Bending of a Curved Bar of Micropolar Elastic Material

Gauthier, Romain; Jahsman, W. E.

doi:10.1115/1.3423899

Cited by 36 publications

(15 citation statements)

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“…It is noted that Equations (58), (59), and (62) are consistent with those reported elsewhere (Nowacki, 1974;Gauthier and Jahsman, 1975;Gauthier and Jahsman, 1976;Eringen, 1999) …”

Section: Triangular Lattice Homogenizationsupporting

confidence: 89%

An Elastic Micropolar Mixture Theory for Predicting Elastic Properties of Cellular Materials

Elangovan

Altan²,

Odegard

2008

49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference &Amp;lt;br> 16th AIAA/ASME/AHS Ada

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An efficient modeling approach is established to predict the elastic response of cellular materials with distributions of cell geometries. The approach does not require complex and timeconsuming computational techniques usually associated with modeling such materials. Unlike most current analytical techniques, the modeling approach directly accounts for the cellular material microstructure. The approach combines micropolar elasticity theory and elastic mixture theory to predict elastic response of cellular materials to a wide range of loading conditions. The modeling approach is applied to the two-dimensional balsa wood material. Predicted properties are in good agreement with experimentally-determined properties, which emphasizes the model's potential to predict the elastic response of other cellular solids, such as open cell and closed cell foams.

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“…It is noted that Equations (58), (59), and (62) are consistent with those reported elsewhere (Nowacki, 1974;Gauthier and Jahsman, 1975;Gauthier and Jahsman, 1976;Eringen, 1999) …”

Section: Triangular Lattice Homogenizationsupporting

confidence: 89%

An Elastic Micropolar Mixture Theory for Predicting Elastic Properties of Cellular Materials

Elangovan

Altan²,

Odegard

2008

49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference &Amp;lt;br> 16th AIAA/ASME/AHS Ada

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“…Equation 4 was obtained by modifying the strain energy function given previously (Huang et al, 2000) from the Cartesian to the polar coordinate case. As in the aforementioned Cartesian case this modified function ignores out of plane displacements and microrotations about orthogonal in plane axes and thus provides a simplification to two dimensions of an earlier three dimensional analysis (Gauthier and Jahsman, 1976). The additional subscript F has been added to the modulus to distinguish between a value obtained from flexing a ring and one obtained in a uniaxial test.…”

Section: Deflection Of a Slender Diametrically Loaded Micropolar Ringmentioning

confidence: 99%

The influence of void size on the micropolar constitutive properties of model heterogeneous materials

Waseem

Beveridge²,

Wheel³

et al. 2013

European Journal of Mechanics - A/Solids

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In this paper the mechanical behaviour of model heterogeneous materials consisting of regular periodic arrays of circular voids within a polymeric matrix is investigated. Circular ring samples of the materials were fabricated by machining the voids into commercially available polymer sheet. Ring samples of differing sizes but similar geometries were loaded using mechanical testing equipment. Sample stiffness was found to depend on sample size with stiffness increasing as size reduced. The periodic nature of the void arrays also facilitated detailed finite element analysis of each sample. The results obtained by analysis substantiate the observed dependence of stiffness on size. Classical elasticity theory does not acknowledge this size effect but more generalized elasticity theories do predict it. Micropolar elasticity theory has therefore been used to interpret the sample stiffness data and identify constitutive properties. Modulus values for the model materials have been quantified. Values of two additional constitutive properties, the characteristic length and the coupling number, which are present within micropolar elasticity but absent from its classic counterpart have also been determined. The dependence of these additional properties on void size has been investigated and characteristic length values compared to the length scales inherent within the structure of the model materials.

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“…Indeed the difficulty arose from the inability to find a material that exhibited micropolar material behaviour to a sufficient extent, but the methods outlined in [6] were the first treatment of the micropolar theory to separate and determine the additional constitutive properties.…”

Section: Experimental Determination Of Constitutive Propertiesmentioning

confidence: 99%

Computational Modelling and Experimental Characterisation of Heterogeneous Materials

Beveridge

Wheel

Nash

2010

Advanced Structured Materials

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Bending of a Curved Bar of Micropolar Elastic Material

Cited by 36 publications

References 0 publications

An Elastic Micropolar Mixture Theory for Predicting Elastic Properties of Cellular Materials

An Elastic Micropolar Mixture Theory for Predicting Elastic Properties of Cellular Materials

The influence of void size on the micropolar constitutive properties of model heterogeneous materials

Computational Modelling and Experimental Characterisation of Heterogeneous Materials

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