A computational approach to obtain nonlinearly elastic constitutive relations of special Cosserat rods

2020 ◽

Vol 842 ◽

pp. 160-167

Author(s):

Lang Wu ◽

Ru Yu Yan ◽

Jun Yao Cai ◽

Hao Li

Keyword(s):

Constitutive Relation ◽

Texture Coefficient ◽

Constitutive Relations ◽

Cubic Crystallites ◽

Voigt Model ◽

Nonlinear Elastic ◽

Nonlinearly Elastic

Under Voigt model, Barsch and Johnson gave the formula of nonliearly elastic constitutive relations for isotropic aggregates of cubic crystallites and orthorhambic aggregates of cubic crystallies, respectively. In this paper, a nonlinear elastic constitutive relation based on Voigt model, which is more general than Barsch's and Johnson's results, is derived for the set of anisotropic cubic grains. The anisotropy of metals is described by the texture coefficient.

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STRAIGHTFORWARD COMPUTATION OF SPATIAL EQUILIBRIA OF GEOMETRICALLY EXACT COSSERAT RODS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405012387 ◽

2005 ◽

Vol 15 (03) ◽

pp. 949-965 ◽

Cited By ~ 15

Author(s):

T. J. HEALEY ◽

P. G. MEHTA

Keyword(s):

Boundary Conditions ◽

Path Following ◽

General Boundary ◽

General Boundary Conditions ◽

Efficient Computation ◽

Cosserat Rods ◽

Straightforward Computation ◽

Well Posed ◽

Nonlinearly Elastic

In this paper, we present a well posed "force" based formulation for nonlinearly elastic Cosserat rods with general boundary conditions enabling straightforward, efficient computation of spatial equilibria. We illustrate the ease and utility of our approach in four example problems, each exhibiting large spatial buckling, employing the path-following software AUTO.

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A generalized computational approach to stability of static equilibria of nonlinearly elastic rods in the presence of constraints

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2010.02.007 ◽

2010 ◽

Vol 199 (25-28) ◽

pp. 1805-1815 ◽

Cited By ~ 21

Author(s):

Ajeet Kumar ◽

Timothy J. Healey

Keyword(s):

Computational Approach ◽

Elastic Rods ◽

Nonlinearly Elastic

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A thermoelastoplastic theory for special Cosserat rods

Mathematics and Mechanics of Solids ◽

10.1177/1081286517754132 ◽

2018 ◽

Vol 24 (3) ◽

pp. 686-700

Author(s):

Smriti ◽

Ajeet Kumar ◽

Alexander Großmann ◽

Paul Steinmann

Keyword(s):

Yield Criterion ◽

Constitutive Relations ◽

Transversely Isotropic ◽

Field Variable ◽

Theory Reduction ◽

One Dimensional ◽

Cosserat Rods ◽

The One ◽

Strain Measures ◽

Additional Equation

A general framework is presented to model coupled thermoelastoplastic deformations in the theory of special Cosserat rods. The use of the one-dimensional form of the energy balance in conjunction with the one-dimensional entropy balance allows us to obtain an additional equation for the evolution of a temperature-like one-dimensional field variable, together with constitutive relations for this theory. Reduction to the case of thermoelasticity leads us to the well-known nonlinear theory of thermoelasticity for special Cosserat rods. Later on, additive decomposition is used to separate the thermoelastic part of the strain measures of the rod from their plastic counterparts. We then present the most general quadratic form of the Helmholtz energy per unit undeformed length for both hemitropic and transversely isotropic rods. We also propose a prototype yield criterion in terms of forces, moments, and hardening stress resultants, as well as associative flow rules for the evolution of plastic strain measures and hardening variables.

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Application of Modified Bloch Waves to Image Analysis of Extended Linear Defects

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010005202x ◽

1974 ◽

Vol 32 ◽

pp. 402-403

Author(s):

S. Nakahara ◽

D. M. Maher

Keyword(s):

Image Analysis ◽

Computational Approach ◽

Dislocation Loops ◽

Plane Wave Expansion ◽

Dynamical Equations ◽

Bloch Waves ◽

Linear Defects ◽

Imperfect Crystal ◽

Localized Defects ◽

Defective Crystals

Since Head first demonstrated the advantages of computer displayed theoretical intensities from defective crystals, computer display techniques have become important in image analysis. However the computational methods employed resort largely to numerical integration of the dynamical equations of electron diffraction. As a consequence, the interpretation of the results in terms of the defect displacement field and diffracting variables is difficult to follow in detail. In contrast to this type of computational approach which is based on a plane-wave expansion of the excited waves within the crystal (i.e. Darwin representation ), Wilkens assumed scattering of modified Bloch waves by an imperfect crystal. For localized defects, the wave amplitudes can be described analytically and this formulation has been used successfully to predict the black-white symmetry of images arising from small dislocation loops.

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