A pear-shaped bounding surface constitutive model for concrete

To investigate the nonlinear properties of concrete under multiaxial cyclic loading, an improved bounding surface model was presented for concrete within the framework of elastoplastic and bounding surface theory. The yield surface is closed and smooth, and in tensile and compressive meridan planes, the yield surface is a pear shape. The shape of bounding surface is similar to yield surface. The first stress invariant and the strain deviation were adoped as the independent variables in the yield function and as the differential variable in the loading and unloading criteria. Based on the similarity of the shape between yield and bounding surfaces, the mapping relations were determined by proportional relations. According to the mapping rules, there always was an image stress point on the bounding surface for a current stress point on the yield surface. The two points had the same normal direction for corresponding surfaces, and a nonassociated flow was adopted to describe the plastic deformation. For the experimental results of concrete specimens under monotonic and cyclic loading along the compression direction in the deviatoric plane, the proposed model was used to simulate the results numerically. The calculated results agree well with experimental data. The model can describe the pre-failure and post-failure stress-strain curve and describe the shear dilatancy of concrete. © 2018, Editorial Board of Journal of Harbin Institute of Technology. All right reserved.