Shear localisation in thick-walled cylinders under internal pressure based on gradient elastoplasticity

Abstract

We studied failure of thick-walled cylinders under external confinement and internal pressurisation. The material is assumed to be pressure-sensitive with dilatant and strain-softening response. The analysis was carried out using Gradient Elastoplasticity, a higher order theory developed to regularise the ill-posed problem caused by material strain-softening. In this theory the stress increment is related to both the strain increment and its Laplacian. The gradient terms in the constitutive equations introduce an extra parameter of internal length related to material micro-structure, allowing robust modelling of the post-peak material behaviour. The governing equations were solved numerically with the displacement finite element formulation, using C1-continuity elements. Numerical results show that at a critical loading threshold the initial axisymmetry of deformation breaks spontaneously and an instability of finite wavenumber develops. With increasing pressurisation, a curved shear-band of finite thickness forms and propagates progressively towards the outer boundary. For high confining pressures this mode of shear failure is more critical than the trivial tensile failure mode. Practical applications can be found in wellbore stability and hydraulic fracturing in petroleum engineering, and in pile driving design and the interpretation of pressuremeter and penetrometer tests in geotechnical engineering.

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ORCID for A. Zervos: orcid.org/0000-0002-2662-9320

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