A general shakedown approach for geo-structures under cyclic loading using ABAQUS Python

Shakedown limit has been recognised as a design criterion against excessive permanent deformation for many geo-structures under cyclic loading. Existing approaches for determining shakedown limits of geo-structures are either case-oriented or time-consuming thus practically hindering their extended applications. This paper is concerned with the development and implementation of a robust shakedown approach of wide applicability. The proposed approach draws on the advantages of the feature of a direct shakedown analysis based on lowerbound shakedown theorem, and powerful processing techniques in ABAQUS using Python. In the shakedown analysis, a time-independent residual stress field is expressed as a function of residual stress rate, which can be directly solved using the finite element theory, self-equilibrium conditions and a return mapping scheme considering a general plastic flow rule. By coding the analysis into a Python script, in cooperation with elastic solutions for only one load cycle and mesh-related matrices from ABAQUS, the shakedown limits of geostructures can be obtained. The accuracy and performance of the approach is first examined by analysing a central-holed plate problem and a pavement problem considering several common-used constitutive models. It is then applied to the analysis of a three-dimensional elliptical cavity under a cyclic inner pressure, revealing a gradual decline of the shakedown limit with increasing aspect ratio, from the analytical shakedown solution for a spherical cavity to the one for a cylindrical cavity. The numerical results demonstrate the proposed approach lends itself to a robust tool of obtaining shakedown limits for various geo-structures.