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.

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