Abstract
The constitutive relation of granular aggregate is one important aspect in solid mechanics research, since many problems involved are nothing like the ordinary mechanical problems. Using the energy method, this paper sets up the constitutive model for the granular material through the homogenization of granular material with structural characteristics. Several important factors that are influential to the characteristics of such material are fully considered by this model: performance of granular connector, its geometric position, directional distribution, morphology and size of statistical domain and the density of the connectors. The analysis of the model reveals that the mechanical properties of the granular material are not only related to the properties of the granular material but also to the arrangement of the granular aggregate, i.e. its fabric characteristics. In addition, the morphology of granules determines how the granules will be connected, which in turn modifies the mechanical performance of connection among granules and hence the performance of the granular aggregate. Besides, the couple stress is an important stress component, which makes classical theory no longer applicable to the granular material. Therefore, the constitutive model for the granular material is a generic model reflecting the granular material performance.
Highlights
There is an agreement reached in recent years over the fact that the structural characteristics of granular materials are important factors affecting the macroscopic properties of the materials (Hu, 1999; He & Shen, 2003; Shi, 1996)
After the analysis of the model, conclusions that are very different from those obtained for uniform and continuous materials based on classical theory are reached: 1) Several important factors influencing the performance of granular material are fully considered in the constitutive model for the granular material: the performance of the connectors, geometic position and directional distribution, morphology and size of the statistical domain and the density of the connectors
When some parameters degenerate to a homogenization state, the model is automatically adapted to the classical theory; 3) We have found out relevant parameters that can fully reflect the essential properties of granular structures by the model
Summary
There is an agreement reached in recent years over the fact that the structural characteristics of granular materials are important factors affecting the macroscopic properties of the materials (Hu, 1999; He & Shen, 2003; Shi, 1996). Despite much work done on microscopic parameters of the granular materials, the influence of these parameters on the macroscopic properties remains to be clarified (Zhang, 2008; Shi, 1996). What is important is to set up both micro- and macroscopic models for granular materials to be used in understanding the specific role that each parameter plays. The constitutive model for granular structure on the macroscopic scale under static state is set up in the presence of external force. The static state here refers to that the granular system remains constant in terms of structure under the action of external force. There is no slipping or separation (reconnection) among granules in the system, or the system is under elastic state (the dynamic problem is discussed in another paper)
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