Shear bands

1. A perturbative approach to shear bands

We have invented the ‘perturbative approach to material stability’, in which a perturbing agent in the form of a concentrated force, a crack, or a lamellar rigid inclusion ‘disturbs’ a uniformly prestressed material.


2. Shear band propagation

We have proposed a weak line inclusion model in a nonlinear elastic solid to analytically quantify and investigate, for the first time, the stress state and growth conditions of a finite-length shear band in a ductile prestressed metallic material. The deformation is shown to become highly focused and aligned coaxial to the shear band and the energy release rate to blow up to infinity, for incremental loading occurring when the prestress approaches the elliptic boundary, concluding that the propagation becomes ‘unrestrainable’.


3. Studies on shear bands and material instabilities

We have found the explicit solutions for strain localization and flutter instability in elastic-plastic materials, and also in anisotropic/elastic-plastic, disclosing the strong and important effects of anisotropy.
We have proposed the use of Hill and Raniecki comparison solids for material instabilities in nonassociative elastoplasticity.
We have analyzed shear band formation in coupled thermo-elastoplasticity.


Related papers:

• D. Bigoni, Nonlinear Solid Mechanics Bifurcation Theory and Material Instability. Cambridge University Press, 2012, ISBN:9781107025417.
• D. Bigoni, P.A. Gourgiotis (2016).
  Folding and faulting of an elastic continuum.
  [Cover Paper] [Open Access] Proceedings of the Royal Society A. 472: 20160018,
  http://dx.doi.org/10.1098/rspa.2016.0018.


• P.A. Gourgiotis, D. Bigoni (2016).
  Stress channelling in extreme couple-stress materials Part I: Strong ellipticity, wave propagation, ellipticity, and discontinuity relations
  Journal of the Mechanics and Physics of Solids. 88, 150-168; doi:10.1016/j.jmps.2015.09.006 [arXiv version]


• P.A. Gourgiotis, D. Bigoni (2016).
  Stress channelling in extreme couple-stress materials Part II: Localized folding vs faulting of a continuum in single and cross geometries
  Journal of the Mechanics and Physics of Solids. 88, 169-185; doi:10.1016/j.jmps.2015.09.005 [arXiv version]


• N. Bordignon, A. Piccolroaz, F. Dal Corso, D. Bigoni
  Strain localization and shear banding in ductile materials. [Open Access]
  Frontiers in Materials, 2015, 2, 1-13, doi: 10.3389/fmats.2015.00022.
• D. Bigoni, Material instabilities in elastic and plastic solids: the perturbative approach. In Mechanics down under, Denier, J.P. and Finn, M.D. Eds., Proc. of the 22th Int. Congress of Theoretical and Applied Mechanics (Adelaide, Australia, 24-29 August 2008) Springer Science, pp. 1-14, 2013; ISBN: 978-94-007-1, DOI 10.1007/078-94-007-5968-8.
• L. Argani, D. Bigoni, D. Capuani and N.V. Movchan
  Cones of localized shear strain in incompressible elasticity with prestress: Green’s function and integral representations
  Proceedings of the Royal Society A, 2014, 470, 20140423.
• L. Argani, D. Bigoni, G. Mishuris Dislocations and inclusions in prestressed metals.
  Proceedings of the Royal Society A, 2013, 469, 2154 20120752; doi:10.1098/rspa.2012.0752.
• 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.
• Dal Corso, F. and Bigoni, D. (2010).
  Growth of slip surfaces and line inclusions along shear bands in a softening material.
  International Journal of Fracture, 166, 225-237.
• Dal Corso, F. and Bigoni, D. (2009).
  The interactions between shear bands and rigid lamellar inclusions in a ductile metal matrix.
  Proceedings of the Royal Society A, 465, 143-163.
• Bigoni, D. and Dal Corso, F. (2008).
  The unrestrainable growth of a shear band in a prestressed material.
  Proceedings of the Royal Society A, 464, 2365-2390. Electronic supplementary material.
• Dal Corso, F., Bigoni, D. and Gei, M. (2008).
  The stress concentration near a rigid line inclusion in a prestressed, elastic material. Part I. Full field solution and asymptotics.
  Journal of the Mechanics and Physics of Solids, 56, 815-838.
• Bigoni, D., Dal Corso, F. and Gei, M. (2008).
  The stress concentration near a rigid line inclusion in a prestressed, elastic material. Part II. Implications on shear band nucleation, growth and energy release rate.
  Journal of the Mechanics and Physics of Solids, 56, 839-857.
• A. Gajo, D. Muir Wood and D. Bigoni, On certain critical material and testing characteristics affecting shear band development in sand.
  Géotechnique, 2007, 57(5), 449-461.
• A. Piccolroaz, D. Bigoni, and J.R. Willis, A dynamical interpretation of flutter instability in a continuous medium.
  Journal of the Mechanics and Physics of Solids, 2006, 54, 2391-2417.
• D. Bigoni and D. Capuani, Time-harmonic Green's function and boundary integral formulation for incremental nonlinear elasticity: dynamics of wave patterns and shear bands.
  Journal of the Mechanics and Physics of Solids, 2005, 53(5), 1163-1187.
• A. Gajo, D. Bigoni and D. Muir Wood, Multiple shear band development and related instabilities in granular materials.
  Journal of the Mechanics and Physics of Solids, 2004, 52(12), 2683-2724.
• A. Benallal and D. Bigoni, Effects of temperature and thermo-mechanical couplings on material instabilities and strain localization of inelastic materials.
  Journal of the Mechanics and Physics of Solids, 2004, 52(3), 725-753.
• M. Brun, D. Bigoni and D. Capuani, A boundary element technique for incremental, nonlinear elasticity. Part. II: Bifurcation and shear bands.
  Computer Methods in Applied Mechanics and Engineering, 192 (22-24), 2003, 2481-2499.
• D. Bigoni and D. Capuani, Green's function for incremental nonlinear elasticity: shear bands and boundary integral formulation.
  Journal of the Mechanics and Physics of Solids, 2002, 50, 471-500.
• D. Bigoni and H. Petryk, A note on divergence and flutter instabilities in elastic-plastic materials.
  International Journal of Solids and Structures, 2002, 39, 911-926.
• D. Bigoni, B. Loret and E. Radi, Localization of deformation in plane elastic-plastic solids with anisotropic elasticity.
  Journal of the Mechanics and Physics of Solids, 2000, 48, 1441-1466, special issue dedicated to Prof. J.R. Willis.
• D. Bigoni and B. Loret, Effects of elastic anisotropy on strain localization and flutter instability in plastic solids.
  Journal of the Mechanics and Physics of Solids, 1999, 47, 1409-1436.
• D. Bigoni, On flutter instability in elastoplastic constitutive models.
  International Journal of Solids and Structures, 1995, 32 (21), 3167-3189.
• D. Bigoni and D. Zaccaria, On the eigenvalues of the acoustic tensor in elastoplasticity .
  European Journal of Mechanics, A/Solids, 1994, 13, 621-638.
• D. Bigoni and D. Zaccaria, Eigenvalues of the elastoplastic constitutive operator.
  Zeitschrift fuer Angewandte Mathematik und Mechanik (ZAMM), 1994, 74, 355-357.
• D. Bigoni and D. Zaccaria, On strain localization analysis of elastoplastic materials at finite strains.
  International Journal of Plasticity, 1993, 9, 21-33.
• D. Bigoni, Strain localization in axially-symmetric compression of brittle­ cohesive materials.
  Engineering Fracture Mechanics, 1992, 42 (4), 617-627.
• D. Bigoni and D. Zaccaria, Loss of strong-ellipticity in non-associative elastoplasticity.
  Journal of the Mechanics and Physics of Solids, 1992, 40 (6), 1313-1331.
• D. Bigoni and D. Zaccaria, Strong ellipticity of comparison solids in elastoplasticity with volumetric non-associativity.
  International Journal of Solids and Structures, 1992, 29 (17), 2123-2136.
• D. Bigoni and T. Hueckel, Uniqueness and localization­ I. Associative and non-associative elastoplasticity.
  International Journal of Solids and Structures, 1991, 28 (2), 197-213.
• D. Bigoni and T. Hueckel, Uniqueness and localization­ II. Coupled elastoplasticity.
  International Journal of Solids and Structures, 1991, 28 (2), 215-224.
• D. Bigoni and T. Hueckel, A note on strain localization for a class of non-associative plasticity rules.
  Ingenieur-Archiv, 1990, 60, 491-499.
• D. Bigoni and T. Hueckel, On uniqueness and strain localization in plane strain and plane stress elastoplasticity.
  Mechanics Research Communications, 1990, 17 (1), 15-23, and 17 (3), 189.

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