Strain Localization and Shear Band Propagation in Ductile Materials

Bordignon, N.; Piccolroaz, A.; Corso, F. Dal; Bigoni, Davide

doi:10.3389/fmats.2015.00022

Cited by 24 publications

(16 citation statements)

References 46 publications

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“…This method can also be effectively applied in the case of elastoplastic thin interphases [15,17]. Here, the transformation to the respective imperfect interface models is far less trivial and requires several assumptions, as well as evaluation dependent on the yield condition [4,12,25].…”

Section: Introductionmentioning

confidence: 99%

Transmission conditions for thin curvilinear close to circular heat-resistant interphases in composite ceramics

Andreeva

Zagnetko

2016

Journal of the European Ceramic Society

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a b s t r a c tThis paper considers the problem of heat transfer in a composite ceramic material where the structural elements are bonded to the matrix via a thin heat resistant adhesive layer. The layer has the form of a circular ring or close to it. Using an asymptotic approach, the interphase is modelled by an infinitesimal imperfect interface, preserving the main features of the temperature fields around the interphase, and allowing a significant simplification where FEM analysis is concerned. The nonlinear transmission conditions that accompany such an imperfect interface are evaluated, and their accuracy is verified by means of dedicated analytical examples as well as carefully designed FEM simulations. The interphases of various geometries are analysed, with an emphasis on the influence of the curvature of their boundaries on the accuracy of the evaluated conditions. Numerical results demonstrate the benefits of the approach and its limitations.

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Section: Introductionmentioning

confidence: 99%

Transmission conditions for thin curvilinear close to circular heat-resistant interphases in composite ceramics

Andreeva

Zagnetko

2016

Journal of the European Ceramic Society

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“…The nominal shear tractiont (inc) 21 generated by a shear wave impinging the shear band can be obtained using equations (12) and (4) into equation (33), thus yieldingt (inc)…”

Section: Boundary Integral Equations and Numerical Proceduresmentioning

confidence: 99%

The dynamics of a shear band

Giarola

Capuani

Bigoni

2018

Journal of the Mechanics and Physics of Solids

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A shear band of finite length, formed inside a ductile material at a certain stage of a continued homogeneous strain, provides a dynamic perturbation to an incident wave field, which strongly influences the dynamics of the material and affects its path to failure. The investigation of this perturbation is presented for a ductile metal, with reference to the incremental mechanics of a material obeying the J 2 -deformation theory of plasticity (a special form of prestressed, elastic, anisotropic, and incompressible solid). The treatment originates from the derivation of integral representations relating the incremental mechanical fields at every point of the medium to the incremental displacement jump across the shear band faces, generated by an impinging wave. The boundary integral equations (under the plane strain assumption) are numerically approached through a collocation technique, which keeps into account the singularity at the shear band tips and permits the analysis of an incident wave impinging a shear band. It is shown that the presence of the shear band induces a resonance, visible in the incremental displacement field and in the stress intensity factor at the shear band tips, which promotes shear band growth. Moreover, the waves scattered by the shear band are shown to generate a fine texture of vibrations, parallel to the shear band line and propagating at a long distance from it, but leaving a sort of conical shadow zone, which emanates from the tips of the shear band.

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“…However, in several problems involving inherent material heterogeneity with length scale similar to the geometry of the considered problem, the use of mesoscale approaches in linear context, yields satisfactory prediction of experimental data [4]. In this context, the nonlocal mechanics, defined in terms of gradients [5][6][7] or integrals [8,9] of the state variables of the problem, provides interesting forecast of wave dispersion and shear bands as well as strain localization in mechanical interfaces [10,11]. Non-local approaches result into mesoscale applications of continuum mechanics theory involving non-homogeneous media introducing the non-local terms to account for the heterogeneity of the representative volume elements of the considered problem.…”

Section: Introductionmentioning

confidence: 99%

A Fractional Approach to Non-Newtonian Blood Rheology in Capillary Vessels

Alotta

Failla

et al. 2019

J Peridyn Nonlocal Model

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In small arterial vessels, fluid mechanics involving linear viscous fluid does not reproduce experimental results that correspond to non-parabolic profiles of velocity across the vessel diameter. In this paper, an alternative approach is pursued introducing long-range interactions that describe the interactions of non-adjacent fluid volume elements due to the presence of red blood cells and other dispersed cells in plasma. These non-local forces are defined as linearly dependent on the product of the volumes of the considered elements and on their relative velocity. Moreover, as the distance between two volume elements increases, the non-local forces decay with a material distance-decaying function. Assuming that decaying function belongs to a power-law functional class of real order, a fractional operator of the relative velocity appears in the resulting governing equation. It is shown that the mesoscale approach involving Hagen-Poiseuille law is able to reproduce experimentally measured profiles of velocity with a great accuracy. Additionally as the dimension of the vessel increases, non-local forces become negligible and the proposed model reverts to the classical Hagen-Poiseuille model.

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Strain Localization and Shear Band Propagation in Ductile Materials

Cited by 24 publications

References 46 publications

Transmission conditions for thin curvilinear close to circular heat-resistant interphases in composite ceramics

Transmission conditions for thin curvilinear close to circular heat-resistant interphases in composite ceramics

The dynamics of a shear band

A Fractional Approach to Non-Newtonian Blood Rheology in Capillary Vessels

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