Bifurcation & Instability

Bifurcation of the incremental response of elastic and elastoplastic solids is addressed. We have found new solutions for bifurcation problems of elastic, thermoelastic and elastoplastic coated cylinders and layered composites.
The problem of unilateral contact between bodies with Coulomb friction, governed by equations similar to those ruling the behaviour to elastoplastic materials is also investigated. In this field we have derived a new framework, based on the concept of ‘linear comparison interface’, for bifurcation analysis of a linear elastic body in unilateral frictional contact with a stiff constraint.

Related papers:

• D. Bigoni, Nonlinear Solid Mechanics Bifurcation Theory and Material Instability. Cambridge University Press, 2012, ISBN:9781107025417.
• D. Bigoni, Bifurcation and instability of nonassociative elastoplastic solids. In CISM Lecture Notes No. 414 "Material Instabilities in Elastic and Plastic Solids", H. Petryk, Ed. Springer-Verlag, Wien­New York, 2000.
• D. Bigoni, M. Gei and S. Roccabianca (2013) Bifurcation of elastic multilayers. In Mathematical Methods and Models in Composites. Edited by: V. Mantic, Imperial College Press, ISBN: 978-1-84816-784-1.
• S. Roccabianca, D. Bigoni and M. Gei Long-wavelength bifurcations and multiple neutral axes in elastic multilayers subject to finite bending.
  Journal of Mechanics of Materials and Structures, 2011, 6, 511–527, special issue dedicated to Marie-Louise and Charles Steele.
• S. Roccabianca, M. Gei and D. Bigoni Plane strain bifurcations of elastic layered structures subject to finite bending: theory versus experiments.
  IMA Journal of Applied Mathematics, 2010, 75, 525-548 .
• M. Gei, D. Bigoni and G. Franceschini, Thermoelastic small-amplitude wave propagation in nonlinear elastic multilayers.
  Mathematics and Mechanics of Solids, 2004, 9, 555-568, special issue dedicated to Prof. R.W. Ogden.
• M. Gei, D. Bigoni and S. Guicciardi, Failure of silicon nitride under uniaxial compression at high temperature.
  Mechanics of Materials, 2004, 36(4), 335-345.
• D. Bigoni and M. Gei, Bifurcations of a coated, elastic cylinder.
  International Journal of Solids and Structures, 2001, 38, 5117-5148.
• E. Radi, D. Bigoni and A. Tralli, On uniqueness for frictional rate problems.
  Journal of the Mechanics and Physics of Solids, 1999, 47, 275-296.
• D. Bigoni, M. Ortiz and A. Needleman, Effect of interfacial compliance on bifurcation of a layer bonded to a substrate.
  International Journal of Solids and Structures, 1997, 34 (33/34), 4305-4326.
• D. Bigoni, On smooth bifurcations in non-associative elastoplasticity.
  Journal of the Mechanics and Physics of Solids, 1996, 44 (8), 1337-1351.

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