A comparison of the primal and semi-dual variational formats of gradient-extended crystal inelasticity

Carlsson, Kristoffer; Runesson, Kenneth; Larsson, Fredrik; Ekh, Magnus

doi:10.1007/s00466-017-1419-y

Cited by 5 publications

(1 citation statement)

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“…In the case where the constitutive equations for the gradient fields are given by (95), the vectorial Equation (30b) is replaced by two scalar equations. It is also quite straightforward to create an incremental potential as in (34) see eg, Section 5.2 in Carlsson et al 48…”

Section: Gradient Hardening Model Based On the Dislocation Tensormentioning

confidence: 99%

Bounds on the effective response for gradient crystal inelasticity based on homogenization and virtual testing

Carlsson

Larsson

Runesson

2019

Numerical Meth Engineering

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This paper presents the application of variationally consistent selective homogenization applied to a polycrystal with a subscale model of gradient-enhanced crystal inelasticity. Although the full gradient problem is solved on Statistical Volume Elements (SVEs), the resulting macroscale problem has the formal character of a standard local continuum. A semi-dual format of gradient inelasticity is exploited, whereby the unknown global variables are the displacements and the energetic micro-stresses on each slip-system. The corresponding time-discrete variational formulation of the SVE-problem defines a saddle point of an associated incremental potential. Focus is placed on the computation of statistical bounds on the effective energy, based on virtual testing on SVEs and an argument of ergodicity. As it turns out, suitable combinations of Dirichlet and Neumann conditions pertinent to the standard equilibrium and the micro-force balance, respectively, will have to be imposed. Whereas arguments leading to the upper bound are quite straightforward, those leading to the lower bound are significantly more involved; hence, a viable approximation of the lower bound is computed in this paper. Numerical evaluations of the effective strain energy confirm the theoretical predictions. Furthermore, heuristic arguments for the resulting macroscale stress-strain relations are numerically confirmed. KEYWORDSboundary conditions, computational homogenization, gradient crystal plasticity Int J Numer Methods Eng. 2019;119:281-304. wileyonlinelibrary.com/journal/nme

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Section: Gradient Hardening Model Based On the Dislocation Tensormentioning

confidence: 99%