Constitutive behaviour of granular materials: from discrete element modelling to data-driven forecasting
Authors:   , Qu Tongming 
Published: April 2022

Granular materials are ubiquitous in engineering activities of our human beings. Constitutive modelling of granular materials, as one of the most fundamental problems in this field, has long received great attention. Over the past decades, analytical or phenomenological models are undoubtedly the most common way to characterise the elastic-plastic behaviour of granular materials. However, although numerous attempts have been made, developing a unified theoretical model to capture the constitutive behaviour of granular materials remains an ongoing challenge.Instead of phenomenological models, numerical and data-driven surrogate models are two emerging alternatives to predict stress-strain responses of materials. Hierarchical multi-scale modelling and data-driven computing are two typical applications of these two constitutive modelling paradigms. Without the use of analytical models, the stress-strain mapping is directly provided by low-scale numerical modelling or data-driven forecasting in continuum-based numerical models. This thesis aims to partially address some open challenges for the constitutive modelling of granular materials from the two new research perspectives.In the discrete element modelling part, a total of 5 individual chapters are incorporated:(1)A novel flexible membrane algorithm has been proposed to simulate conventional triaxial testing for granular materials. The influence of flexible or rigid servo-wall conditions on the measured responses of granular materials in triaxial testing has been compared in detail via a series of numerical tests.(2)A hybrid analytical-computational calibration framework is proposed to calibrate particle-scale elastic parameters. The proposed calibration framework is tested through a collection of 2D and 3D discrete element models with both mono- and poly-disperse granular packings.(3)A physics-informed adaptive moment optimisation method is proposed to calibrate bond parameters in bonded particle models. A validation example of SiC ceramic is used to validate the proposed algorithm.(4)The ability of discrete element models with spheres to clumped particles in reproducing the constitutive behaviour of granular materials is explored through 4 perspectives. It is found that although discrete element models with spheres or clumped particles are capable of qualitatively describing the salient mechanical behaviour of granular materials, some qualitative deviations between experiments and the simulations are also observed, in terms of the stress-dilatancy behaviour and principal stress ratio against axial strain.(5)An adaptive granular representative volume element (RVE) model with an evolutionary periodic boundary is proposed for hierarchical multiscale analysis. The proposed adaptive RVE model avoids the reinitialisation of the RVE box that even undergoes extremely large shear deformation; meanwhile, a more eÿcient algorithm is presented to treat the interaction between boundary particles and other image particles.In the data-driven modelling part, a total of 2 individual chapters are involved:(1)A deep learning-based constitutive modelling strategy with the prediction model directly learning from triaxial testing data via discrete element modelling is explored. The predic-tion performance of two common recurrent neural networks (RNNs), i.e. Long short-term memory (LSTM) and gated recurrent unit (GRU) networks are compared in detail through hyperparameter investigations.(2)Micromechanical knowledge is used to discover critical microstructural variables associated with the constitutive behaviour of granular materials. Depending on the strategy to exploit a priori micromechanical knowledge, three di˙erent training models are examined. The first strategy uses only the measurable external variables to make stress predictions; the second strategy utilises a directed graph to link all the external strain sequences and internal microstructural evolution variables into a single prediction model comprised of a set of sub-mappings, and the third strategy explicitly integrates the physically important non-temporal properties with external strain paths into training through an enhanced GRU.