Abstract
In this article, a microscopic constitutive model is established that includes friction, plastic, and spring elements and has clear physical meaning. The friction unit reflects the mutual friction between crack surfaces, the plastic unit reflects the development of concrete plasticity, and the fracture of the spring unit reflects the formation and expansion of interior cracks in concrete. In addition, the integration of the random field theory into this model uncovers the physical underpinnings of the relationship between concrete's nonlinearity and randomness. The multi-scale modeling of the concrete static damage constitutive model is then realized once the parameters of the random field are discovered using the macro test results. In order to apply the model's applicability in finite element programs, a subroutine was ultimately constructed. The experimental data and the anticipated values from the numerical simulation are in good agreement, supporting the model's realism.