Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity

By T. Liebe, Paul Steinmann. 2001

86 citations recorded by the source corpus.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/15e40f39acc741042cc59797aae9cfc619997d7c

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

A Finite Element approach with patch projection for strain gradient plasticity formulations (2007, unknown): “…with quadratic shape functions or mixed degrees of freedom in displacement and strains can be achieved on element level (Shu et al., 1999; Liebe and Steinmann, 2001; Meissonnier et al., 2001; Bittencourt et al., 2003; Soh and Wangji, 2004 and Cheong et al., 2005), these Element…”
Mixed variational principles and robust finite element implementations of gradient plasticity at small strains (2013, methodology): “This is in sharp contrast to the global active set search considered by Liebe and Steinmann [10] and an important ingredient for the robustness of the proposed formulation.”
A regularization framework for damage–plasticity models via gradient enhancement of the free energy (2011, background): “Nevertheless, there are several other choices as well: a plastic softening variable [12], a generalized effective plastic strain [13], or the plastic strain tensor increment [14].”
Gradient crystal plasticity as part of the computational modelling of polycrystals (2007, background): “Liebe and Steinmann [9] used a thermodynamic setting which is identical to the one proposed in this paper; however, isotropic gradient hardening is achieved in practice (rather than the anisotropic hardening that is brought about by restricting the gradient effect to each slip direction, as proposed”
A gradient-enhanced damage model coupled to plasticity—multi-surface formulation and algorithmic concepts (2018, background): “…Steinmann, 1999), for gradient plasticity formulations (de Borst and Mühlhaus, 1992; de Borst et al., 1999; Gurtin, 2010; Kuroda and Tvergaard, 2010; Liebe and Steinmann, 2001; Liebe et al., 2003; Mühlhaus and Aifantis, 1991; Polizzotto, 2009; Reddy et al., 2008; Voyiadjis and Deliktas, 2009),…”
A multi-field incremental variational framework for gradient-extended standard dissipative solids (2011, methodology): “This induces a multi-field treatment of continua with micro-structure in the spirit of the works by Capriz (1989), Mariano (2001), and Frémond (2002).”
A discontinuous Galerkin formulation for classical and gradient plasticity - Part 1: Formulation and analysis (2007, methodology): “Gradient plasticity We consider next a simple strain gradient plasticity model, first introduced in [5] and studied computationally in [6,12], in which the classical yield condition (9) is replaced by one in which the yield condition depends also on the Laplacian of the scalar hardening parameter or”
Localization properties of strain-softening gradient plasticity models. Part II: Theories with gradients of internal variables (2009, background): “Based on an extended form of the principle of virtual work, Fleck and Hutchinson (2001) showed that the divergence of the higher-order stress s that is work-conjugate with the gradient of the cumulative plastic strain should appear in the yield condition (Svedberg and Runesson, 1997; Polizzotto and ”
A discontinuous Galerkin formulation for classical and gradient plasticity. Part 2: Algorithms and numerical analysis (2007, methodology): “Related work, also using a conforming approximation, is that of Liebe and Steinmann [7].”