Calibration of parallel bond parameters in bonded particle models via physics-informed adaptive moment optimisation

This study proposes an automated calibration procedure for bond parameters in bonded discrete element modelling. By exploring the underlying physical correlations between microscopic parameters of bonds and macroscopic strength parameters of the continuum to be modelled, the microscopic shear strength and tensile strength are identified as independent variables for calibration purpose. Then a physics-informed iterative scheme is proposed to automatically approximate the bond parameters by viewing the micro-macro relation as an implicitly defined mathematical mapping function. As a result of highly non-convex features of this implicit mapping, the adaptive moment estimation (Adam), which is especially suitable for problems with noisy gradients, is adopted as the basic iterative scheme, in conjunction with other numerical techniques to approximately evaluate the partial derivatives involved. The whole procedure offers a simple and effective framework for bond parameter calibration. A numerical example of SiC ceramic is provided for validation. By compared with some existing calibration methods, the proposed method shows significant advantages in terms of calibration efficiency and accuracy

Deep Learning Predicts Stress–Strain Relations of Granular Materials Based on Triaxial Testing Data

This study presents an AI-based constitutive modelling framework wherein the prediction model directly learns from triaxial testing data by combining discrete element modelling (DEM) and deep learning. A constitutive learning strategy is proposed based on the generally accepted frame-indifference assumption in constructing material constitutive models. The low-dimensional principal stress-strain sequence pairs, measured from discrete element modelling of triaxial testing, are used to train recurrent neural networks, and then the predicted principal stress sequence is augmented to other high-dimensional or general stress tensor via coordinate transformation. Through detailed hyperparameter investigations, it is found that long short-term memory (LSTM) and gated recurrent unit (GRU) networks have similar prediction performance in constitutive modelling problems, and both satisfactorily predict the stress responses of granular materials subjected to a given unseen strain path. Furthermore, the unique merits and ongoing challenges of data-driven constitutive models for granular materials are discussed

The role of foam in improving the workability of sand : insights from DEM

Foam as a soil conditioner can transform the mechanical properties of the excavated natural muck and lubricate the interface between the cutting tools and muck, thus reducing the tools’ wear and promoting the efficiency of earth pressure balance (EPB) shield tunneling. This paper aims to explore the meso-mechanism of foam in improving the workability of sand by combining discrete element modeling (DEM) with experimental investigations of slump tests. A “sand-foam” mixture DEM model was generated by simplifying the sand grains and foam as individual particles with different properties. The particle-scale simulated parameters were calibrated based on a series of experimental observations. The effects of foam on the inter-particle contact distribution and the evolution of contact forces during the slumping process were investigated in detail through numerical modeling. It was found that injecting foam into sand specimens could increase the coordination number and the contact number around sand grains. Although the force transmission pattern changes from “sand-sand” into the coexistence of “sand-foam”, “sand-sand” and “foam-foam” contacts, the magnitude of contact forces transferred by foam particles is significantly lower than that by sand particles. The presence of foam reduces contact-scale frictional strength and thus reduces the stability of the microstructures of sand. In addition, the normal direction of inter-particle contact force deflects from the vertical to the horizontal and the magnitude of contact force decreases significantly with the influence of foam

Calibration of linear contact stiffnesses in discrete element models using a hybrid analytical-computational framework

Efficient selections of particle-scale contact parameters in discrete element modelling remain an open question. The aim of this study is to provide a hybrid calibration framework to estimate linear contact stiffnesses (normal and tangential) for both two-dimensional and three-dimensional simulations. Analytical formulas linking macroscopic parameters (Young's modulus, Poisson's ratio) to mesoscopic particle parameters for granular systems are derived based on statistically isotropic packings under small-strain isotropic stress conditions. By taking the derived analytical solutions as initial approximations, the gradient descent algorithm automatically obtains a reliable numerical estimation. The proposed framework is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. The results show that this hybrid method practically reduces the time for artificial trials and errors to obtain reasonable stiffness parameters. The proposed framework can be extended to other parameter calibration problems in DEM

Constitutive behaviour of granular materials: from discrete element modelling to data-driven forecasting

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

Towards data-driven constitutive modelling for granular materials via micromechanics-informed deep learning

The analytical description of path-dependent elastic-plastic responses of a granular system is highly complicated because of continuously evolving microstructures and strain localisation within the system undergoing deformation. This study offers an alternative to the current analytical paradigm by developing micromechanics-informed machine-learning based constitutive modelling approaches for granular materials. A set of critical variables associated with the constitutive behaviour of granular materials are identified through an incremental stress-strain relationship analysis. Depending on the strategy to exploit the priori micromechanical knowledge, three different training strategies are explored. The first model uses only the measurable external variables to make stress predictions; the second model utilises a directed graph to link all the external strain sequences and internal microstructural evolution variables into a single prediction model comprised of a series of sub-mappings, and the third model explicitly integrates the physically important non-temporal properties with external strain paths into training through an enhanced Gated Recurrent Unit (GRU). These three models show satisfactory agreement with unseen test specimens based on multi-directional loading cases. The features and applications of each model are explained. Furthermore, the key factors for constitutive training, potential applications and deficiencies of the current work are also discussed in detail

A neural network-based material cell for elastoplasticity and its performance in FE analyses of boundary value problems

This research focuses on evaluating the capacity and performance of a network-based material cell as a constitutive model for boundary-value problems. The proposed material cell aims to replicate constitutive relationships learned from datasets generated by random loading paths following a stochastic Gaussian process. The material cell demonstrates its effectiveness across three progressively complex constitutive models by incorporating physical extensions and symmetry constraint as prior knowledge. To address the challenge of magnitude gaps between strain increments in training sets and finite element simulations, an adaptive linear transformation is introduced to mitigate prediction errors. The material cell successfully reproduces constitutive relationships in finite element simulations, and its performance is comprehensively evaluated by comparing two different material cells: the sequentially trained gated recurrent unit (GRU)-based material cell and the one-to-one trained deep network-based material cell. The GRU-based material cell can be trained without explicit calibration of the internal variables. This enables us to directly derive the constitutive model using stress–strain data without consideration of the physics of internal variables

Deep active learning for constitutive modelling of granular materials: From representative volume elements to implicit finite element modelling

Constitutive relation remains one of the most important, yet fundamental challenges in the study of granular materials. Instead of using closed-form phenomenological models or numerical multiscale modelling, machine learning has emerged as an alternative paradigm to revolutionise the constitutive modelling of granular materials. However, deep neural networks (DNNs) require massive training data and often fail to make credible extrapolations. This study aims to develop a deep active learning strategy to (i) identify unreliable forecasts without knowing the ground truth; and (ii) continuously improve and verify a data-driven constitutive model until the desired generalisation is satisfied. The role of active learning in constitutive modelling is instantiated through three scenarios: (i) off-line strain-stress data pool of granular materials; (ii) interactive constitutive training and strain-stress data labelling; and (iii) finite element modelling (FEM) driven by deep learning-based constitutive models. The results confirm the capability of active learning in advancing data-driven constitutive modelling of granular materials toward developing a faithful surrogate constitutive model with less data. The same active learning strategy can also be applied to other data-centric applications across various science and engineering fields

Effect of water head on the permeability of foam-conditioned sands: Experimental and analytical investigation

The water permeability of conditioned soils is one of the most essential properties for Earth Pressure Balance (EPB) tunnelling in coarse-grained soils. Permeability tests are conducted to study the influence of water heads on the permeability of foam-conditioned sands. The initial permeability coefficient of foam-conditioned sands increases with the water head, while the stable permeability coefficient and the initial stable period duration decrease. Meanwhile, a novel analytical model is proposed to estimate the initial permeability coefficient. In this model, the effect of the water head on the initial permeability coefficient is incorporated by calculating void ratios of the foam and effective diameters of foam bubbles under different water pressures. Experimental results are in close agreement with analytical solutions, indicating the excellent performance of the proposed calculation method. In addition, the physical mechanisms of how the water head affects the permeability of foam-conditioned sands are discussed from the contraction and evolution of foam bubbles