Dislocations in second strain gradient elasticity

By Markus Lazar, G. Maugin, Elias C. Aifantis. 2006

201 citations recorded by the source corpus.

Abstract A second strain gradient elasticity theory is proposed based on first and second gradients of the strain tensor. Such a theory is an extension of first strain gradient elasticity with double stresses. In particular, the strain energy depends on the strain tensor and on the first and second gradient terms of it. Using a simplified but straightforward version of this gradient theory, we can connect it with a static version of Eringen’s nonlocal elasticity. For the first time, it is used to study a screw dislocation and an edge dislocation in second strain gradient elasticity. By means of this second gradient theory it is possible to eliminate both strain and stress singularities. Another important result is that we obtain nonsingular expressions for the force stresses, double stresses and triple stresses produced by a straight screw dislocation and a straight edge dislocation. The components of the force stresses and of the triple stresses have maximum values near the dislocation line and are zero there. On the other hand, the double stresses have maximum values at the dislocation line. The main feature is that it is possible to eliminate all unphysical singularities of physical fields, e.g., dislocation density tensor and elastic bend-twist tensor which are still singular in the first strain gradient elasticity.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f69bc81383fb59ac786f72ea84e2fcaddfa3b0a6

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Second strain gradient elasticity of nano-objects (2016, result): “This finding should be related to the identification of negative first strain gradient higher order elastic moduli sometimes found by comparison with the results of atomistic simulations, see Maranganti and Sharma (2007). Negative surface elasticity properties were also found in the context of bulk ”
Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua (2010, background): “A special case of the previous theory has been considered by various authors (Shu, 1998; Shu and Fleck, 1999; Lazar et al., 2006) in order to reduce the complexity of the higher order constitutive equations.”
Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua (2012, unknown): “[52], [95], [94], [69], [100], [3], [54], [55], [57], [59], [56], [58], [101]), [93].”
Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity (2005, methodology): “(3)In the meantime [47], we have calculated the double and triple stresses of screw and edge dislocations in second strain gradient elasticity.”