Journal ArticleDOI
Uniqueness and localization—I. Associative and non-associative elastoplasticity
Davide Bigoni,Tomasz Hueckel +1 more
TLDR
In this paper, the authors studied the critical hardening modulus for deformation into a planar band in the incremental response of elasto-plastic material in the case of small strains and rotations.About:
This article is published in International Journal of Solids and Structures.The article was published on 1991-01-01. It has received 238 citations till now. The article focuses on the topics: Plane stress & Uniqueness.read more
Citations
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Journal ArticleDOI
On the Portevin–Le Chatelier effect: theoretical modeling and numerical results
Egidio Rizzi,P. Hähner +1 more
TL;DR: In this article, a new model is presented for a physically consistent description of plastic material instabilities referred to as Portevin-Le Chatelier (PLC) effect, namely the oscillatory plastic flow that may be observed in metallic alloys subjected to load-or displacement-controlled plastic deformation in a certain range of strain, strain rate and temperature.
Book
Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability
TL;DR: In this article, the authors apply local and global uniqueness and stability criteria to non-associative elastoplasticity for wave propagation, stability and bifurcation of elastic solids.
Journal ArticleDOI
Failure in geomaterials: continuous and discrete analyses
TL;DR: In this paper, the authors considered Hill's condition of stability and diffuse modes of failure in geomaterials in a dual framework: continuum mechanics and discrete mechanics, and concluded that the second order work criterion (under its dual form: continuous and discrete) can be a proper tool to analyse diffuse mode of failure.
Journal ArticleDOI
Bifurcations in elastic-plastic materials
TL;DR: In this article, the authors proposed to use the loss of strong ellipticity criterion as a necessary condition for localization of elastic materials. But they only considered the symmetric part of the tangent modulus tensor of the acoustic tensor.
Journal ArticleDOI
Interface debonding models: a viscous regularization with a limited rate dependency
TL;DR: In this paper, a new kind of viscous regularization is proposed for the Tvergaard debonding model, which has a limited rate dependency and can be used to simulate various scales of composite debonding effects such as decohesion between matrix and fibers and delamination in laminates.
References
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Journal ArticleDOI
Conditions for the localization of deformation in pressure-sensitive dilatant materials
John W. Rudnicki,James R. Rice +1 more
TL;DR: In this paper, the authors investigated the hypothesis that localization of deformation into a shear band may be considered a result of an instability in the constitutive description of homogeneous deformation.
Journal ArticleDOI
A general theory of uniqueness and stability in elastic-plastic solids
TL;DR: A sufficient condition for uniqueness of the boundary-value problem set by given velocities on a part of the surface of a body and given nominal traction-rates on the remainder is established in this paper.
Book ChapterDOI
The Linear Theory of Elasticity
TL;DR: Linear elasticity is one of the more successful theories of mathematical physics and its pragmatic success in describing the small deformations of many materials is uncontested The origins of the three-dimensional theory go back to the beginning of the 19th century and the derivation of the basic equations by Cauchy, Navier, and Poisson The theoretical development of the subject continued at a brisk pace until the early 20th century with the work of Beltrami, Betti, Boussinesq, Kelvin, Kirchhoff, Lame, Saint-Venant, Somigl
Journal ArticleDOI
Acceleration waves in solids
TL;DR: In this article, a general matrix equation is obtained for the possible wave speeds and polarizations (with modifications when the material is incompressible) for a wide range of elastic/plastic solids.