On the relevance of generalized disclinations in defect mechanics

Zhang, Chiqun; Acharya, Amit

doi:10.1016/j.jmps.2018.06.020

Cited by 28 publications

(27 citation statements)

References 60 publications

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“…For a single disclination, Ω = 0 in the core. Following the arguments in [ZA16], one can create a non-simply connected domain by excluding the core cylinder/curve from the overall simplyconnected body. By making an appropriate cut one can then render the body without the core simply-connected again (but not continuously deformable to the original body with the core).…”

Section: Disclinations In Small and Finite Deformation Theorymentioning

confidence: 99%

“…constant regardless of the spin field (and corresponding cut-surface) involved. Let us denote this constant jump for a single disclination as W and it can be shown, following the arguments in [ZA16], that…”

Section: Disclinations In Small and Finite Deformation Theorymentioning

confidence: 99%

“…Here we solve an edge dislocation problem, interpreted as a g.disclination dipole, as discussed in [ZA16,Sec. 4.3].…”

Section: Single Dislocationmentioning

confidence: 99%

“…In this context, two opposite-sign g.disclinations are prescribed with the distortion differences as pure rotation differences (g.disclinations become pure disclinations), with Frank vector Ω and −Ω respectively. Based on the results in [ZA16], the Burgers vector b for this disclination dipole in small deformation theory is given as b = Ω × δr, where δr is the dipole vector (the vector that separates the two disclinations in the dipole). Figure 9(a) is the stress field σ 11 from the g.disclination dipole model and Figure 9(b) is the stress field σ 11 for the classical linear elastic dislocation with the corresponding Burgers vector b = Ω ×δr.…”

Section: Single Dislocationmentioning

confidence: 99%

“…Consider a disclination loop in a 3d domain that is discussed in [ZA16]. The configuration of the disclination loop is shown in Figure 36, where AB and CD are wedge disclinations while AD and BC are twist disclinations.…”

Section: Disclination Loopmentioning

confidence: 99%

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Finite element approximation of the fields of bulk and interfacial line defects

Zhang

Acharya

Puri

2018

Journal of the Mechanics and Physics of Solids

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A generalized disclination (g.disclination) theory [AF15] has been recently introduced that goes beyond treating standard translational and rotational Volterra defects in a continuously distributed defects approach; it is capable of treating the kinematics and dynamics of terminating lines of elastic strain and rotation discontinuities. In this work, a numerical method is developed to solve for the stress and distortion fields of g.disclination systems. Problems of small and finite deformation theory are considered. The fields of a single disclination, a single dislocation treated as a disclination dipole, a tilt grain boundary, a misfitting grain boundary with disconnections, a through twin boundary, a terminating twin boundary, a through grain boundary, a star disclination/penta-twin, a disclination loop (with twist and wedge segments), and a plate, a lenticular, and a needle inclusion are approximated. It is demonstrated that while the far-field topological identity of a dislocation of appropriate strength and a disclination-dipole plus a slip dislocation comprising a disconnection are the same, the latter microstructure is energetically favorable. This underscores the complementary importance of all of topology, geometry, and energetics in understanding defect mechanics. It is established that finite element approximations of fields of interfacial and bulk line defects can be achieved in a systematic and routine manner, thus contributing to the study of intricate defect microstructures in the scientific understanding and predictive design of materials. Our work also represents one systematic way of studying the interaction of (g.)disclinations and dislocations as topological defects, a subject of considerable subtlety and conceptual importance [Mer79, AMK17]. energies for finite bodies. In [AF12, AF15], a continuum model is introduced for the g.disclination static equilibrium as well as dynamic behaviors, where the singularities are well-handled. The Weingarten theorem for g.disclinations established in [AF15] is characterized further in [ZA16], with the derivation of explicit formula for important topological properties of canonical g.disclination configurations. Relationships between the representations of the dislocation, disclination, and the g.disclination from the Weingarten point of view and in g.disclination theory are established therein. Concrete connections are also established between g.disclinations as mathematical objects and the physical ideas of interfacial and bulk line defects like defected grain and phase boundaries, dislocations, and disclinations. The papers [AF12, AF15, ZA16] explain the theoretical and physical basis for the results obtained in the present work.This paper focuses on the applications of the g.disclination model through computation. The goal is to show that the g.disclination model is capable of solving various material-defect problems, within both the small and finite deformation settings. Finite element schemes to solve for the stress and energy density fields of g.disc...

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Section: Disclinations In Small and Finite Deformation Theorymentioning

confidence: 99%

Section: Disclinations In Small and Finite Deformation Theorymentioning

confidence: 99%

“…Here we solve an edge dislocation problem, interpreted as a g.disclination dipole, as discussed in [ZA16,Sec. 4.3].…”

Section: Single Dislocationmentioning

confidence: 99%

Section: Single Dislocationmentioning

confidence: 99%

Section: Disclination Loopmentioning

confidence: 99%

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Finite element approximation of the fields of bulk and interfacial line defects

Zhang

Acharya

Puri

2018

Journal of the Mechanics and Physics of Solids

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Singularity-free defect mechanics for polar media

Mousavi

2019

Continuum Mech. Thermodyn.

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We present singularity-free solution for cracks within polar media in which material points possess both position and orientation. The plane strain problem is addressed in this study for which the generalized continua including micropolar, nonlocal micropolar, and gradient micropolar elasticity theories are employed. For the first time, the variationally consistent boundary conditions are derived for gradient micropolar elasticity. Moreover, having reviewed the solution to line defects including glide edge dislocation and wedge disclination from the literature, the fields of a climb edge dislocation within micropolar, nonlocal micropolar and gradient micropolar elasticity are derived. This completes the collection of line defects needed for an inplane strain analysis. Afterward, as the main contribution, using both types of line defects (i.e., dislocation being displacement discontinuity and disclination being rotational discontinuity), the well-established dislocation-based fracture mechanics is systematically generalized to the dislocation-and disclination-based fracture mechanics of polar media for which we have three translations together with three rotations as degrees of freedom. Due to the application of the line defects, incompatible elasticity is employed throughout the paper. Cracks under three possible loadings including stress and couple stress components are analyzed, and the corresponding line defect densities and stress and couple stress fields are reported. The singular fields are obtained once using the micropolar elasticity, while nonlocal micropolar, and gradient micropolar elasticity theories give rise to singularity-free fracture mechanics. IntroductionGeneralized (or extended) continua include (strong) nonlocal theories as well as higher-order (or microcontinuum) and higher-grade (or weak nonlocal) extensions to the classical continuum theories. Within nonlocal elasticity, nonlocal stresses at a material point is expressed as a function of weighted values of the entire stress field. On the other hand, by increasing the order of the theory, microcontinuum field theories (e.g., micromorphic elasticity, microstretch elasticity, micropolar elasticity, and dilatation elasticity) are obtained. Further, higher-grade versions include gradient elasticity theories.A microcontinuum is a continuous collection of deformable point particles [14] for which the stress measures include force stress as well as couple stress [13,54,55]. Microcontinuum field theories address media for which the microstructure is no longer rigid (e.g., polar media). These theories are in fact a two-level continuum models where macroscopic deformation field is enhanced with the microscopic deformation. Within Communicated by Victor Eremeyev, Holm Altenbach.

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IGA Approximations of Elastic Interfaces and their Defects in an Elastic Medium with Couple Stress

Zegpi,

Casquero,

Zhang

et al. 2024

Engineering with Computers

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The objective of this work is to develop and implement a computational algorithm for calculating stress and couple-stress fields induced by bulk and interfacial line defects such as dislocations and generalized disclinations within phase/grain boundaries. The thermodynamic driving forces on line and planar defects, responsible for coupled plasticity and interface motion, fully coupled to stress, couple-stress and applied boundary conditions are also computed. A continuum approach for small deformations is considered following the formulation outlined in Acharya and Fressengeas (Continuum mechanics of the interaction of phase boundaries and dislocations in solids. In: Differential Geometry and Continuum Mechanics, pages 123–165, 2015), extended herein in the thermodynamics to accommodate physically necessary ingredients that arose in the modeling in Zhang and Acharya (J Mech Phys Solids 119:188–223, 2018), Zhang et al. (J Mech Phys Solids 114:258–302, 2018). Constitutive relations are derived from kinematics, balance laws and from the use of the second law of thermodynamics in global form. One of the challenges presented by this approach is the inclusion of couple stresses, Toupin (Arch Rational Mech Anal 17(2):85–112, 1964), and the consequent treatment of 4th order systems arising from the equations of balances of linear and angular momentum. In order to deal with these equations, the classical FEM approach is replaced by iso-geometric analysis (IGA), as proposed by Hughes et al. (Comput Methods Appl Mech Eng 194(39):4135–4195, 2005). Results on stress and couple stress fields of the various defects involved are computed. Further, the coupling of the dislocation density with the eigenwall allows for the capturing of the shear parallel to the grain boundary, which has been observed experimentally and through molecular dynamics.

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On the relevance of generalized disclinations in defect mechanics

Cited by 28 publications

References 60 publications

Finite element approximation of the fields of bulk and interfacial line defects

Finite element approximation of the fields of bulk and interfacial line defects

Singularity-free defect mechanics for polar media

IGA Approximations of Elastic Interfaces and their Defects in an Elastic Medium with Couple Stress

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