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Journal of Elasticity

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11-07-2018

On Weingarten-Volterra Defects

Author: Amit Acharya

Published in: Journal of Elasticity | Issue 1/2019

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Abstract

The kinematic theory of Weingarten-Volterra line defects is revisited, both at small and finite deformations. Existing results are clarified and corrected as needed, and new results are obtained. The primary focus is to understand the relationship between the disclination strength and Burgers vector of deformations containing a Weingarten-Volterra defect corresponding to different cut-surfaces.

previous article Two-Dimensional Defective Crystals with Non-constant Dislocation Density and Unimodular Solvable Group Structure

next article Torsion of Chiral Porous Elastic Beams

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As an aside, Zubov’s notation is non-standard, e.g., the action of a tensor \({\boldsymbol{A}}\) on a vector \({\boldsymbol{b}}\) is written as \({\boldsymbol{b}}\cdot {\boldsymbol{A}}\); for \(Q^{M}\) (curvilinear) coordinates on the current configuration with position vectors represented as \({\boldsymbol{R}}\) and \(q_{s}\) as coordinates on the reference configuration with position vectors represented as \({\boldsymbol{r}}\), the deformation gradient is written as \(( \frac{\partial Q^{M}}{\partial q^{s}} ) {\boldsymbol{r}} ^{s} \otimes {\boldsymbol{R}}_{M}\), where \({\boldsymbol{r}}^{s}\) represents (an element of) the dual basis in the reference configuration corresponding to coordinates \(q_{s}\), and \({\boldsymbol{R}}_{M}\) is the natural basis in the current configuration (instead of the more standard notation that would be \(( \frac{\partial Q^{M}}{\partial q^{s}} ) {\boldsymbol{R}}_{M} \otimes {\boldsymbol{r}}^{s}\); the correspondence of upper and lower case letters with objects on the current and reference configuration in this footnote also follows Zubov’s notation).

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Title: On Weingarten-Volterra Defects
Author: Amit Acharya
Publication date: 11-07-2018
Publisher: Springer Netherlands
Published in: Journal of Elasticity / Issue 1/2019
Print ISSN: 0374-3535
Electronic ISSN: 1573-2681
DOI: https://doi.org/10.1007/s10659-018-9681-6

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Other articles of this Issue 1/2019

Representation of Hashin–Shtrikman Bounds in Terms of Texture Coefficients for Arbitrarily Anisotropic Polycrystalline Materials

Torsion of Chiral Porous Elastic Beams

Two-Dimensional Defective Crystals with Non-constant Dislocation Density and Unimodular Solvable Group Structure

The Number of Independent Invariants for Symmetric Second Order Tensors

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