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Journal of Elasticity

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01-01-2015

Cauchy’s Construction for Flat Complex Bodies

Author: Paolo Podio-Guidugli

Published in: Journal of Elasticity | Issue 1/2015

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Abstract

An argument imitating Cauchy’s is presented to construct the stress fields induced in a non-simple flat body of the type considered in Fosdick and Royer-Carfagni (J. Elast., 2014) by the diffused and concentrated contact interactions between its adjacent parts.

previous article Singular Shear-Force States in Elementary Plate Theory

next article A Note on the Legendre Series Solution of the Laplace Equation for Cylindrical Problems

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In-plane force interactions are here ignored, as they were in [1], for the sake of simplicity.

Note that the construct (n′⊗t′+n′′⊗t′′) vanishes both at regular boundary points and at cusps.

Note that, in agreement with (10),

$$\widetilde{Q}_1(x_0)+\widetilde{Q}_2(x_0)= {\boldsymbol {Q}}(x_0)\cdot(\boldsymbol {n}_1\otimes{\boldsymbol {e}}_1+ \boldsymbol {n}_2\otimes{\boldsymbol {e}}_2 )=- \widetilde{Q}_0(x_0). $$

Fosdick, R., Royer-Carfagni, G.: Singular shear-force states in elementary plate theory. J. Elast. (2014). doi:10.1007/s10659-014-9480-7

Podio-Guidugli, P., Vianello, M.: Hypertractions and hyperstresses convey the same mechanical information. Contin. Mech. Thermodyn. 22(3), 163–176 (2010) ADSCrossRefMathSciNetMATH

Title: Cauchy’s Construction for Flat Complex Bodies
Author: Paolo Podio-Guidugli
Publication date: 01-01-2015
Publisher: Springer Netherlands
Published in: Journal of Elasticity / Issue 1/2015
Print ISSN: 0374-3535
Electronic ISSN: 1573-2681
DOI: https://doi.org/10.1007/s10659-014-9481-6

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Other articles of this Issue 1/2015

Singular Shear-Force States in Elementary Plate Theory

A Two-Dimensional Gradient-Elasticity Theory for Woven Fabrics

Power-Law Solutions of Anisotropic Multi-material Elasticity Problems

Numerical Implementation of the Equivalent Inclusion Method for 2D Arbitrarily Shaped Inhomogeneities

A Note on the Legendre Series Solution of the Laplace Equation for Cylindrical Problems

On the Inverse Elastic Scattering by Interfaces Using One Type of Scattered Waves

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