Finite deformation of particulate geomaterials: frictional and anisotropic Critical State elasto-plasticity

Abstract

This thesis is concerned with the theoretical development and numerical implementation of efficient constitutive models for the analysis of particulate media (specifically clays) in structures undergoing geometrically non-linear behaviour. The Mohr-Coulomb and modified Cam-clay constitutive models have both been examined and extended to provide greater realism. Findings from this thesis will interest engineers working in numerical methods in solid mechanics, along with those investigating continuum mechanics, inelastic constitutive modelling and large strain plasticity. Although focused on soil plasticity, this research has relevance to other areas, such as metal forming and bio-engineering.

Initially the concepts of material and geometric non-linearity are reviewed. A general implicit backward Euler stress integration algorithm is detailed, including the derivation of the algorithmic consistent tangent. A framework for the analysis of anisotropic finite deformation elasto-plasticity is presented and a full incremental finite-element formulation provided. The first constitutive model developed in this thesis is a non-associated frictional perfect plasticity model based on a modified Reuleaux triangle. It is shown, through comparison with experimental data, that this model has advantages over the classical Mohr-Coulomb and Drucker-Prager models whilst still allowing for analytical implicit stress integration. An isotropic hyperplastic family of models which embraces the concept of a Critical State is then developed. This family is extended to include inelastic behaviour within the conventional yield surface and a Lode angle dependency on the anisotropic yield function which maintains convexity of both the surface and uniqueness of the Critical State cone. A calibration procedure is described and the integration and linearisation of the constitutive relations are detailed. All of the developed models are compared with established experimental data. Finally the models are verified for use within finite deformation finite-element analyses. The importance of deriving the algorithmic consistent tangent is demonstrated and the influence of varying levels of model sophistication assessed in terms of both global behaviour and simulation run-time.