General model for constitutive relationships of concrete and its composite structures

This paper presents a unified mathematical model that can be used to construct various constitutive relationships for concrete materials and its composite interfaces. The unified model has a single expression and a maximum of six variables/parameters, whereas in most cases, three to four parameters are sufficient. The model is simple, continuous, and easy to be integrated and differentiated. Its parameters can be assigned clear physical meanings, and used to control variations of different parts of the curve separately. Its greater versatility and flexibility enables possible applications in almost all kinds of constitutive relationships for concrete and its composite structures. For example, it is demonstrated to be suitable for stress–strain relationships of plain and confined concrete, bond–slip relationships of steel bar-to-concrete interfaces, externally-bonded fiber-reinforced polymer (FRP) interfaces, near surface mounted FRP interfaces, etc. Furthermore, a simple equation for the bond–slip relationship of steel reinforcement-to-concrete interface is derived using the unified model to replace the four-segment CEB-FIP code model.