Gradient material mechanics: Perspectives and Prospects

Aifantis, Elias C.

doi:10.1007/s00707-013-1076-y

Cited by 57 publications

(23 citation statements)

References 51 publications

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“…The simplicity and attraction of the pioneer Aifantis and co-workers' formulations relies in the fact that only one additional constitutive constant is required. However, as been observed by Elias Aifantis in a recent review article (Aifantis, 2014), there is still no available framework for relating internal lengths to physical properties even though the need has been documented in several studies (among others: Fleck and Hutchinson, 2001;Ghoniem and Walgraef, 2008;Gurtin and Anand, 2009). Internal lengths are usually treated as pure phenomenological constants and, with few exceptions, not much progress has been made toward their physical identification through microstructure modeling simulations or laboratory tests.…”

Section: Introductionmentioning

confidence: 97%

A note on stress fields and crack growth in porous materials subjected to a contact load

Isaksson

2015

International Journal of Solids and Structures

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a b s t r a c tIn materials where inherent heterogeneities like cells and pores are relatively large compared to other relevant mechanical dimensions, such as the contact surface in indentation tests or the length of an existing crack, stress and strain fields predicted by classical continuum elasticity theories may become too harsh because of absence of internal lengths in the equations that characterize the underlying microstructure. To overcome this deficiency a gradient enhanced elasticity continuum theory may be applied, which include length parameters in the constitutive equations that limit the magnitude of deformation gradients and is able to capture internal length effects. In this study, microscopic stress fields in porous materials subjected to a cylindrical contact load are estimated with such a gradient enhanced continuum model. To judge the model's ability to capture the mechanical behavior in this class of materials, calculated stress fields in the contact region, given by the gradient theory, are contrasted with microscopic stress fields computed in discrete high-resolution finite element models of cellular wood-like structures having varying average pore sizes but identical macroscopic geometry and boundary conditions as the gradient model. X-ray computed tomography experiments on wood illustrate the phenomenon. It is observed, in both experiment and finite element models, that the region of high shear stresses, where a crack may grow despite a confining pressure, is located deeper down in the material than what is predicted in classical continuum theories. On the other hand, the gradient enhanced model produces remarkably similar stress/strain fields as the finite element models and experiment and is thus seemingly able to capture microstructural size effects.

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Section: Introductionmentioning

confidence: 97%

A note on stress fields and crack growth in porous materials subjected to a contact load

Isaksson

2015

International Journal of Solids and Structures

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“…[2][3]) in the respective stress-strain curves. Such size-dependent behavior is captured by using a combined gradient-stochastic plasticity model as reviewed recently by Aifantis [4] and references quoted therein. Both deterministic gradients (to model the localization of deformation occurring as a result of local material softening) and stochastic terms (to model the inherent fluctuations of internal stress) enter in the governing expression for the flow stress.…”

Section: Introductionmentioning

confidence: 99%

“…Recent work [4,12] has shown the effectiveness of Tsallis q-statistics [13] for describing the statistics measured or predicted during plastic deformation. Along these lines, Tsallis q-statistics will also be utilized in this article for obtaining information on the stochastic nature of strain bursts during Mo micropillar compression [14], instead of "artificially" using a Weibull distribution.…”

Section: Introductionmentioning

confidence: 99%

On the combined gradient-stochastic plasticity model: Application to Mo-micropillar compression

Konstantinidis

Zhang²,

Aifantis

2015

AIP Conference Proceedings

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“…In order to extend its use to those situations involving complex multiaxial load histories, this approach has to be applied along with an appropriate multiaxial fatigue damage model. Researchers [1] has been proven that the highest level of accuracy is obtained by applying the PM along with the socalled Modified Wöhler Curve Method (MWCM) [5,6] and gradient elasticity [7][8][9][10], through length scale parameter ℓ (1). The MWCM is a biparametrical critical plane approach, the critical plane being that material plane experiencing the maximum shear stress amplitude τa.…”

Section: Introductionmentioning

confidence: 99%

“…The MWCM quantifies the extent of fatigue damage not only via τa, but also via the mean value, σn,m, and the amplitude, σn,a, of the stress perpendicular to the critical plane. Recent efforts [7][8][9][10] in the mechanics, materials science, and applied physics communities have introduced internal length in phenomenological gradient models to account for internal micro/nanostructures and derive, among other things, non-singular analytical expressions for dislocation/crack fields, as well as to interpret deformation localization phenomena (shear bands, dislocation patterns) along with size effects. As a result further development can be expected by combining gradient elasticity with TCD and MWCM.…”

Section: Introductionmentioning

confidence: 99%

Determination of Critical Size of Corrosion Pit on Mechanical Elements in Hydro Power Plants

Mitrović¹,

Momčilović²,

Atanasovska³

2018

Applied Engineering Letters

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Abstract:Researchers in the field of fracture mechanics, predominantly developing appropriate solution algorithms for problems of solid bodies with cracks. Problems in mechanics generally, related with fracture and fatigue for solid bodies with various geometries of sharp notches, are studied to a much lesser extent. This situation can be explained by analytical difficulties arising in solving problems of elasticity theory for bodies with rounded notches. To solve problems of such class, starting from data on stress concentration in the rounded notch tip with a significant radius of curvature, simplified solutions with are therefore of great importance. Recent years, due to constant rise of computing power and development of numerical methods, re-evaluation of stress concentration factors from a viewpoint of theory of elasticity is present. This is mainly as a feedback from industry, which have requirements toward mega and nanostructures. Corrosion represents an important limitation to the safe and reliable use of many alloys in various industries. Pitting corrosion is a form of serious damage on metals surface such as high-strength aluminum alloys and stainless steel, which are susceptible to pitting when exposed to a corrosive attack in aggressive environments. This is particularly valid for dynamic loaded structures. The basic idea behind this paper is finding links between different scientific and engineering disciplines, which will enable useful level of applicability of existing knowledge. The subject of this paper is application of new method of determine length scale parameter for estimating the mechanistic aspect of corrosion pit under uniaxial/multiaxial high-cycle fatigue loading… ARTICLE HISTORY

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Gradient material mechanics: Perspectives and Prospects

Cited by 57 publications

References 51 publications

A note on stress fields and crack growth in porous materials subjected to a contact load

A note on stress fields and crack growth in porous materials subjected to a contact load

On the combined gradient-stochastic plasticity model: Application to Mo-micropillar compression

Determination of Critical Size of Corrosion Pit on Mechanical Elements in Hydro Power Plants

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