Localisation in computational geomechanics: a nonlinear micropolar approach

Abstract

The localisation of strain into narrow bands of intense deformations is a pervasive phenomenon in geomechanics. It is closely associated with catastrophic failure - landslides, slope collapses, rock faulting, etc. - and has significant implications for the design, integrity, and risk assessment of geotechnical infrastructure. However, traditional computational modelling techniques cannot capture localised failure in a rigorous or reliable way. Classical continuum theories overlook microstructural effects, including those responsible for triggering and governing localisation processes, and mesh-based approaches like the finite element method typically break down under the large deformations induced by geotechnical failure.

This thesis addresses these challenges by employing the generalised implicit material point method, which discretises the domain using particles to circumvent mesh tangling, and by developing a geometrically-nonlinear elastoplastic micropolar (Cosserat) continuum formulation. This nonlocal theory enriches the classical theory with a field of independent microrotations to represent the relative motion of individual soil particles, as well as internal length scales indicative of particle size. Consequently, localised shear bands emerge naturally and analyses converge to physically meaningful results.

First, strain localisation is introduced as an engineering phenomenon and an analytical subject. This is followed by an outline of the material point method, a classical formulation of which is used to demonstrate its deficiencies in simulating localised failure. To address these shortcomings, a review of existing regularisation approaches is provided, leading to the derivation and implementation of the proposed micropolar continuum - initially for purely hyperelastic material behaviour, before extending the model to elastoplasticity. Numerical examples - encompassing a biaxial test and a column collapse problem - demonstrate the method’s capacity to capture complex, evolving failure mechanisms in a robust, convergent, and physically realistic manner. Finally, the analytical consistent linearisation required for the Newton–Raphson solution algorithm is presented in detail in the appendices.