Abstract:The macroscopic mechanical behaviours of granular materials are affected by not just material properties such as particle composition but also state parameters of granular assembly, like porosity and coordination number, etc. Meanwhile, granular materials are of complex loading path- and loading history-dependent features. Establishing a constitutive model incorporating multiple internal variables and their inherent relations for granular materials is an important scientific challenge. Different from the traditional phenomenological constitutive model based on the framework of yield surface, flow rule and hardening function, this study establishes a directed graph-based data-driven constitutive model with the average porosity, fabric tensor and equivalent elastic stiffness tensor being considered as internal variables, which are critical to the constitutive behaviour of granular materials from the perspectives of the particulate mechanics. The constitutive models containing different internal variables and having different predictive capabilities are represented by different directed graphs with various internal variables linking networks. The recurrent neural network is trained to represent the source-target mapping relationships of the information flows between internal variables. The process of establishing constitutive models is simplified as a sequence of forming graph edges with the goal of finding the optimal combination of internal variables. Therefore, the modelling of the constitutive model can be formulated as a Markov decision process and implemented by the deep reinforcement learning algorithm. Specifically, the well-known AlphaGo Zero algorithm is used to automatically discover the optimal data-driven constitutive modelling path for granular materials. Our numerical examples show that this modeling framework can produce constitutive models with higher prediction accuracy. Furthermore, this study provides a new research paradigm by integrating different theoretical models from the point of data and leveraging the algorithms in artificial intelligence to develop a superior model. The same idea can be extended to seek new insights for similar scientific problems.