A three dimensional constitutive model for plain cement concrete

Abstract

The validity of some of the assumptions made during systematic development of constitutive relation – homogeneity, isotropy, and non-dissipative response – is examined experimentally by testing plain concrete cylinders in the circumferential displacement controlled uniaxial compression tests. The tested cylinders indicate that the surface strains are not uniform and that the principal direction of the strain varies with the magnitude of the applied load. Hence, these cylinders are either deforming from a stressed state or anisotropic or both. The percentage dissipation computed as the area between the loading and unloading curves normalized using the area under the unloading curve is less than 10 percent up to 90 percent of the peak load. Therefore the mechanical response of concrete can be considered as non-dissipative. Assuming that the magnitude of the residual stresses present in the concrete panels would be small compared to the stresses arising due to the applied load, these residual stresses are ignored. Consequently, using the implicit constitutive theory framework for isotropic and compressible materials undergoing a non-dissipative process from a stress-free reference configuration, a three-dimensional constitutive relation for plain concrete is proposed. The material parameters in the proposed model are estimated from the uniaxial compression test and equal biaxial compression test. These parameters are expressed using initial Young’s modulus, initial Poisson’s ratio, maximum uniaxial compressive stress, the axial and transverse strain corresponding to the maximum uniaxial compressive stress, maximum equal biaxial compressive stress and the equal biaxial strain corresponding to maximum equal biaxial compressive stress. The ability of the proposed model to capture the response of various grade and type of concrete in ten biaxial experiments reported in the literature is examined. It is found that despite the limiting assumptions, the compression-compression, compression-tension and tension-tension stress strain response of the concrete in these ten experiments are adequately captured by the proposed model with mean R2 value of 0.94.