Nonsingular dislocation and crack fields: implications to small volumes

Kioseoglou, Joseph; Konstantopoulos, I.; Ribárik, Gabor; Dimitrakopulos, G. P.; Aifantis, Elias C.

doi:10.1007/s00542-008-0700-6

Cited by 13 publications

(7 citation statements)

References 20 publications

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“…More recently, the robust and simple gradient elasticity model of Aifantis was used to describe characteristics at the atomic scale, such as dislocation core sizes, as well as to interpret measurements pertaining to the dislocation density tensor and internal strain states through X-ray profile analysis (Kioseoglou et al, 2006(Kioseoglou et al, , 2008(Kioseoglou et al, , 2009Aifantis, 2009a). The length scale parameter values estimated from these measurements are directly related to the lattice spacing, as expected.…”

Section: Experimental Validationmentioning

confidence: 93%

Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results

Askes

Aifantis

2011

International Journal of Solids and Structures

770

503

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a b s t r a c tIn this paper, we discuss various formats of gradient elasticity and their performance in static and dynamic applications. Gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher-order spatial derivatives of strains, stresses and/or accelerations. We focus on the versatile class of gradient elasticity theories whereby the higher-order terms are the Laplacian of the corresponding lower-order terms. One of the challenges of formulating gradient elasticity theories is to keep the number of additional constitutive parameters to a minimum. We start with discussing the general Mindlin theory, that in its most general form has 903 constitutive elastic parameters but which were reduced by Mindlin to three independent material length scales. Further simplifications are often possible. In particular, the Aifantis theory has only one additional parameter in statics and opens up a whole new field of analytical and numerical solution procedures. We also address how this can be extended to dynamics. An overview of length scale identification and quantification procedures is given. Finite element implementations of the most commonly used versions of gradient elasticity are discussed together with the variationally consistent boundary conditions. Details are provided for particular formats of gradient elasticity that can be implemented with simple, linear finite element shape functions. New numerical results show the removal of singularities in statics and dynamics, as well as the size-dependent mechanical response predicted by gradient elasticity.

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Section: Experimental Validationmentioning

confidence: 93%

Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results

Askes

Aifantis

2011

International Journal of Solids and Structures

770

503

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“…These and the rest of the results listed in this section, which are also reviewed in a recent article by the author and co-workers [9], will be discussed in detail in [10]. The results depicted in Figures 4 and 5 suggest that careful measurements seem to validate the predictions of Gradela.…”

mentioning

confidence: 48%

“…To support this further we provide in Figures 6 and 7 results pertaining to polycrystals with ultrafine grain size produced by the ECAP method. As already mentioned, some of these results are included in a recent article on applications of gradient theory [9], but an extended discussion focussing on the application of Gradela to X-ray line profile analysis is forthcoming [10] where details on the relevance of Figures 6 and 7 will be given. …”

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confidence: 99%

Non-singular dislocation fields

Aifantis

2009

IOP Conf. Ser.: Mater. Sci. Eng.

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“…In this context the equilibrium, as well as, the kinematic restraints of the non-local elastic continuum theory remain unchanged but the Navier governing equations of the elastic problem involves higher-order derivatives of the unknown displacement field. Some recent applications of the gradient theory of non-local elasticity has been recently proposed in nanoscale engineering applications (Aifantis, 2009;Kioseoglou et al, 2009). Some recent strategies to provide experimental measures of the elastic coefficients of the internal microstructure as well as a mathematically consistent formulation of the non-standard boundary conditions have been recently proposed (Maraganti and Sharma, 2007;Polizzotto, 2003).…”

Section: Introductionmentioning

confidence: 99%

Mechanically-based approach to non-local elasticity: Variational principles

Paola

Pirrotta

Zingales

2010

International Journal of Solids and Structures

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The mechanically-based approach to non-local elastic continuum, will be captured through variational calculus, based on the assumptions that non-adjacent elements of the solid may exchange central body forces, monotonically decreasing with their interdistance, depending on the relative displacement, and on the volume products. Such a mechanical model is investigated introducing primarily the dual state variables by means of the virtual work principle. The constitutive relations between dual variables are introduced defining a proper, convex, potential energy. It is proved that the solution of the elastic problem corresponds to a global minimum of the potential energy functional. Moreover, the Euler-Lagrange equations together with the natural boundary conditions associated to the total potential energy functional are established with variational calculus and they coincide with analogous relations already obtained by means of mechanical considerations. Numerical analysis of a tensile specimen has been introduced to show the capabilities of the proposed approac

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Nonsingular dislocation and crack fields: implications to small volumes

Cited by 13 publications

References 20 publications

Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results

Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results

Non-singular dislocation fields

Mechanically-based approach to non-local elasticity: Variational principles

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