Steady-state propagation of a mode II crack in couple stress elasticity

International Journal of Solids and Structures

Corso

2015

Please cite this article as: Zisis, Th., Gourgiotis, P.A., Dal Corso, F., A contact problem in couple stress thermoelasticity: The indentation by a hot flat punch, International Journal of Solids and Structures (2015), doi: http://dx. AbstractIt is well known, that thermo-elastic effects may have significant results upon the macroscopic response in the mechanics of contact. On the other hand, as the scales in the contact system reduce progressively (micro to nano-scales), the internal material lengths become important and their effect upon the macroscopic response cannot be ignored. The present work extends the classical contact solution for a hot flat punch indenting a homogeneous elastic half-plane, where heat conduction is permitted (Comninou et al., 1981), to the analogous case of an indented microstructured solid. The behavior of the indented material is modelled through the couple-stress elasticity theory, which introduces characteristic material lengths and is appropriately modified in order to incorporate the thermal effects. The problem formulation is based on singular integral equations, resulted from a treatment of the mixed boundary value problems via integral transforms and generalized functions. The results show significant departure from the predictions of classical thermoelasticity showing that the microstructural characteristics of the material should not be ignored.

mentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

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A contact problem in couple stress thermoelasticity: The indentation by a hot flat punch

Zisis

International Journal of Solids and Structures

Corso

2015

“…A detailed presentation of the couple-stress theory (called also ‘constrained Cosserat theory’) can be found in [7] (see also [4,8]).…”

Section: Dynamics Of Couple-stress Elasticitymentioning

confidence: 99%

The dynamics of folding instability in a constrained Cosserat medium

Phil. Trans. R. Soc. A.

Bigoni

2017

Different from Cauchy elastic materials, generalized continua, and in particular constrained Cosserat materials, can be designed to possess extreme (near a failure of ellipticity) orthotropy properties and in this way to model folding in a three-dimensional solid. Following this approach, folding, which is a narrow zone of highly localized bending, spontaneously emerges as a deformation pattern occurring in a strongly anisotropic solid. How this peculiar pattern interacts with wave propagation in the time-harmonic domain is revealed through the derivation of an antiplane, infinite-body Green’s function, which opens the way to integral techniques for anisotropic constrained Cosserat continua. Viewed as a perturbing agent, the Green’s function shows that folding, emerging near a steadily pulsating source in the limit of failure of ellipticity, is transformed into a disturbance with wavefronts parallel to the folding itself. The results of the presented study introduce the possibility of exploiting constrained Cosserat solids for propagating waves in materials displaying origami patterns of deformation.This article is part of the themed issue ‘Patterning through instabilities in complex media: theory and applications.’

“…Detailed presentations of the couple-stress theory can be found in the fundamental papers of Mindlin and Tiersten (1962), and Koiter (1964). An exposition of the theory under plane-strain conditions was given in the work by Muki and Sternberg (1965), and more recently by Gourgiotis and Piccolroaz (2014) in the elastodynamic case including micro-inertial effects.…”

Section: Basic Equations Of Couple-stress Elasticity In Plane-strainmentioning

confidence: 99%

Analysis of the tilted flat punch in couple-stress elasticity

International Journal of Solids and Structures

Zisis

Baxevanakis

2016

Abstract. In the present paper we explore the response of a half-plane indented by a tilted flat punch with sharp corners in the context of couple-stress elasticity theory. Contact conditions arise in a number of modern engineering applications ranging from structural and geotechnical engineering to micro and nanotechnology. As the contact scales reduce progressively the effects of the microstructure upon the macroscopic material response cannot be ignored. The generalized continuum theory of couple-stress elasticity introduces characteristic material lengths in order to describe the pertinent scale effects that emerge from the underlying material microstructure. The problem under investigation is interesting for three reasons: Firstly, the indentor's geometry is simple so that benchmark results may be extracted. Secondly, important deterioration of the macroscopic results may emerge in the case that a tilting moment is applied on the indentor inadvertently or in the case that the flat punch itself is not self-aligning so that asymmetrical contact pressure distributions arise on the contact faces. Thirdly, the voluntary application of a tilting moment on the flat punch during an experiment gives rise to potential capabilities of the flat punch for the determination of the material microstructural characteristic lengths. The solution methodology is based on singular integral equations which have resulted from a treatment of the mixed boundary value problems via integral transforms and generalized functions. The results show significant departure from the predictions of classical elasticity revealing that valuable information may be deducted from the indentation of a tilted punch of a microstructured solid.