Model of Infinitesimal Nonlinear Elastic Response of Concrete Subjected to Uniaxial Compression

Unreinforced portland-cement concrete exhibits a nonlinear relationship between applied stress and observed strain, even though the strains are at magnitudes that warrant the infinitesimal strain approximation (i.e., the norm of the displacement gradient is appropriately small). Previous efforts to model this nonlinear response of concrete express a dependence of stress on the deformation gradient (via the infinitesimal strain). However, models derived from the class of Cauchy elastic bodies do not allow a nonlinear relationship between the stress and linearized strain. Nonlinear constitutive relations that are implicit relations between the stress and a proper measure of strain, or nonlinear expressions of an appropriate measure of strain as a function of stress, lead to a logical linearization procedure wherein the linearized strain can be a nonlinear function of the stress. Using such a constitutive model, the authors accurately characterize both axial strain and circumferential strain in concrete that occurs under axial compression, up to the peak compressive stress (i.e., the failure stress). The phenomenological coefficients of the constitutive models are given predictive power via correlation with compressive strength and the air content of the ten concrete mixtures (comprising 23 concrete cylinders) that were experimentally tested under unconfined uniaxial compression.