An implicit tensorial gradient plasticity model – Formulation and comparison with a scalar gradient model

Abstract

a b s t r a c tMany rate-independent models for metals utilize the gradient of effective plastic strain to capture sizedependent behavior. This enhancement, sometimes termed as ''explicit'' gradient formulation, requires higher-order tractions to be imposed on the evolving elasto-plastic boundary and the resulting numerical framework is complicated. An ''implicit'' scalar gradient model was thus developed in Peerlings [Peerlings, R.H.J., 2007. On the role of moving elastic-plastic boundaries in strain gradient plasticity. Model. Simul. Mater. Sci. Eng. 15, 109-120] that has only C 0 continuity requirements and its implementation is straightforward. However, both explicit and implicit scalar gradient models can be problematic when the effective plastic strains do not have smooth profiles. To address this limitation, an implicit tensorial gradient model is proposed in this paper based on the generalized micromorphic framework. It is also demonstrated that the scalar and tensorial implicit gradient models give similar results when the effective plastic strains fluctuate smoothly.

Nonlinear regularization operators as derived from the micromorphic approach to gradient elasticity, viscoplasticity and damage

“…The analysis was essentially limited to scalar micromorphic degrees of freedom for the sake of simplicity, even though tensorial examples were also given. Scalar plastic microstrain approaches suffer from limitations like indeterminacy of flow direction at cusps of the cumulative plastic strain in bending, for instance, see [60,97,98]. Those limitations can be removed by the use of tensorial micromorphic variable (microstrain or microdeformation tensors).…”

Análise da influência dos processos de plasticidade e fratura no comportamento mecânico de microestruturas de Compósitos de Matriz Metálica

“…O modelo multi-escala empregado neste trabalho parte do pressuposto que a tensão em um ponto da macro-escala num determinado instante está relacionada com a deformação acumulada até este instante: (3) onde: e representam a tensão e a deformação no instante , respectivamente; e é o tensor constitutivo simétrico.…”

“…Deste modo, o conhecimento da resposta constitutiva de um corpo submetido a um determinado estado de excitação configura-se como uma importante ferramenta para a ciência [1]. A princípio, essa questão foi respondida com o auxílio das teorias constitutivas fenomenológicas [2,3], cuja resposta pode ser obtida com base na análise de determinadas variáveis do problema. Contudo, os avanços tecnológicos levam à necessidade de respostas constitutivas mais realísticas, o que tornou limitada a utilização das teorias fenomenológicas.…”

A model for the shear displacement distribution of a flow line in the adiabatic shear band based on gradient-dependent plasticity

“…Averaging these local plastic shear strains over the entire ASB will lead to the nonlocal plastic shear strain, as can be easily confirmed through integrating (1) with respect to the coordinate y 2 ( w/2 −w/2 γ p (y 2 )dy 2 ), and then divided by the ASB width. For two and three-dimensional cases, the Laplacian will appear in GDP [Askes et al 2000;Peerlings et al 2001;Simone et al 2004;Voyiadjis and Abu Al-Rub 2005;Peerlings 2007;Poh et al 2011]. GDP can be derived from the nonlocal theory [Askes et al 2000;Peerlings et al 2001] by expanding the plastic strain into a Taylor series, and by neglecting gradient terms of order four and higher.…”

“…The phenomenon of the same shear stress corresponding to different shear strains cannot be uniquely described by classical continuum models where no internal length parameter is included, so that the nonuniform strain distribution and nonlinear displacement distribution in the localized zone, as well as the zone size, cannot be accurately obtained. Among the enriched continuum models, nonlocal and gradient continua have been widely used to avoid pathological localization in numerical simulation [De Borst and Mühlhaus 1992;Pamin and De Borst 1995;Askes et al 2000;Menzel and Steinmann 2000;Peerlings et al 2001;Simone et al 2004;Voyiadjis and Abu Al-Rub 2005;Peerlings 2007;Poh et al 2011], as have the Cosserat continuum and viscoplastic theories [Bažant and Pijaudier-Cabot 1988;Shawki and Clifton 1989]. In gradient continua, second-order gradient-dependent plasticity (GDP) is usually adopted, and a few analytical solutions of the strain and strain rate distribution in the localized band have been derived in the one-dimensional tensile and shear cases [De Borst and Mühlhaus 1992;Pamin and De Borst 1995;Menzel and Steinmann 2000].…”