticity finite element simulations of polycrystalline titanium alloys (2011, neutral): “11(b)) has been proposed in Engelen et al. (2003).”
Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua (2010, methodology): “(20), the previous state laws lead to the following partial differential equation: vp A Hv D vp ¼ p ð28Þ which is identical to the additional partial differential equation used in the so-called implicit gradient-enhanced elastoplasticity in Engelen et al. (2003).”
An evaluation of higher-order plasticity theories for predicting size effects and localisation (2006, methodology): “In the plasticity-damage formulation of Engelen et al. (1999, 2003) the local contribution h is always positive, whereas �h is always negative.”
Localization properties of strain-softening gradient plasticity models. Part II: Theories with gradients of internal variables (2009, methodology): “Drawing inspiration from implicit gradient damage models (Peerlings et al., 1996), Geers, Engelen and coworkers proposed an implicit gradient plasticity model based on the concept of ductile damage (Geers et al., 2001; Engelen et al., 2003; Geers, 2004).”