A small-deformation strain-gradient theory for isotropic viscoplastic materials

Lele, Suvrat P.; Anand, Lallit

doi:10.1080/14786430802087031

Cited by 59 publications

(48 citation statements)

References 30 publications

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“…(34) is not physically acceptable. The inclusion of a rate-dependence in this class of theories, as in Gurtin and Anand [5] and Lele and Anand [16], can eliminate temporal stress discontinuities. However, at any abrupt change in direction of the boundary conditions for which the rate-independent limit undergoes stress jumps, the dependence on the parameter setting the rate-dependence will be exceptionally strong and difficult to justify physically.…”

Section: Strain Gradient Version Of J 2 Flow Theory 2: Higher Order Smentioning

confidence: 99%

“…Thus, the incorporation of ratedependence side steps the problem without resolving the fundamental physical issue. Lele and Anand [16] have explored the sensitivity of this class of strain gradient formulations to the level of rate-dependence for problems without abrupt changes in boundary conditions.…”

Section: Strain Gradient Version Of J 2 Flow Theory 2: Higher Order Smentioning

confidence: 99%

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Generalizing J 2 flow theory: Fundamental issues in strain gradient plasticity

Hutchinson

2012

Acta Mech Sin

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It has not been a simple matter to obtain a sound extension of the classical J 2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J 2 theory have been proposed: one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhaus and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy thermodynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J 2 flow theory of plasticity to include a dependence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermodynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher order stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J 2 flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J 2 deformation theory of gradient plasticity for deformation histories characterized by proportional straining.

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Section: Strain Gradient Version Of J 2 Flow Theory 2: Higher Order Smentioning

confidence: 99%

Section: Strain Gradient Version Of J 2 Flow Theory 2: Higher Order Smentioning

confidence: 99%

Generalizing J 2 flow theory: Fundamental issues in strain gradient plasticity

Hutchinson

2012

Acta Mech Sin

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“…2 has been used as the basis of a computational investigation, in two space dimensions, of the effect of dissipative microstresses. In the works of Gurtin, Anand and coworkers (see, for example, [15,17,19,32,33]), viscoplastic regularization entails extensions of Eq. (2.42) which take the form …”

Section: A Viscoplastic Model and Its Numerical Implementationmentioning

confidence: 99%

Some theoretical and computational aspects of single‐crystal strain‐gradient plasticity

Reddy

2013

Z Angew Math Mech

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Variational formulations are constructed for rate-independent problems in single-crystal strain-gradient plasticity. The framework makes use of the flow rule expressed in terms of a dissipation function. The formulation extends to the finitedeformation context earlier work on this problem. Provision is made for energetic and dissipative microstresses, and a range of defect energies is accounted for. The minimization problem corresponding to the time-discrete formulation is derived.Two special cases are then treated: first, for the small-strain problem with energetic microstresses, results on wellposedness, convergence of finite element approximations, the associated algorithms, and computational examples, are discussed. Secondly, recent computational work on the the related large-deformation viscoplastic problem, with both energetic and dissipative effects, is presented and discussed for problems involving ensembles of grains.

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“…The homogeneous Dirichlet condition, known as the micro-hard boundary condition, has been widely used to account for the grain boundary or an interface (see e.g. Ekh et al, 2007;Evers et al, 2004b;Kuroda and Tvergaard, 2008;Lele and Anand, 2008;Ohno and Okumura, 2007). Clearly this boundary condition ignores the complex geometric structures in the vicinity of the grain boundary.…”

Section: Introductionmentioning

confidence: 99%

Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

Gottschalk

McBride

Reddy

et al. 2016

Computational Materials Science

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A detailed theoretical and numerical investigation of the infinitesimal single-crystal gradientplasticity and grain-boundary theory of Gurtin (2008) "A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation". Journal of the Mechanics and Physics of Solids 56 (2), 640-662, is performed. The governing equations and flow laws are recast in variational form. The associated incremental problem is formulated in minimization form and provides the basis for the subsequent finite element formulation. Various choices of the kinematic measure used to characterize the ability of the grain boundary to impede the flow of dislocations are compared. An alternative measure is also suggested. A series of threedimensional numerical examples serve to elucidate the theory.

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A small-deformation strain-gradient theory for isotropic viscoplastic materials

Cited by 59 publications

References 30 publications

Generalizing J 2 flow theory: Fundamental issues in strain gradient plasticity

Generalizing J 2 flow theory: Fundamental issues in strain gradient plasticity

Some theoretical and computational aspects of single‐crystal strain‐gradient plasticity

Computational and theoretical aspects of a grain-boundary model that accounts for grain misorientation and grain-boundary orientation

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