Experimental Micro Mechanics Methods for Conventional and Negative Poisson’s Ratio Cellular Solids as Cosserat Continua

Lakes, Roderic S.

doi:10.1115/1.2903371

Cited by 128 publications

(68 citation statements)

References 36 publications

(64 reference statements)

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“…The plane strain state is described by two in-plane displacements u 1 , u 2 and one out-of-plane microrotation φ 3 . In addition to stresses σ 11 , σ 12 , σ 21 , σ 22 (note, that σ 12 = σ 21 ), two couple-stresses m 13 , m 23 are introduced (figure 1), and the following constitutive equations hold [4].…”

Section: Mathematical Foundations Of Plane Micropolar Elasticitymentioning

confidence: 99%

Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity

Atroshchenko

Bordas

2015

Proc. R. Soc. A.

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Artículo de publicación ISIIn this paper, both singular and hypersingular fundamental solutions of plane Cosserat elasticity are derived and given in a ready-to-use form. The hypersingular fundamental solutions allow to formulate the analogue of Somigliana stress identity, which can be used to obtain the stress and couple-stress fields inside the domain from the boundary values of the displacements, microrotation and stress and couple-stress tractions. Using these newly derived fundamental solutions, the boundary integral equations of both types are formulated and solved by the boundary element method. Simultaneous use of both types of equations (approach known as the dual boundary element method (BEM)) allows problems where parts of the boundary are overlapping, such as crack problems, to be treated and to do this for general geometry and loading conditions. The high accuracy of the boundary element method for both types of equations is demonstrated for a number of benchmark problems, including a Griffith crack problem and a plate with an edge crack. The detailed comparison of the BEM results and the analytical solution for a Griffith crack and an edge crack is given, particularly in terms of stress and couple-stress intensity factors, as well as the crack opening displacements and microrotations on the crack faces and the angular distributions of stresses and couple-stresses around the crack tip.Fondecyt Chile 11130259 European Research Council 27957

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Section: Mathematical Foundations Of Plane Micropolar Elasticitymentioning

confidence: 99%

Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity

Atroshchenko

Bordas

2015

Proc. R. Soc. A.

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“…In this context the following approaches can be cast: the wellknown Eringen's integral theory [1,2], involving a stress-strain relation between the stress at a given point and the strain in the whole volume of the continuum; the gradient elasticity theories [3,4], with constitutive equations depending on the gradients of stresses or strains; the peridynamic theory [5], involving long-range elementary forces depending on relative displacements between non-adjacent points; the well-known micropolar ''Cosserat'' theory [6] and the couple-stress theory [7], according to which any material point is endowed with translational and rotational degrees of freedom, with resulting workconjugate curvatures and couple stresses. Regarding micropolar or couple-stress theories, many interesting studies have been devoted to explain, on a physical basis, the relation with microstructural effects, see for instance those by Kröner [8] and Lakes [9].…”

Section: Introductionmentioning

confidence: 99%

A new displacement-based framework for non-local Timoshenko beams

2015

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In this paper, a new theoretical framework is presented for modeling non-locality in shear deformable beams. The driving idea is to represent non-local effects as long-range volume forces and moments, exchanged by non-adjacent beam segments as a result of their relative motion described in terms of pure deformation modes of the beam. The use of these generalized measures of relative motion allows constructing an equivalent mechanical model of non-local effects. Specifically, long-range volume forces and moments are associated with three spring-like connections acting in parallel between couples of nonadjacent beam segments, and separately accounting for pure axial, pure bending and pure shear deformation modes. The variational consistency of the proposed non-local beam model is demonstrated by minimization of an appropriate total potential energy functional. Numerical results concerning the static behavior for different boundary and loading conditions are presented. It is shown that the proposed nonlocal beam model is able to capture experimental data on the static deflection of micro-beams, available in the literature.

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“…Generally, the Poisson's ratio is a function of the spatially and temporally changing moduli and stresses, and varies accordingly. For instance, we have ( ) Auxetic materials have a negative Poisson's ratio for large spatial; and temporal domains and are expected to have interesting mechanical properties, such as high energy absorption, fracture toughness, indentation resistance and enhanced shear moduli, which may be useful in some applications [2][3][4][5][6]. Scientists have been aware of the existence of auxetic materials for over a hundred years, though without very special attention, and treating them as an accident or a curiosity.…”

Section: Introductionmentioning

confidence: 99%

On the Damped Beams with Hysteresis

Poienariu¹,

Ionescu²,

Girip³

et al. 2011

WJM

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This paper discusses the hysteretic behavior of beams with external elements made from auxetic materials. The damping force is modeled by using the nonlocal theory. Unlike the local models, the damping force is modeled as a weighted average of the velocity field over the temporal and spatial domains, determined by a kernel function based on distance measures. The hysteresis operator is continuous and it is defined in connection with the Euler-Bernoulli equation. The problem is solved by reducing it to a system of differential inclusions.

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Experimental Micro Mechanics Methods for Conventional and Negative Poisson’s Ratio Cellular Solids as Cosserat Continua

Cited by 128 publications

References 36 publications

Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity

Fundamental solutions and dual boundary element methods for fracture in plane Cosserat elasticity

A new displacement-based framework for non-local Timoshenko beams

On the Damped Beams with Hysteresis

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