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.

Discrete element modeling of acoustic emission in rock fracture

The acoustic emission （AE） features in rock fracture are simulated numerically with discrete element model （DEM）. The specimen is constructed by using spherical particles bonded via the parallel bond model. As a result of the heterogeneity in rock specimen, the failure criterion of bonded particle is coupled by the shear and tensile strengths, which follow a normal probability distribution. The Kaiser effect is simulated in the fracture process, for a cubic rock specimen under uniaxial compression with a constant rate. The AE number is estimated with breakages of bonded particles using a pair of parameters, in the temporal and spatial scale, respectively. It is found that the AE numbers and the elastic energy release curves coincide. The range for the Kaiser effect from the AE number and the elastic energy release are the same. Furthermore, the frequency-magnitude relation of the AE number shows that the value of B determined with DEM is consistent with the experimental data.

Effects of model size and particle size on the response of sea-ice samples created with a hexagonal-close-packing pattern in discrete-element method simulations

We investigated the effects of model size and particle size on the simulated macroscopic mechanical properties, uniaxial compressive strength, Young＇s modulus, and flexural strength of sea-ice samples, using the discrete-element method （DEM） with a bonded-particle model. Many different samples with a hexagonal-close-packing pattern and a unique particle size were considered, and several ratios of particle size to sample dimension （D/L） were studied for each sample. The macroscopic mechanical properties simulated by the DEM decrease monotonously with an increase in D/L. For different samples with different particle sizes, the macroscopic mechanical properties will be identical when D/L is constant. The quanti- tative relationships between macroscopic mechanical properties and ratio of particle size to sample size are important aspects in engineering applications of the DEM method. The results provide guidance on the choice of a particle size in the DEM simulation for numerical samples with a hexagonal-close-packing pattern.