A novel continuum damage model for quasi-brittle materials: application to concrete

The macroscopic behaviour of concrete is quasi-brittle, and its fracture behaviour is greatly influenced by the fracture process zone (FPZ).The experimental studies on plain concrete show that the load-displacement response of the concrete is characterized by an initial elastic phase followed by a nonlinear behaviour up to peak load and subsequent non-linear softening response.Continuum Damage Mechanics (CDM) is a widely used approach for modeling the fracture behavior of quasi-brittle materials.In CDM, softening is represented by stiffness degradation, modeled using a monotonically decreasing damage parameter.This damage variable is characterized through area reduction in the cross-section, degradation of elastic stiffness, microcrack density, etc.However, the evolution equations in most of the models are not consistent with their physical meaning.In this work, we relate damage to a probability measure that modifies the load-carrying area or volume (in a diffused sense).The damage variable evolves in a manner analogous to transition probability density in non-conserved processes, like those observed in killed diffusion processes.The evolution equation consists of a killing rate term that controls the rate of damage/degradation.The structure of the killing rate is such that it consists of a term that controls initial elastic behaviour, and a parameter that controls the rate of fracture.To ensure the monotonic reduction in this variable, the killing rate is ensured to always be a positive quantity.Softening in the load-displacement response is captured similarly to that of CDM through a gradual reduction in stress in the linear momentum balance equation.We validate our model by reproducing the crack pattern and load-displacement responses observed in corresponding experimental studies of plain concrete.