In order to study the ductile deformation characteristics and failure process of plain concrete under uniaxial compression, this paper proposes a new constitutive model. The new model was used to fit and analyze the constitutive curve of concrete under uniaxial compressive under various degradation forms and was compared with the traditional constitutive models. Finally, the new model was used to quantitatively analyze and predict the stress–strain curve of concrete in different degradation periods of a set of freeze–thaw measured data. The results show that, compared with the traditional constitutive model, the new model is simple in form and has few parameters, and the numerical value of the parameter can reflect the ductile deformation capacity of concrete. The fitting curve of the new model has the highest fitting degree with the measured stress–strain curve of concrete, and the goodness of fit (R2) is also the largest. The new model is suitable for fitting the stress–strain curve of concrete under uniaxial compression under various deteriorating forms, and the degree of fit between the constitutive prediction curve and the measured curve is high. It can be seen from the fitting results of the new model parameters that the ductile deformation capacity of concrete decreases first and then increases slightly, which is inconsistent with the law of gradual deterioration of strength. There is a minimum moment of ductility deformation capacity of concrete (MDC). The MDC of O-C40 concrete is about 114 freeze–thaw cycles, and the MDC of O-C50 concrete is about 116 freeze–thaw cycles; the degree of fit between the constitutive prediction curve and the measured curve is high. We hope that the improvement mentioned offers valid reference to the study of ductile deformation characteristics and failure process of compressed concrete under different deterioration forms.

The numerical simulation of rock fracture mechanics has been a major research hotspot and challenging area in the field of rock mechanics. Based on this background, a smooth particle dynamics numerical simulation method (RGIMP) is proposed to consider the failed material point. The RGIMP algorithm is simple in form, does not need to use multiple velocity fields, takes advantage of the efficient computational efficiency and stability of the GIMP itself, and simulates the brittle fracture process of the rock by the failure process of the material point, and the resulting cracks are display cracks. The accuracy of the RGIMP algorithm proposed in this paper was verified by uniaxial compressive numerical simulations of single-cleft standard cube specimen, double-cleft standard cube specimen, and double-cleft Brazilian disc specimen. The research results provide a certain reference for the application of smooth particle dynamics methods in rock mechanics engineering and understanding of rock fracture mechanisms.