Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity

By Markus Lazar, G. Maugin. 2005

257 citations recorded by the source corpus.

Abstract The aim of this paper is to study the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin’s gradient elasticity. We consider simple but rigorous versions of Mindlin’s first gradient elasticity with one material length (gradient coefficient). Using the stress function method, we find modified stress functions for all six types of Volterra defects (dislocations and disclinations) situated in an isotropic and infinitely extended medium. By means of these stress functions, we obtain exact analytical solutions for the stress and strain fields of dislocations and disclinations. An advantage of these solutions for the elastic strain and stress is that they have no singularities at the defect line. They are finite and have maxima or minima in the defect core region. The stresses and strains are either zero or have a finite maximum value at the defect line. The maximum value of stresses may serve as a measure of the critical stress level when fracture and failure may occur. Thus, both the stress and elastic strain singularities are removed in such a simple gradient theory. In addition, we give the relation to the nonlocal stresses in Eringen’s nonlocal elasticity for the nonsingular stresses.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/da9007df557a202b7dbf3c401d40c0ee2393ffa4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

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].”
Modelling size-dependent bending, buckling and vibrations of 2D triangular lattices by strain gradient elasticity models: Applications to sandwich beams and auxetics (2018, background): “10) leading to the so-called simplified strain gradient elasticity model [13, 48] with g denoting an intrinsic structural length scale parameter with unit of length.”
Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results (2011, background): “(4) as has been argued by Lazar and Maugin (2005).”
Geometrically nonlinear higher-gradient elasticity with energetic boundaries (2013, background): “Javili, A., Steinmann, P., 2010b.”
On the gradient approach - Relation to Eringen's nonlocal theory (2011, background): “In this connection, it is noted that in Feynman’s linear theory of gravity (Feynman, 1995) – see also the discussion by Lazar and Maugin (2005) contained in the reference for Feynman listed in the bibliography – an expression like Mindlin’s given by Eq.”