Plasticity in multi-phase solids with incoherent interfaces and junctions

Basak, Anup; Gupta, Anurag

doi:10.1007/s00161-015-0441-6

Cited by 8 publications

(9 citation statements)

References 34 publications

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“…The theory of incoherent interfaces, which includes junctions and diffusion, is in fact applicable to a more general situation where the grains are allowed to deform plastically. The resulting framework would be useful for phenomena which involves coupling of plastically deforming bulk with moving incoherent interfaces and junctions [31]. Second, the kinetic relations derived for the tricrystal can be used to study the coupled motion in polycrystalline materials containing large number of grains and junctions.…”

Section: Discussionmentioning

confidence: 99%

A three-dimensional study of coupled grain boundary motion with junctions

Basak

Gupta

2015

Proc. R. Soc. A.

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A novel continuum theory of incoherent interfaces with triple junctions is applied to study coupled grain boundary (GB) motion in three-dimensional polycrystalline materials. The kinetic relations for grain dynamics, relative sliding and migration of the boundary and junction evolution are developed. In doing so, a vectorial form of the geometrical coupling factor, which relates the tangential motion at the GB to the migration, is also obtained. Diffusion along the GBs and the junctions is allowed so as to prevent nucleation of voids and overlapping of material near the GBs. The coupled dynamics has been studied in detail for two bicrystalline and one tricrystalline arrangements. The first bicrystal consists of two cubic grains separated by a planar GB, whereas the second is composed of a spherical grain embedded inside a larger grain. The tricrystal has an arbitrary-shaped grain embedded inside a much larger bicrystal made of two cubic grains. In all these cases, analytical solutions are obtained wherever possible while emphasizing the role of various kinetic coefficients during the coupled motion.

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Section: Discussionmentioning

confidence: 99%

A three-dimensional study of coupled grain boundary motion with junctions

Basak

Gupta

2015

Proc. R. Soc. A.

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“…The last three integrals are non-standard. The first of these is to account for excess entropy generation due to a part of the interface S entering/leaving the fixed domain Ω [4,5], where w ∈ V is the intrinsic velocity of the edge ∂S, such that w = U N + W ν. The second one provides a correction to the mechanical power due to interfacial traction.…”

Section: Dissipation Inequality and Kinetic Lawsmentioning

confidence: 99%

“…where C is the boundary of a small semi-circular disc of radius centred at a point on D 0 [4,5]. In writing (32) 1 , we assume the bulk concentration field C to remain bounded at the film edge.…”

Section: Growing Thin Film Over a Growing Substratementioning

confidence: 99%

“…where the superscripts γ and η denote the two distinct surfaces in the stress-free configuration both related to the single interface in B 0 or B t . The relaxation of the interface into two distinct surfaces is a consequence of the incoherency of the interface [15,25]. For a coherent interface, H γ = H η , or equivalently G γ = G η ; the jumps in H and G are then necessarily rank-one.…”

Section: (B) Growth Kinematicsmentioning

confidence: 99%

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Biological growth in bodies with incoherent interfaces

Swain

Gupta

2018

Proc. R. Soc. A.

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A general theory of thermodynamically consistent biomechanical-biochemical growth in a body, considering mass addition in the bulk and at an incoherent interface, is developed. The incoherency arises due to incompatibility of growth and elastic distortion tensors at the interface. The incoherent interface therefore acts as an additional source of internal stress besides allowing for rich growth kinematics. All the biochemicals in the model are essentially represented by nutrient concentration fields, in the bulk and at the interface. A nutrient balance law is postulated which, combined with mechanical balances and kinetic laws, yields an initial-boundary-value problem coupling the evolution of bulk and interfacial growth, on one hand, and the evolution of growth and nutrient concentration on the other. The problem is solved, and discussed in detail, for two distinct examples:annual ring formation during tree growth and healing of cutaneous wounds in animals.

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“…Thus, assuming that the body is initially unloaded and undeformed, which corresponds to assuming that f (x, 0) = 0 for almost all x ∈ with homogeneous initial conditions, we obtained the following existence result for the weak formulation (86) of our model. 99)- (103) with the norms in (104) and the functionals a, j and in ( 88)- (90), the weak formulation (86) when written as the variational inequality of the second kind (91) has a solution w = (u, ε p , γ p ) in H 1 ([0, T]; Z) withẇ ∈ L 2 ([0, T]; W). Remark 4.2.…”

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confidence: 99%

A fourth-order gauge-invariant gradient plasticity model for polycrystals based on Kröner’s incompatibility tensor

Ebobisse

Neff

2019

Mathematics and Mechanics of Solids

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In this paper we derive a novel fourth order gauge-invariant phenomenological model of infinitesimal rate-independent gradient plasticity with isotropic hardening and Kröner's incompatibility tensor inc(ε p ) := Curl [(Curl ε p ) T ], where ε p is the symmetric plastic strain tensor. Here, gauge-invariance denotes invariance under diffeomorphic reparametrizations of the reference configuration, suitably adapted to the geometrically linear setting. The model features a defect energy contribution which is quadratic in the tensor inc(ε p ) and it contains isotropic hardening based on the rate of the plastic strain tensorε p . We motivate the new model by introducing a novel rotational invariance requirement in gradient plasticity, which we call micro-randomness, suitable for the description of polycrystalline aggregates on a mesoscopic scale and not coinciding with classical isotropy requirements. This new condition effectively reduces the increments of the non-symmetric plastic distortionṗ to their symmetric counterpartε p = symṗ. In the polycrystalline case, this condition is a statement about insensitivity to arbitrary superposed grain rotations. We formulate a mathematical existence result for a suitably regularized non-gauge-invariant model. The regularized model is rather invariant under reparametrizations of the reference configuration including infinitesimal conformal mappings. Appendix 322 Aifantis writes in [4, p. 218]: "... In conformity with established results -that the plastic strain rateεp is a state variable, rather than the strain εp itself."3 The plastic spin in the finite deformation flow theory of plasticity is defined as the skew-symmetric part of the so-called plastic distortion rate i.e., Wp := skew(ḞpF −1 p ) , while its counter-part in the small strain theory is simply skew(ṗ) , where p is the non-symmetric infinitesimal plastic distortion.

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Plasticity in multi-phase solids with incoherent interfaces and junctions

Cited by 8 publications

References 34 publications

A three-dimensional study of coupled grain boundary motion with junctions

A three-dimensional study of coupled grain boundary motion with junctions

Biological growth in bodies with incoherent interfaces

A fourth-order gauge-invariant gradient plasticity model for polycrystals based on Kröner’s incompatibility tensor

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